| Internet-Draft | Blind BBS Signatures | January 2024 |
| Kalos & Bernstein | Expires 14 July 2024 | [Page] |
This document defines an extension to the BBS Signature scheme that supports blind digital signatures, i.e., signatures over messages not known to the Signer.¶
This note is to be removed before publishing as an RFC.¶
Source for this draft and an issue tracker can be found at https://github.com/BasileiosKal/blind-bbs-signatures.¶
This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.¶
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This Internet-Draft will expire on 14 July 2024.¶
Copyright (c) 2024 IETF Trust and the persons identified as the document authors. All rights reserved.¶
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The BBS digital signature scheme, as defined in [I-D.irtf-cfrg-bbs-signatures], can be extended to support blind signatures functionality. In a blind signatures setting, the user (called the Prover in the context of the BBS scheme) will request a signature on a list of messages, without revealing those messages to the Signer (who can optionally also include messages of their choosing to the signature).¶
By allowing the Prover to acquire a valid signature over messages not known to the Signer, blind signatures address some limitations of their plain digital signature counterparts. In the BBS scheme, knowledge of a valid signature allows generation of BBS proofs. As a result, a signature compromise (by an eavesdropper, a phishing attack, a leakage of the Signer's logs etc.,) can lead to impersonation of the Prover by malicious actors (especially in cases involving "long-lived" signatures, as in digital credentials applications etc.,). Using Blind BBS Signatures on the other hand, the Prover can commit to a secret message (for example, a private key) before issuance, guaranteeing that no one will be able to generate a valid proof without knowledge of their secret.¶
Furthermore, applications like Privacy Pass ([I-D.ietf-privacypass-protocol]) may require a signature to be "scoped" to a specific audience or session (as to require "fresh" signatures for different sessions etc.,). However, simply sending an audience or session identifier to the Signer (to be included in the signature), will compromise the privacy guarantees that these applications try to enforce. Using blind signing, the Prover will be able to require signatures bound to those values, without having to reveal them to the Signer.¶
The presented protocol, compared to the scheme defined in [I-D.irtf-cfrg-bbs-signatures], introduces an additional communication step between the Prover and the Signer. The Prover will start by constructing a "hiding" commitment to the messages they want to get a signature on (i.e., a commitment which reveals no information about the committed values), together with a proof of correctness of that commitment. They will send the (commitment, proof) pair to the Signer, who, upon receiving the pair, will attempt to verify the commitment's proof of correctness. If successful, they will use it in generating a BBS signature over the messages committed by the Prover, including their own messages if any.¶
This document, other than defining the operation for creating and verifying a commitment, it also details a core signature generation operation, different from the one presented in [I-D.irtf-cfrg-bbs-signatures], meant to handle the computation of the blind signature. The document will also define a new BBS Interface, which is needed to handle the different inputs (i.e., messages committed by the Prover or chosen by the Signer etc.,). The signature verification and proof generation core cryptographic operations however, will work as described in [I-D.irtf-cfrg-bbs-signatures]. To further facilitate deployment, both the exposed interface as well as the core cryptographic operation of proof verification will be the same as the one detailed in [I-D.irtf-cfrg-bbs-signatures].¶
Below is a basic diagram describing the main entities involved in the scheme.¶
(3) Blind Sign (1) Commit
+----- +-----
| | | |
| | | |
| \ / | \ /
+----------+ +-----------+
| | | |
| | | |
| |<-(2)* Commitment + Proof of Correctness--| |
| Signer | | Prover |
| |-------(4)* Send signature + msgs-------->| |
| | | |
| | | |
+----------+ +-----------+
|
|
|
(5)* Send proof
+
disclosed msgs
|
|
\ /
+-----------+
| |
| |
| |
| Verifier |
| |
| |
| |
+-----------+
| / \
| |
| |
+-----
(6) ProofVerify
Note The protocols implied by the items annotated by an asterisk are out of scope for this specification¶
Terminology defined by [I-D.irtf-cfrg-bbs-signatures] applies to this draft.¶
Additionally, the following terminology is used throughout this document:¶
Notation defined by [I-D.irtf-cfrg-bbs-signatures] applies to this draft.¶
Additionally, the following notation and primitives are used:¶
list = [a, b, c] and elements = [d, a], the result of list.append(elements) will be [a, b, c, d, a].¶
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.¶
This document makes use of various operations defined by the BBS Signature Scheme document [I-D.irtf-cfrg-bbs-signatures]. For clarity, whenever an operation will be used defined in [I-D.irtf-cfrg-bbs-signatures], it will be prefixed by "BBS." (e.g., "BBS.CoreProofGen" etc.). More specifically, the operations used are the following:¶
BBS.CoreVerify: Refers to the CoreVerify operation defined in Section 3.6.2 of [I-D.irtf-cfrg-bbs-signatures].¶
BBS.CoreProofGen: Refers to the CoreProofGen operation defined in Section 3.6.3 of [I-D.irtf-cfrg-bbs-signatures].¶
BBS.create_generators: Refers to the create_generators operation defined in Section 4.1.1 of [I-D.irtf-cfrg-bbs-signatures].¶
BBS.messages_to_scalars: Refers to the messages_to_scalars operation defined in Section 4.1.2 of [I-D.irtf-cfrg-bbs-signatures].¶
BBS.get_random_scalars: Refers to the get_random_scalars operation defined in Section 4.2.1 of [I-D.irtf-cfrg-bbs-signatures].¶
BBS.hash_to_scalar: Refers to the hash_to_scalar operation defined in Section 4.2.2 of [I-D.irtf-cfrg-bbs-signatures].¶
This operation is used by the Prover to create a commitment to a set of messages (committed_messages), that they intend to include to the blind signature. Note that this operation returns both the serialized combination of the commitment and its proof of correctness (commitment_with_proof), as well as the random scalar used to blind the commitment (secret_prover_blind).¶
(commitment_with_proof, secret_prover_blind) = Commit(
committed_messages,
api_id)
Inputs:
- committed_messages (OPTIONAL), a vector of octet strings. If not
supplied it defaults to the empty
array ("()").
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- (commitment_with_proof, secret_prover_blind), a tuple comprising from
an octet string and a
random scalar in that
order.
Procedure:
1. M = length(committed_messages)
2. generators = BBS.create_generators(M + 2, api_id)
3. (Q_2, J_1, ..., J_M) = generators[1..M+1]
4. (msg_1, ..., msg_M) = BBS.messages_to_scalars(committed_messages,
api_id)
5. (secret_prover_blind, s~, m~_1, ..., m~_M)
= BBS.get_random_scalars(M + 2)
6. C = Q_2 * secret_prover_blind + J_1 * msg_1 + ... + J_M * msg_M
7. Cbar = Q_2 * s~ + J_1 * m~_1 + ... + J_M * m~_M
8. challenge = calculate_blind_challenge(C, Cbar, generators, api_id)
9. s^ = s~ + secret_prover_blind * challenge
10. for m in (1, 2, ..., M): m^_i = m~_1 + msg_i * challenge
11. proof = (s^, (m^_1, ..., m^_M), challenge)
12. commit_with_proof_octs = commitment_with_proof_to_octets(C, proof)
13. return (commit_with_proof_octs, secret_prover_blind)
¶
This operation is used by the Signer to verify the correctness of a commitment_proof for a supplied commitment, over a list of points of G1 called the blind_generators, used to compute that commitment.¶
result = verify_commitment(commitment, commitment_proof,
blind_generators, api_id)
Inputs:
- commitment (REQUIRED), a commitment (see (#terminology)).
- commitment_proof (REQUIRED), a commitment_proof (see (#terminology)).
- blind_generators (REQUIRED), vector of pseudo-random points in G1.
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- result: either VALID or INVALID
Deserialization:
1. (s^, commitments, cp) = commitment_proof
2. M = length(commitments)
3. (m^_1, ..., m^_M) = commitments
4. if length(blind_generators) != M + 1, return INVALID
5. (Q_2, J_1, ..., J_M) = blind_generators
Procedure:
1. Cbar = Q_2 * s^ + J_1 * m^_1 + ... + J_M * m^_M + commitment * (-cp)
2. cv = calculate_blind_challenge(commitment, Cbar, blind_generators,
api_id)
3. if cv != cp, return INVALID
4. return VALID
¶
The following section defines a BBS Interface for blind BBS signatures. The identifier of the Interface is defined as ciphersuite_id || BLIND_H2G_HM2S_, where ciphersuite_id the unique identifier of the BBS ciphersuite used, as is defined in Section 6 of [I-D.irtf-cfrg-bbs-signatures]). Each BBS Interface MUST define operations to map the inputted messages to scalar values and to create the generators set, required by the core operations. The inputted messages to the defined Interface will be mapped to scalars using the messages_to_scalars operation defined in Section 4.1.2 of [I-D.irtf-cfrg-bbs-signatures]. The generators will be created using the create_generators operation defined in Section Section 4.1.1 of [I-D.irtf-cfrg-bbs-signatures].¶
Other than the BlindSign operation defined in Section 4.2.1, which uses the CoreBlindSign procedure, defined in Section 4.3.1, all other interface operations defined in this section use the core operations defined in Section 3.6 of [I-D.irtf-cfrg-bbs-signatures].¶
This operation returns a BBS blind signature from a secret key (SK), over a header, a set of messages and optionally a commitment value (see Section 1.1). If supplied, the commitment value must be accompanied by its proof of correctness (commitment_with_proof, as outputted by the Commit operation defined in Section 4.1.1). The issuer can also further randomize the supplied commitment, by supplying a random scalar (signer_blind), that MUST be computed as,¶
signer_blind = BBS.get_random_scalars(1)¶
If the signer_blind input is not supplied, it will default to the zero scalar (0).¶
The BlindSign operation makes use of the CoreBlindSign procedure defined in Section 4.3.1.¶
blind_signature = BlindSign(SK, PK, commitment_with_proof, header,
messages, signer_blind)
Inputs:
- SK (REQUIRED), a secret key in the form outputted by the KeyGen
operation.
- PK (REQUIRED), an octet string of the form outputted by SkToPk
provided the above SK as input.
- commitment_with_proof (OPTIONAL), an octet string, representing a
serialized commitment and
commitment_proof, as the first
element outputted by the Commit
operation. If not supplied, it
defaults to the empty string ("").
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string ("").
- messages (OPTIONAL), a vector of octet strings. If not supplied, it
defaults to the empty array ("()").
- signer_blind (OPTIONAL), a random scalar value. If not supplied it
defaults to zero ("0").
Parameters:
- api_id, the octet string ciphersuite_id || "BLIND_H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and
"BLIND_H2G_HM2S_"is an ASCII string composed of 15 bytes.
- (octet_point_length, octet_scalar_length), defined by the ciphersuite.
Outputs:
- blind_signature, a blind signature encoded as an octet string; or
INVALID.
Deserialization:
1. L = length(messages)
// calculate the number of blind generators used by the commitment,
// if any.
2. M = length(commitment_with_proof)
3. if M != 0, M = M - octet_point_length - octet_scalar_length
4. M = M / octet_scalar_length
5. if M < 0, return INVALID
Procedure:
1. generators = BBS.create_generators(M + L + 1, api_id)
2. message_scalars = BBS.messages_to_scalars(messages, api_id)
3. blind_sig = CoreBlindSign(SK,
PK,
commitment_with_proof,
generators,
header,
messages,
signer_blind,
api_id)
4. if blind_sig is INVALID, return INVALID
5. return blind_sig
¶
This operation validates a blind BBS signature (signature), given the Signer's public key (PK), a header (header), a set of known to the Signer messages (messages) and if used, a set of committed messages (committed_messages), the secret_prover_blind as returned by the Commit operation (Section 4.1.1) and a blind factor supplied by the Signer (signer_blind).¶
This operation makes use of the CoreVerify operation as defined in Section 3.6.2 of [I-D.irtf-cfrg-bbs-signatures].¶
result = Verify(PK, signature, header, messages, committed_messages,
secret_prover_blind, signer_blind)
Inputs:
- PK (REQUIRED), an octet string of the form outputted by the SkToPk
operation.
- signature (REQUIRED), an octet string of the form outputted by the
Sign operation.
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string.
- messages (OPTIONAL), a vector of octet strings. If not supplied, it
defaults to the empty array "()".
- committed_messages (OPTIONAL), a vector of octet strings. If not
supplied, it defaults to the empty
array "()".
- secret_prover_blind (OPTIONAL), a scalar value. If not supplied it
defaults to zero "0".
- signer_blind (OPTIONAL), a scalar value. If not supplied it defaults
to zero "0".
Parameters:
- api_id, the octet string ciphersuite_id || "BLIND_H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and
"BLIND_H2G_HM2S_"is an ASCII string composed of 15 bytes.
Outputs:
- result: either VALID or INVALID
Deserialization:
1. L = length(messages)
2. M = length(committed_messages)
Procedure:
1. message_scalars = ()
2. if secret_prover_blind != 0, message_scalars.append(
secret_prover_blind + signer_blind)
3. message_scalars.append(BBS.messages_to_scalars(
committed_messages, api_id))
4. message_scalars.append(BBS.messages_to_scalars(messages, api_id))
5. generators = BBS.create_generators(length(message_scalars) + 1,
api_id)
6. res = BBS.CoreVerify(PK, signature, generators, header, messages,
api_id)
7. return res
¶
This operation creates a BBS proof, which is a zero-knowledge, proof-of-knowledge, of a BBS signature, while optionally disclosing any subset of the signed messages. Note that in contrast to the ProofGen operation of [I-D.irtf-cfrg-bbs-signatures] (see Section 3.5.3), the ProofGen operation defined in this section accepts 2 different lists of messages and disclosed indexes, one for the messages known to the Signer (messages) and the corresponding disclosed indexes (disclosed_indexes) and one for the messages committed by the Prover (committed_messages) and the corresponding disclosed indexes (disclosed_commitment_indexes).¶
To Verify a proof however, the Verifier expects only one list of messages and one list of disclosed indexes (see Section 4.2.4). This is done to avoid revealing which of the disclosed messages where committed by the Prover and which are known to the Verifier. To this end, the BlindProofGen operation defined in this section, uses the get_disclosed_data defined in Section 5 to combine the different messages and indexes lists, to return the disclosed messages and the disclosed indexes that the prover should present to the Verifier.¶
Lastly, the the operation also expects the secret_prover_blind (as returned from the Commit operation defined in Section 4.1.1) and signer_blind (as inputted in the BlindSign operation defined in Section 4.2.1) values. If the BBS signature is generated using a commitment value, then the secret_prover_blind returned by the Commit operation used to generate the commitment should be provided to the ProofGen operation (otherwise the resulting proof will be invalid).¶
Note that the BlindProofGen operation defined in this section returns both the generated proof as an octet string, together with a vector (disclosed_data) containing all the disclosed messages and their indexes, that would be later revealed to the proof Verifier.¶
This operation makes use of the CoreProofGen operation as defined in Section 3.6.3 of [I-D.irtf-cfrg-bbs-signatures].¶
(proof, disclosed_msgs, disclosed_idxs)
= BlindProofGen(PK,
signature,
header,
ph,
messages,
committed_messages,
disclosed_indexes,
disclosed_commitment_indexes,
secret_prover_blind,
signer_blind)
Inputs:
- PK (REQUIRED), an octet string of the form outputted by the SkToPk
operation.
- signature (REQUIRED), an octet string of the form outputted by the
Sign operation.
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string.
- ph (OPTIONAL), an octet string containing the presentation header. If
not supplied, it defaults to an empty string.
- messages (OPTIONAL), a vector of octet strings. If not supplied, it
defaults to the empty array "()".
- committed_messages (OPTIONAL), a vector of octet strings. If not
supplied, it defaults to the empty
array "()".
- disclosed_indexes (OPTIONAL), vector of unsigned integers in ascending
order. Indexes of disclosed messages. If
not supplied, it defaults to the empty
array "()".
- disclosed_commitment_indexes (OPTIONAL), vector of unsigned integers
in ascending order. Indexes
of disclosed committed
messages. If not supplied, it
defaults to the empty array
"()".
- secret_prover_blind (OPTIONAL), a scalar value. If not supplied it
defaults to zero "0".
- signer_blind (OPTIONAL), a scalar value. If not supplied it defaults
to zero "0".
Parameters:
- api_id, the octet string ciphersuite_id || "BLIND_H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and
"BLIND_H2G_HM2S_"is an ASCII string composed of 15 bytes.
Outputs:
- (proof, disclosed_msgs, disclosed_idxs) a tuple comprising from an
octet string, an array of
octet strings and an array of
non-zero integers; or INVALID.
Deserialization:
1. L = length(messages)
2. M = length(committed_messages)
3. if length(disclosed_indexes) > L, return INVALID
4. for i in disclosed_indexes, if i < 0 or i >= L, return INVALID
5. if length(disclosed_commitment_indexes) > M, return INVALID
6. for j in disclosed_commitment_indexes,
if i < 0 or i >= L, return INVALID
Procedure:
1. message_scalars = ()
2. if secret_prover_blind != 0, message_scalars.append(
secret_prover_blind + signer_blind)
4. message_scalars.append(BBS.messages_to_scalars(
committed_messages, api_id))
5. message_scalars.append(BBS.messages_to_scalars(messages, api_id))
6. generators = BBS.create_generators(length(message_scalars) + 1,
api_id)
7. disclosed_data = get_disclosed_data(
messages,
committed_messages,
disclosed_indexes,
disclosed_commitment_indexes,
secret_prover_blind)
8. if disclosed_data is INVALID, return INVALID.
9. (disclosed_msgs, disclosed_idxs) = disclosed_data
10. proof = BBS.CoreProofGen(PK, signature, generators, header, ph,
message_scalars, disclosed_idxs, api_id)
11. return (proof, disclosed_msgs, disclosed_idxs)
¶
To verify a proof generated by the BlindProofGen operation defined in Section 4.2.3, the Verifier can directly use the ProofVerify operation defined in Section 3.5.4 of [I-D.irtf-cfrg-bbs-signatures], instantiated with the following parameter¶
api_id = ciphersuite_id || "BLIND_H2G_HM2S_", where ciphersuite_id is
defined by the ciphersuite and "BLIND_H2G_HM2S_"is an ASCII
string composed of 15 bytes.
¶
The purpose of the above is to reduce the information a Verifier may get, regarding which of the disclosed messages were committed by the Prover and which were known to the Issuer. For this purpose, the Prover MUST follow the procedure described in Section 5 to prepare the data that will be supplied to the proof Verifier.¶
This operation computes a blind BBS signature, from a secret key (SK), a set of generators (points of G1), a supplied commitment with its proof of correctness (commitment_with_proof), a header (header) and a set of messages (messages). The operation also accepts a random scalar (signer_blind) and the identifier of the BBS Interface, calling this core operation.¶
blind_signature = CoreBlindSign(SK,
PK,
generators,
commitment_with_proof,
header,
messages,
signer_blind,
api_id)
Inputs:
- SK (REQUIRED), a secret key in the form outputted by the KeyGen
operation.
- PK (REQUIRED), an octet string of the form outputted by SkToPk
provided the above SK as input.
- generators (REQUIRED), vector of pseudo-random points in G1.
- commitment_with_proof (OPTIONAL), an octet string, representing a
serialized commitment and
commitment_proof, as the first
element outputted by the Commit
operation. If not supplied, it
defaults to the empty string ("").
- header (OPTIONAL), an octet string containing context and application
specific information. If not supplied, it defaults
to an empty string.
- messages (OPTIONAL), a vector of octet strings. If not supplied, it
defaults to the empty array "()".
- signer_blind (OPTIONAL), a random scalar value. If not supplied it
defaults to zero "0".
Parameters:
- api_id, the octet string ciphersuite_id || "BLIND_H2G_HM2S_", where
ciphersuite_id is defined by the ciphersuite and
"BLIND_H2G_HM2S_"is an ASCII string composed of 15 bytes.
Outputs:
- blind_signature, a blind signature encoded as an octet string; or
INVALID.
Definitions:
1. signature_dst, an octet string representing the domain separation
tag: api_id || "H2S_" where "H2S_" is an ASCII string
composed of 4 bytes.
Deserialization:
1. L = length(messages)
2. (msg_1, ..., msg_L) = messages
3. commit_res = deserialize_and_validate_commit(commitment_with_proof,
generators,
api_id)
4. if commit_res is INVALID, return INVALID
// if commitment_with_proof == "", then commit_res = (Identity_G1, 0).
4. (commit, M) = commit_res
5. Q_1 = generators[0]
6. Q_2 = Identity_G1
7. if commitment_with_proof != "", Q_2 = generators[1]
8. (H_1, ..., H_L) = generators[M + 1..M + L + 1]
Procedure:
1. domain = calculate_domain(PK, generators, header, api_id)
2. e_octs = serialize((SK, domain, msg_1, ..., msg_L, signer_blind))
3. e = BBS.hash_to_scalar(e_octs || commitment_with_proof,
signature_dst)
// if a commitment is not supplied, Q_2 = Identity_G1, meaning that
// signer_blind will be ignored.
4. commit = commit + Q_2 * signer_blind
5. B = P1 + Q_1 * domain + H_1 * msg_1 + ... + H_L * msg_L + commit
6. A = B * (1 / (SK + e))
7. return signature_to_octets((A, e))
8. return signature
¶
To avoid revealing which messages are committed to the signature, and which were known to the Signer to the proof Verifier, after calculating a BBS proof, the Prover will need to combine the disclosed committed messages as well as the disclosed messages known to the Signer to a single disclosed messages list. The same holds for the disclosed message indexes, where the ones corresponding to committed messages and the ones corresponding to messages known by the Signer should be combined together.¶
disclosed_data = get_disclosed_data(messages,
committed_messages,
disclosed_indexes,
disclosed_commitment_indexes,
secret_prover_blind)
Inputs:
- messages (OPTIONAL), vector of scalars. If not supplied, it defaults
to the empty array "()".
- committed_messages (OPTIONAL), vector of scalars. If not supplied, it
defaults to the empty array "()".
- disclosed_indexes (OPTIONAL), vector of unsigned integers in ascending
order. Indexes of disclosed messages. If
not supplied, it defaults to the empty
array "()".
- disclosed_commitment_indexes (OPTIONAL), vector of unsigned integers
in ascending order. Indexes
of disclosed messages. If not
supplied, it defaults to the
empty array "()".
Outputs
- disclosed_data, a vector comprising of two vectors, one corresponding
to the disclosed messages and one to the disclosed
indexes.
Deserialization:
1. L = length(messages)
2. M = length(committed_messages)
3. (i1, ..., iL) = disclosed_indexes
4. (j1, ...., jL) = disclosed_commitment_indexes
5. if length(disclosed_indexes) > L, return INVALID
6. if length(disclosed_commitment_indexes) > M, return INVALID
Procedure:
// determine if a commitment was used
1. if secret_prover_blind == 0, comm_used = 0, else comm_used = 1
// combine the disclosed indexes
2. indexes = ()
3. for i in disclosed_commitment_indexes: indexes.append(i + comm_used)
4. for j in disclosed_indexes: indexes.append(M + j + comm_used)
// combine the disclosed messages
5. disclosed_messages = (messages[i1], ..., messages[iL])
6. disclosed_committed_messages = (committed_messages[j1], ...
..., committed_messages[jM])
7. disclosed_messages.append(disclosed_committed_messages)
8. return (disclosed_messages, indexes)
¶
challenge = calculate_blind_challenge(C, Cbar, generators, api_id)
Inputs:
- C (REQUIRED), a point of G1.
- Cbar (REQUIRED), a point of G1.
- generators (REQUIRED), an array of points from G1, of length at
least 1.
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Definition:
- blind_challenge_dst, an octet string representing the domain
separation tag: api_id || "H2S_" where
ciphersuite_id is defined by the ciphersuite and
"H2S_" is an ASCII string composed of 4 bytes.
Deserialization:
1. if length(generators) == 0, return INVALID
2. M = length(generators) - 1
Procedure:
1. c_arr = (C, Cbar, M)
2. c_arr.append(generators)
3. c_octs = serialize(c_arr)
4. return BBS.hash_to_scalar(c_octs, blind_challenge_dst)
¶
The following is a helper operation used by the CoreBlindSign procedure (Section 4.3.1) to validate an optional commitment. The commitment input to CoreBlindSign is optional. If a commitment is not supplied, or if it is the Identity_G1, the following operation will return the Identity_G1 as the commitment point, which will be ignored by all computations during CoreBlindSign.¶
(commit, blind_gen_no) = deserialize_and_validate_commit(
commitment_with_proof,
generators,
api_id)
Inputs:
- commitment_with_proof (OPTIONAL), octet string. If it is not supplied
it defaults to the empty octet
string ("").
- generators (OPTIONAL), vector of points of G1. If it is not supplied
it defaults to the empty set ("()").
- api_id (OPTIONAL), octet string. If not supplied it defaults to the
empty octet string ("").
Outputs:
- (commit, blind_gen_no), a tuple comprising from commitment, a
commitment_proof (see (#terminology)), in that
order; or INVALID.
Procedure:
1. if commitment_with_proof is the empty string (""), return
(Identity_G1, 0)
2. com_res = octets_to_commitment_with_proof(commitment_with_proof)
3. if com_res is INVALID, return INVALID
4. (commit, commit_proof) = com_res
5. M = length(commit_proof[1]) + 1
6. if length(generators) < M + 1, return INVALID
7. blind_generators = generators[1..M + 1]
8. validation_res = verify_commitment(commit, commit_proof,
blind_generators, api_id)
9. if validation_res is INVALID, return INVALID
10. (commitment, M)
¶
commitment_octets = commitment_with_proof_to_octets(commitment, proof)
Inputs:
- commitment (REQUIRED), a point of G1.
- proof (REQUIRED), a vector comprising of a scalar, a possibly empty
vector of scalars and another scalar in that order.
Outputs:
- commitment_octets, an octet string or INVALID.
Procedure:
1. commitment_octs = serialize(commitment)
2. if commitment_octs is INVALID, return INVALID
3. proof_octs = serialize(proof)
4. if proof_octs is INVALID, return INVALID
5. return commitment_octs || proof_octs
¶
commitment = octets_to_commitment_with_proof(commitment_octs)
Inputs:
- commitment_octs (REQUIRED), an octet string in the form outputted from
the commitment_to_octets operation.
Parameters:
- (octet_point_length, octet_scalar_length), defined by the ciphersuite.
Outputs:
- commitment, a commitment in the form (C, proof), where C a point of G1
and proof a vector comprising of a scalar, a possibly
empty vector of scalars and another scalar in that order.
Procedure:
1. commit_len_floor = octet_point_length + 2 * octet_scalar_length
2. if length(commitment) < commit_len_floor, return INVALID
3. C_octets = commitment_octs[0..(octet_point_length - 1)]
4. C = octets_to_point_g1(C_octets)
5. if C is INVALID, return INVALID
6. if C == Identity_G1, return INVALID
7. j = 0
8. index = octet_point_length
9. while index < length(commitment_octs):
10. end_index = index + octet_scalar_length - 1
11. s_j = OS2IP(proof_octets[index..end_index])
12. if s_j = 0 or if s_j >= r, return INVALID
13. index += octet_scalar_length
14. j += 1
15. if index != length(commitment_octs), return INVALID
16. if j < 2, return INVALID
17. msg_commitment = ()
18. if j >= 3, set msg_commitment = (s_2, ..., s_(j-1))
19. return (C, (s_0, msg_commitments, s_j))
¶
Security considerations detailed in Section 6 of [I-D.irtf-cfrg-bbs-signatures] apply to this draft as well.¶
The random scalar value secret_prover_blind calculated and returned by the Commit operation is responsible for "hiding" the committed messages (otherwise, in many practical applications, the Signer may be able to retrieve them). Furthermore, it guarantees that the entity generating the BBS proof (see BlindProofGen defined in Section 4.2.3) has knowledge of that factor. As a result, the secret_prover_blind MUST remain private by the Prover and it MUST be generated using a cryptographically secure pseudo-random number generator. See Section 6.7 of [I-D.irtf-cfrg-bbs-signatures] on recommendations and requirements for implementing the BBS.get_random_scalars operation (which is used to calculate the secret_prover_blind value).¶
One natural use case for the blind signatures extension of the BBS scheme is key binding. In the context of BBS Signatures, key binding guarantees that only entities in control of a specific private key can compute BBS proofs. This can be achieved by committing to the private key prior to issuance, resulting to a BBS signature that includes that key as one of the signed messages. Creating a BBS proof from that signature will then require knowledge of that key (similar to any signed message). The Prover MUST NOT disclose that key as part of a proof generation procedure. Note also that the secret_prover_blind value returned by the Commit operation defined in Section 4.1.1 (see Section 7.1), has a similar property, i.e., it's knowledge is required to generate a proof from a blind signature. Many applications however, requiring key binding, mandate that the same private key is used among multiple signatures, whereas the secret_prover_blind is uniquely generated for each blind signature issuance request. In those cases, a commitment to a private key must be used, as described above.¶
A commitment is "randomized" using the secret_prover_blind random value. The Signer MAY elect to re-randomize a commitment by using it's own randomness. This can be helpful for applications that need to guarantee the uniqueness of each commitment (and of the resulting signatures) supplied by (untrusted) Provers. Examples include voting systems, where each unique signature will provide a single vote. To re-randomize a commitment, the Signer can provide the signer_blind input to the BlindSign operation defined in Section 4.2.1. If used, the signer_blind MUST be computed using the BBS.get_random_scalars operation. In contrast with the secret_prover_blind value however, the signer_blind doesn't need to be secret. The Signer will need to return it to the Prover, who requires it to verify the signature and generate the proofs.¶
This document uses the BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_ and BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_ defined in Section 6.2.1 and Section 6.2.2 correspondingly, of [I-D.irtf-cfrg-bbs-signatures].¶
Mocked RNG parameters:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "2"
committed_messages = "[ ]"
secret_prover_blind = "30bd5c9bd2b61c44dd169c92cf28bb607830c56073f10e7a8
00c857cb05ec249"
commitment_with_proof = "95a6f21801b2010a9016c590cd6f0d59682e908a46cdc98
56eea2c5000545626fc755c13ce93a71e371b0ae0549132
6302a8e40b4fc1197d75c46d2114c711d9186e4af0498da
b260ae56f81dbc59f7b2a9f4883479ce40e765a32b64817
66ed5aeeddecd2decd277460a5e129a22934"
¶
Mocked RNG parameters:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
countsource ~./ = "7"
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f
8fcb1525c93b649"
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "2"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
SK = "2eee0f60a8a3a8bec0ee942bfd46cbdae9a0738ee68f5a64e7238311cf09a079"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
commitment_with_proof = "95a6f21801b2010a9016c590cd6f0d59682e908a46cdc98
56eea2c5000545626fc755c13ce93a71e371b0ae0549132
6302a8e40b4fc1197d75c46d2114c711d9186e4af0498da
b260ae56f81dbc59f7b2a9f4883479ce40e765a32b64817
66ed5aeeddecd2decd277460a5e129a22934"
header = "11223344556677889900aabbccddeeff"
messages = "[ ]"
committed_messages = "[ ]"
secret_prover_blind = "30bd5c9bd2b61c44dd169c92cf28bb607830c56073f10e7a8
00c857cb05ec249"
signer_blind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e
0a1e3c7f"
Signature trace:
B = "b34e5cf13d77074c4762d92f98cc6b8c2567c816a2ea792d0f49263b8da314b
5493830b78563fdb9e2abcab2a7a3c21f"
domain = "41f87ee87af7a093831d77576c64d41e0d89bcd05ea6c9dd5be25bce3c
728c55"
signature = "90c93d864fb857dc4290e1cb2f6c82973c2562b4bfb8edb61c2300da84b
7d709733024c215acc0e224ee4b64ab5987d0312e84786009cece2aee01
884b19c81a592aefb557f025fccdd8c67ca0a5d8c3"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
SK = "2eee0f60a8a3a8bec0ee942bfd46cbdae9a0738ee68f5a64e7238311cf09a079"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
header = "11223344556677889900aabbccddeeff"
messages = "[ ]"
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f
8fcb1525c93b649"
signer_blind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e
0a1e3c7f"
Signature trace:
B = "a537c41dd0dac2de5d21296e32e43f07b27e2ea4c1757247c36fdf7d5541d9e
97a483e0b729a8b83638f15fba0cbda29"
domain = "2ff95924f5218644c1a5d1722d815146e5b2c195d231421aea572e0052
7849d2"
signature = "b788904003da89dc167016c3d58a296a145c411df7cc616cfeb79db8d07
d5361210ef79599453acc7ee706d80e114be369ca4043e008ea4373e1d3
d7bb60c11161d1d6d67ad23a808f0ce52677c724dd"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "2"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
SK = "2eee0f60a8a3a8bec0ee942bfd46cbdae9a0738ee68f5a64e7238311cf09a079"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
commitment_with_proof = "95a6f21801b2010a9016c590cd6f0d59682e908a46cdc98
56eea2c5000545626fc755c13ce93a71e371b0ae0549132
6302a8e40b4fc1197d75c46d2114c711d9186e4af0498da
b260ae56f81dbc59f7b2a9f4883479ce40e765a32b64817
66ed5aeeddecd2decd277460a5e129a22934"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message = "[ ]"
secret_prover_blind = "30bd5c9bd2b61c44dd169c92cf28bb607830c56073f10e7a8
00c857cb05ec249"
signer_blind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e
0a1e3c7f"
Signature trace:
B = "92c9bd227788c660f82397b7cadbebdcb83bfc4256362605caebd57849ca173
71c5dd67af7b763f0c207eb73cd0d9d97"
domain = "1561412ed694d0eb532e042ae2098fc999325394317c686ce94a84db29
552100"
signature = "81d03e119cf3a1257a58b288c27132d0ec37e3695eb37ecc064094221ba
a4f9775483ed57227385659498480f8e92d8d28a9f576cbdc2f2613c68d
6184598dc47d9c12cc94654072bd9ee708f72d02b5"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
SK = "2eee0f60a8a3a8bec0ee942bfd46cbdae9a0738ee68f5a64e7238311cf09a079"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f
8fcb1525c93b649"
signer_blind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e
0a1e3c7f"
Signature trace:
B = "aad174dad5a717f105ef200da94a6a16ee1354f3a0095f082b9b3f621072e43
8f6889182cfec55d2db07d1b899e96c3d"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
SK = "2eee0f60a8a3a8bec0ee942bfd46cbdae9a0738ee68f5a64e7238311cf09a079"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f
8fcb1525c93b649"
signer_blind = "null"
Signature trace:
B = "81717a1f1c72a748c6a071d58bab0f830169da872d79decde1212ef439f8a15
3340dcc9e61522f518980d0e584969178"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
signature = "b074112a56caea128a775a9588ab9d2c168fbc40450ecb7b559d6ffb619
89896f24783816324ffb55bade3d75c4edfdd03c8effa3dddc82612be45
4e3c22df986af1e230c136d20cdaa3f4ad2195e39b"
¶
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
SK = "2eee0f60a8a3a8bec0ee942bfd46cbdae9a0738ee68f5a64e7238311cf09a079"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
commitment_with_proof = "null"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message = "null"
secret_prover_blind = "null"
signer_blind = "null"
Signature trace:
B = "94ff8f3965846c90397b2e3a38dd0349f4b7ba049209fc99048f482ba21147e
1c5bbe7f102fea9af93f47a7c5ad5a899"
domain = "4e6f04eeb36ed65d8f088e7adf6c106c0db79527243ce19389514b389a
cf7adf"
signature = "8886984283bc433d56ac0f29bab40fb2273d0e7e42f5891c80c357473b5
04e2aae77658efbb0035cbf32771b7fe8dbbc3509d8e6d2a2a9917304e5
a0650e9a6583edb53f82263222a92b41a531784d6e"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "6"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ]"
disclosed_commitment_indexes = "[ 0, 1, 2, 3, 4 ]"
proverBlind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f8fcb1525
c93b649"
signerBlind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e0
a1e3c7f"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
2: "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
3: "835889a40744813a892eff9deb1edaeb"
4: "e1ca9729410dc6ba"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
7: "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075f9b80"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
9: "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
11: "515ae153e22aae04ad16f759e07237b4"
12: "d183ddc6e2665aa4e2f088af"
13: "ac55fb33a75909ed"
14: "96012096"
15: ""
}
Proof trace:
T1 = "83b4acb093f60f6b91850bb4aa8c77d596a823770821106ecb41022d64dc5d
199f9cb2e178919b41babc06490900c384"
T2 = "b410ae7cabfbf8c754299a7b597978f38012122b56e04ce28da24ec0ffbf82
62391ae894b410d69bbc77a4aceb4c6a25"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
// random scalars
r1 = "49269fc9884182a1591f959e813384df71ffb220660cb2a4aa3956e27936d4
d8"
r2 = "66b80c544ba7563a7de236678d228a36195f2b483daec4c49470b63c7231cb
11"
e~ = "6714fe17c1529464fd269b37dda00e6cdd2b82b592a497cc52e78f24930eff
da"
r1~ = "1da4b2f8fe1790bbff2efabd71c8ed624f9fedd10d62dc7a3ca1088657ebf
220"
r3~ = "2354f9de39e2689b893f357e14cead4e405ab3486f188a0b5a503e733d007
588"
// m_tilde_scalars
m~_1 = "42510c348487be3c19994565911729eafcd4804dacf25a7cb7b7a634ddef
c3b5"
proof = "b9e17ab6b187f62b1d57aa0601e837362237c17bf4f0262b9bf0c7245945cef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"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "8"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ]"
disclosed_commitment_indexes = "[ 0, 2, 4 ]"
proverBlind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f8fcb1525
c93b649"
signerBlind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e0
a1e3c7f"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
3: "835889a40744813a892eff9deb1edaeb"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
7: "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075f9b80"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
9: "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
11: "515ae153e22aae04ad16f759e07237b4"
12: "d183ddc6e2665aa4e2f088af"
13: "ac55fb33a75909ed"
14: "96012096"
15: ""
}
Proof trace:
T1 = "b5c0697764d1f1dd7a080e37b4ab743ae90c754426f456f2317cac34ce2d830
48f54cc7212017e9c7b62c2c0323d380f"
T2 = "a929548dde575de8fed7bfc439f2d02788bd0b378048bc3c0c14ec3507f9245
f51e7c781187ee13899952cd1d187edb9"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f47
29f95"
// random scalars
r1 = "11119e21b175fb9fc7c17cbbaf9f5193ff29018deab299e0179517f518c887c
a"
r2 = "293d6d461a4cfd449607b211dcc500540c49cc73d6c77b1ec62eb982be4935b
4"
e~ = "3bc9fe82bbca21200fbbff238cf666d79270bbfc9293ea3fed177ac128cff30
e"
r1~ = "5224e6c760e66d54dae6fac6adee3edca19df9f12f84416980b5c2820b647f
fd"
r3~ = "723457f7d95dfeb89077f16f58f343b1d53b44d474004564a8cc9be5c5cd32
44"
// m_tilde_scalars
m~_1 = "107b5b89bc2574eed71a48bf869b094351bcb2a32fe4ed0f5c62b9063a086
d4b"
m~_2 = "6c757b1e66cc101e9e69c2a7c665d68ce19193f11a28ac1efc0a41b5292a1
a87"
m~_3 = "635ef91197c84f74b14ef14ed7b74ea6a2c4770a1f665cd545854330e3550
221"
proof = "a14083a6bcab28b937970650144a8b28819f723929aacf17a0f56b6f5e5d3bb
ce24fad0e3f8c76b5bad349d41705083189ae2702bc4a5b2bca322d3988d6ff
35055ac1b37589897e4424c4eee64c199a8b58263466f5b1859c24f5ee0e6d2
1bfaece4081d36caa8b80574072388dc2d17c72558fc725de00259c873596b7
6654e1291479d8f79fe4594e6b86310bebe738db8cab6c33e7104ddbbce9a34
3eba4b5788247ba0844bce2f589839ee771eb3d2e0cc0d56b43f2850dc24016
1aac8c3cb4e557ec444714505c8ff8c2a231a72a6a0fb335fcba737d1f3de54
a226533f3a008661279e80837e18bd81767ebd447f472600499ced38ce26502
f25e842b5cce3dc4cca9ab29bab1e7ee17675e6c2b9e94552dee5cb48f73db0
2934946da153ee8805cb89e73941d186ed255d9033b2c68ac32a9956b38b9cb
0688967bd6ae7a993aaac3047d0c6e611d2583ed5d0abe445cb55e8143822e1
f243f646a56d01b77c1e3aae12567d4a90b634e8063"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "11"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "[ 0, 1, 2, 3, 4 ]"
proverBlind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f8fcb1525
c93b649"
signerBlind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e0
a1e3c7f"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
2: "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
3: "835889a40744813a892eff9deb1edaeb"
4: "e1ca9729410dc6ba"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
12: "d183ddc6e2665aa4e2f088af"
14: "96012096"
}
Proof trace:
T1 = "8b1b7f8070626bc7bcfbc210e00d513b10e412668b83360eade3201bebf2d5
421365816f841d08d142e61a28f8051817"
T2 = "89d4e2d5f19d2f2cd01a503d68eb57ea69ce4c640a1d58322aa8b6ab5d68b2
03ee58108d9bc818e754c22b0317ef36db"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
// random scalars
r1 = "517c6ba25814e7e8a6b1e1e7a1eaefbd13a47b874a249094592b51295c896b
e6"
r2 = "17d278dc4ff520d8bcde7c7f35e635c19d9d0e19e0f32e4900e4a69af300b2
f6"
e~ = "658838c65c01e42cd39fe21885284cef7006630bf8b8ab9183bcc2d212778d
ee"
r1~ = "21e2ce874aaef017a9d67f01e432cd16bcf2794299e6594f5065b417d0039
f42"
r3~ = "51a834a77851b6f5b476bd8ce9440019c0ba3b19a1739ae20e0834abca1fa
cd4"
// m_tilde_scalars
m~_1 = "586ad615bf1d62d511c8737ebb6a0492e0769faed21e1fb23cbbdf898b25
ad55"
m~_2 = "441e55f5927fb14f4059f4d4c7aad45b72349b50436cd8d2cd5ae3666ecd
64dd"
m~_3 = "10292482d9e08dc8d3a14223dfdbe4a14433ddfbff0950732a12f99edd78
efd9"
m~_4 = "1acd7900624f83027ee6c7700c579d10eaa0060dba6b9432247094971739
4645"
m~_5 = "4e525012cc1649cd7a6a4d3a16899e39b9d877243716e6212effb6320294
a382"
m~_6 = "65f2bf6e3dcde2dece63dd45ffcdecc8019f04664cb245f45ecdbc945e8a
4772"
proof = "a6056ca76a8d342646fe509aff0a0a9a473d1dd9a740325dcbcb8c2391e27c4
1fae3560e68014c258847cdfb825ffbc08b4dd4f6dac26e245243e77e0450a9
f57b5c2a26201e628f477307e4b1ba46239b5b37789e805f4494f0a79eb58a4
175b1ced5d5f5b401169891c734feb00829f62d575131114d5deac4c293134f
ad7f9485497935db52da96694e61b4498634723fb71bbdfb3bcb922474dadc7
80ccf8370f601f2313e2e133e480a397d715c262ac48aa3a5ea18c8fbe37269
061ddeb5fea27583a19e8547468bf275785e5261d84cf2442fedf89ed8ab432
3f6e10e337521794e056ff7e9ca417da7b18f5319e99832031eb46f74215e52
0190995041738445b92e42cd44eea874a9101a47477745473d4d01e259183a8
b7211083d9dfa557c6ab12266982176fd94c0859d53eca062406ce741ac9ef2
9d79a4da7bad78208e70eefc7c1c5f01a862095c21450fdaa0b68bf5748c589
612721fd7b183b0514fa72afa0a814ac4838b50a4bb6486078f7c1f289951d3
e09f5970496a5d2d0cd3c92d2751f3b661bc0a7a9682441c2b29a667443cee0
cca618c0df1f763c2e7b5eb622c2ce72db1cabcbb055d45c33cee4b2b0e0849
38f8a44341dec62aa4e673c5c0b21dc30cc97a925a6dea"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "13"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "[ 0, 2, 4 ]"
proverBlind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f8fcb1525
c93b649"
signerBlind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e0
a1e3c7f"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
3: "835889a40744813a892eff9deb1edaeb"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
12: "d183ddc6e2665aa4e2f088af"
14: "96012096"
}
Proof trace:
T1 = "a74374d7455d32209645a5e151c87315ec98cc5f6aa0427dc8a25f9efb5f3b
dcfa97bd59a6b503741ec7ed5b555ccc61"
T2 = "b79ddab7ec3fb0e0f6f0e8b63a741f433e90b29c1c77ec95547ca8859ab439
9e8104f89a5697ed230685bb24dd024593"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
// random scalars
r1 = "11ac0d86f78a0bcdc7c20417d73522b46d20a8f7e3ac008d2d3bd77730614b
34"
r2 = "2697d76e223bda4ed35e2428030bac7c2ca77122e3bab7b5d6b8bffca307a3
d3"
e~ = "0fc4a68d61483036dbf45878430cc8382283c481c8c1cd3c9d3fe9aec9263b
e3"
r1~ = "1baffa5c4d6187496310d4014bc9f15d0150f215868722186679b8e68d84b
682"
r3~ = "05b85a30f2f49348d34ca44242820c77421979b9b312a05b0fab16690026d
86a"
// m_tilde_scalars
m~_1 = "6f7e7893731097ba853486fea7eb62f66e3e14be47b0565b388c5a917013
5b86"
m~_2 = "45a4a12e1a7a518a63b66eebbce90605c29f249f570c85685bc0232c8011
fbf3"
m~_3 = "2ca1dd61fa58bc6670268750f5acdb19dbeca06ff2eb1a352d69e2131804
2772"
m~_4 = "0c79f4d9a6373202c102adf291522c06e2bf7f0da76f8e6cc3d6762bcc6b
ee1f"
m~_5 = "48f8c3fdcdde12d9949c6ba62661e5694363145f140be07d928b4ea9521a
838b"
m~_6 = "382d6baa8558a7cd49b2fb6ad333114d7d4842c1c29aa2fcb8d6159aa40e
84f2"
m~_7 = "53ae47dc3e329331a0cc2f46920d6f8b07f27afc4ad662ddad0e61d5e1b7
4751"
m~_8 = "6165660f8dde9349f501d169e463ddef10b94a248f2de5701966e65ba16b
656a"
proof = "a96a052121e1f2782cfb286fa1652c18cf92bcf9d27da34c6e68e97ca750b4e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"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "16"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "[ ]"
proverBlind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f8fcb1525
c93b649"
signerBlind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e0
a1e3c7f"
(disclosed_msgs, disclosed_idxs) = {
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
12: "d183ddc6e2665aa4e2f088af"
14: "96012096"
}
Proof trace:
T1 = "97653c8db8622f9e682acaa8b47f33aeb77325883d64c628e1e434375286c0
df961514bb77651d32cc5572591f9a67c4"
T2 = "97d3a42ec1606394a72c334560af477bed3b1de11b59a94a7488c6fa87cf61
c439d59f2de1a38b806daf7993c145fa7d"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
// random scalars
r1 = "211c1037bcd1316e4160817643c34a7bbb83021ddd3b1f22f37ed5253da52e
25"
r2 = "6ca3bb81e84cd13823f2630f90f28084d1409bca3d08983d9901f290450ef5
2e"
e~ = "2a37d3d049c506148362bb3411255f08bd504553caf90b877569b7250ca7f9
8c"
r1~ = "3427333b9226659b999a422946edc23b382d9a355ac03ec8dc45ed57cbe56
bc4"
r3~ = "633a0ef2d7d6a96a6d273e6984d0dc3a4d8a619fad2be125dd3e4237bfe2e
53a"
// m_tilde_scalars
m~_1 = "5f2b419df907cc204177fb0f60a8865cafc792fec2a5eee336146ad811cb
d483"
m~_2 = "03c340104c6b71dd62b77ed31d2b4863e9a6925cb9b78666a0b8c400c4ca
31f8"
m~_3 = "45f9d520e8682e349a036b8763fd647d2a1cbb81a77f61da5879d563948c
ffe4"
m~_4 = "4010f0d66857c907ebb8f7544e04ff1ba4bdc2baa19f63b4a146f5ccc385
3544"
m~_5 = "4ca37c03d4ab19de664f57d18874d7b86434cff1389cf9865506bcc49f63
b4f8"
m~_6 = "47965b117a3d83c8133a1f915f858c0b4e1f3d648af84dadbf722696ab0d
62f2"
m~_7 = "68bbcf9066fd79d6224a0a8d289bc38cc7768bca389779edfa29b0fe874b
2645"
m~_8 = "6185e602029fe3df6f0023323d20d33c67e8e0093e4d603e00506869aa2f
a57c"
m~_9 = "47f3355d90deaa185a76e02fc2bb521714682686569e36f016f5161babdc
3006"
m~_10 = "461a8b4fc326abf2bc18c43df883fd512d460419c4ee361a45714d8466b
5750f"
m~_11 = "4da6a68e742b02785c398f1693b856908138fa2376c03546ab2b4168853
c255b"
proof = "a46cea8d9d0f919fdc86ca3dd1ac8b2a3e2378e284ba821202cd8de28d07cf9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"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "18"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ ]"
disclosed_commitment_indexes = "[ 0, 2, 4 ]"
proverBlind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f8fcb1525
c93b649"
signerBlind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e0
a1e3c7f"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
3: "835889a40744813a892eff9deb1edaeb"
5: ""
}
Proof trace:
T1 = "b2a0a9b2349b2f5c8cf2cc9a49b21fb6e904a42499f576b81e76abe82d21ef
6591525a43bc83a4186d493e84259d926e"
T2 = "9501f821a461b6374c58c316875c4bb535e566c3b57bf776a77603510e466e
05380daccb13c3f085c03f5f4740211e06"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
// random scalars
r1 = "72202656d242b95e869fbcd40581b1924183ac11ac323ebbe011d63536d828
7c"
r2 = "1b6f80e77f00fd46a7ab1e46be33db2582fbadbf8358e7dfb157c69f577b90
63"
e~ = "48e116be2272e66dac308ec305869640dcc107d3de941659e7dfa80359a3a3
3d"
r1~ = "67dbca3425cd03873b9ef9240389de348618c4eb142eb963f03e99f5cc857
55f"
r3~ = "38beeb508bc526d9f70af680eb5e747daf0b0abf9c5dd2da78a795eb082c8
91e"
// m_tilde_scalars
m~_1 = "41e0af39eb876d842a6fa22e739bd8557782d8bc64f1e3e8caa407acf21e
9d83"
m~_2 = "34318199184c1d1b0088b30f12b59b5be5eaf0a6d4f1bd06cae1844ce794
93db"
m~_3 = "449a1a27becc25364804695002bb8671d66119c6b47ca0090a42690f108b
8743"
m~_4 = "0db0eb8b857927356955a1e251ad1df40e45427e8dd488b822608565a62a
5a31"
m~_6 = "21e0abb919758a5b8bfd32cc6417b36ca94d091a4ef4b6e9e6840a174ed1
93d4"
m~_5 = "3030cf9de98a457fdfe9cfbe693e53a2eefbe6590557b04bc5abcc981b2c
5b53"
m~_8 = "38af70a2dc939db80ec191f993d38ce477fbf53f0de85c8676e0bd32fb65
29b9"
m~_7 = "6d46722a4f82d87d5012bab944b18239571c6c20b7133b529d0cd8199925
1eee"
m~_9 = "39c92b70c8e3635a623da5dfeccb3b2a706e8179f1c94c5185f8cf3a4147
f0e4"
m~_10 = "1521952789a9f1a2c8e88d102574fc3b11644dcd57e4658bcf37f44ba57
5a69f"
m~_11 = "5ecc4872b50ac3e9159dc3eef11260766090788a864607e669c50ebc489
d5a75"
m~_12 = "68c917c66ecd829f333f0f9b12fcaf0c93e6f085fbb0d490e1e1a43ba59
d6a94"
m~_13 = "60f3ae300246e53d20ec89d0bce7f4ea8bb2f669f9b972f5e475401ab9a
44ad1"
proof = "b5b84e7a44fe9c864d7aefa086af221b5635c08c91e07d51c735dec90b13a7b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"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RAN
DOM_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "21"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "a90a9c986623c7df72f1b55f885a7f25070d5b73178f713
9fd6e948067e9f748b1cc0d4db3cbb9123a18851714ec9c
161b678690dbd0ae67f4bac061bb80824ba208906d58158
6971c6a32e2a162eddf0ed4a8cc260f2cc9b505fd5ea078
d21ae76159866c476cb129ad719511edbac763ec9b34c79
43c520f598bacd7775e8345a9b3c2c2490fab27c97f1529
ff319b4995ea15ff5e46ec26347d6a6bbf2e4b2a8da145f
6afd5444464d86f79cd7df32fcc665b9245e138c752decf
b3d507f2024af86b202741bf946e199ac77730a070821d7
df69ce563d2d4142572431047dc6b544e4a8280ada8c3c0
1a2d3f454e4cf1dc293f09e6a5b743f275286ce601f28b1
838441265c1c18b4425b8bd3d5c"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "95ef34d43451fe55d3887c7d32955641dbd13814db0d5d55e63fee1f0d8
e2bf5601924eb4e5015e895b5affe96f96d274bfcd2c2c902883cb210f2
bfca6b6c50b8e6768cda43000e6db777e2e0961fd9"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ ]"
disclosed_commitment_indexes = "[ ]"
proverBlind = "41fb2f74c30256398c927a262602b5ac3ebc6f84d9169476f8fcb1525
c93b649"
signerBlind = "49541deb67dc42d5509d39548637959bc43e105fff02c780a308c78e0
a1e3c7f"
(disclosed_msgs, disclosed_idxs) = {
}
Proof trace:
T1 = "80006e495e8293da2a6f5451548e593623e5988da761bdf8c0be7530387e01
29a0fbf757f78e146a85f651b03958bcb3"
T2 = "b8cd62c9ba796c99037d951360a5217fc137cfef4bf43585defeb718b4fe35
0d8edc445d309cdbdb99985efa681d3b4a"
domain = "279f17f14e7e3986bb71cf6c8a1018460596e62eea6ed91bb81b9706f4
729f95"
// random scalars
r1 = "2aa67d3759b3aa6cdc1e57822f10e4ac850a7f80a82f0967cd5fd21899ca0b
69"
r2 = "1e946e0a41c6a6dcc24894f477899f060f0f6bbe5b913022848d39e356d83c
f1"
e~ = "6d6c354149a71ca3c43e5657fee3b95652c5978125350c6d317cebc9fb8829
2a"
r1~ = "2508a44ef5e20176698f111e2375bfa84661ee27189c300bde8b9d946ceb5
8d7"
r3~ = "35632248dc2eea031c09ae0797e1b9974d675d60df32035a5fde566ff71dd
247"
// m_tilde_scalars
m~_1 = "26f66a47894e184b5fe32a2e6568c0786af376d089e2a11e632978c183a6
f3fb"
m~_2 = "6d3606b3086f0c44c209c5af201d48d20e015f0fc80fd00a10259f7f46ea
6eed"
m~_3 = "22063ed43999f4ae40a03c4ea9f934b3f946dc167957b20d501a13442669
5cc0"
m~_4 = "29930e487c3e109322d0f2e097616ece04d87d91649dff92bda1dc438400
256f"
m~_5 = "4b0cff28fe171b5179977f6bed33413ba420e0656e468a579a7fdac983d2
4314"
m~_6 = "6451fce17b93ed5dbf4d2aafbbd6afaa18e6f222046ac31ed2dc1d6df9a3
3291"
m~_7 = "1f9c3ab790fbad9b71f74783969fb01a14fc7e1f417a38696b0430a77b68
fe94"
m~_8 = "480b325408ff54ddd292d3c3ce8253c540cc8c32ef42308389bc9543c471
c2da"
m~_9 = "5e02607fbd4d0af561e61c377e2b31c2ae1c589ba835f93bd7be3814f65e
a450"
m~_10 = "6849cc6bf9367386c4189859998d9c4993c84488f9b03d311c197499dda
1ee0c"
m~_11 = "51b9c711f25213b6a63a9ae2ade5b0d517539992c40bb45297d0709b216
db36e"
m~_12 = "6be3bcea66b6872421a2572b0c37cfdd0541d226a18fefdd60619217554
eb08d"
m~_13 = "48fd2d36c9e119fba1ad5f5fef059838c7b0150f7a4088919ed9bf6934f
7c90b"
m~_14 = "2c7589a2b29e0be25b1f592ecb84d072fb17659c4bfc6dfc54dba002623
f5a0c"
m~_15 = "55976175ecac1373e3e27ed645de08514e66d50600363a6de6e791f3358
b06f2"
m~_16 = "5a4d330bd5d5fe02528f8c3b2a7d3dcc223d11452f2f772e95cc36b74fc
4c60c"
proof = "8de2b23c71d0cd0a2b1088ac05eca3956789465b81288f6a3d0597c9ca60b9d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"
¶
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_
RANDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XOF:SHAKE-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RAND
OM_SCALARS_DST_"
count = "11"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "null"
PK = "92d37d1d6cd38fea3a873953333eab23a4c0377e3e049974eb62bd45949cdeb18f
b0490edcd4429adff56e65cbce42cf188b31bddbd619e419b99c2c41b38179eb00
1963bc3decaae0d9f702c7a8c004f207f46c734a5eae2e8e82833f3e7ea5"
signature = "8886984283bc433d56ac0f29bab40fb2273d0e7e42f5891c80c357473b5
04e2aae77658efbb0035cbf32771b7fe8dbbc3509d8e6d2a2a9917304e5
a0650e9a6583edb53f82263222a92b41a531784d6e"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "null"
proverBlind = "null"
signerBlind = "null"
(disclosed_msgs, disclosed_idxs) = {
0: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
2: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
4: "496694774c5604ab1b2544eababcf0f53278ff50"
6: "d183ddc6e2665aa4e2f088af"
8: "96012096"
}
Proof trace:
T1 = "a16e8bfa6283d39547678e9d02ac67ce786b6f322e6417b6d53b1609ee11e9
c037b9da87048824c9e5647832b7f917bc"
T2 = "af8fdc785001adf4baf4513baf913a158409172ece061c6e452d0f97f556b8
10aa8710e9cb2431d993084809e3af62bd"
domain = "4e6f04eeb36ed65d8f088e7adf6c106c0db79527243ce19389514b389a
cf7adf"
// random scalars
r1 = "517c6ba25814e7e8a6b1e1e7a1eaefbd13a47b874a249094592b51295c896b
e6"
r2 = "17d278dc4ff520d8bcde7c7f35e635c19d9d0e19e0f32e4900e4a69af300b2
f6"
e~ = "658838c65c01e42cd39fe21885284cef7006630bf8b8ab9183bcc2d212778d
ee"
r1~ = "21e2ce874aaef017a9d67f01e432cd16bcf2794299e6594f5065b417d0039
f42"
r3~ = "51a834a77851b6f5b476bd8ce9440019c0ba3b19a1739ae20e0834abca1fa
cd4"
// m_tilde_scalars
m~_1 = "586ad615bf1d62d511c8737ebb6a0492e0769faed21e1fb23cbbdf898b25
ad55"
m~_2 = "441e55f5927fb14f4059f4d4c7aad45b72349b50436cd8d2cd5ae3666ecd
64dd"
m~_3 = "10292482d9e08dc8d3a14223dfdbe4a14433ddfbff0950732a12f99edd78
efd9"
m~_4 = "1acd7900624f83027ee6c7700c579d10eaa0060dba6b9432247094971739
4645"
m~_5 = "4e525012cc1649cd7a6a4d3a16899e39b9d877243716e6212effb6320294
a382"
proof = "8fa620d86d48ae44e658bfc2b414fad0e6f1333e3a852eb455b38144760850d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"
¶
Mocked RNG parameters:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "2"
committed_messages = "[ ]"
secret_prover_blind = "1b6f406b17aaf92dc7deb911c7cae49756a6623b5c385b5ae
6214d7e3d9597f7"
commitment_with_proof = "8bd94b05cd4e006145bc974cf5cdcc80e544a8c4624b0a7
f6a5509430c79be788be86536b725ea93dd0a035b4ef822
631dc4e8c1a02cc212cc9f914ecfab3470901d5d1573e4d
03653af76ebf3bd891a226635ac82ee6cc94bc201354713
65d2bb278e21eae8e71661ecd3f6301c7ba3"
¶
Mocked RNG parameters:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20
249afb4abd37589"
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "2"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
SK = "60e55110f76883a13d030b2f6bd11883422d5abde717569fc0731f51237169fc"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
commitment_with_proof = "8bd94b05cd4e006145bc974cf5cdcc80e544a8c4624b0a7
f6a5509430c79be788be86536b725ea93dd0a035b4ef822
631dc4e8c1a02cc212cc9f914ecfab3470901d5d1573e4d
03653af76ebf3bd891a226635ac82ee6cc94bc201354713
65d2bb278e21eae8e71661ecd3f6301c7ba3"
header = "11223344556677889900aabbccddeeff"
messages = "[ ]"
committed_messages = "[ ]"
secret_prover_blind = "1b6f406b17aaf92dc7deb911c7cae49756a6623b5c385b5ae
6214d7e3d9597f7"
signer_blind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33a
baaa94e2"
Signature trace:
B = "aa963d9eae5bf642b7b080c9b6cf33f19564e501638d85a0a1f862a86ee0b26
e992fe52bbfc103c82038a41146994ede"
domain = "1666eb9faaa4d028797e16a9e89478b067615039c763c931c3df5012ef
153b33"
signature = "a001fb708fb48dc1c02c84114edfe4cce81a80c067159050c29b9036806
21c830e93213872305957c25122de78194a913165b2ffdd806e3152c4e2
d712c396bd2619028cce1857d07ca96a9f5157f4c8"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
SK = "60e55110f76883a13d030b2f6bd11883422d5abde717569fc0731f51237169fc"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
header = "11223344556677889900aabbccddeeff"
messages = "[ ]"
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20
249afb4abd37589"
signer_blind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33a
baaa94e2"
Signature trace:
B = "85f7a6c2593bb4c1ecf6bd84aa3fe29e4d2c7d59f236523efbad684a25b941c
cf9abb83a8531e9badb7bf1bdb433808b"
domain = "1a0842369c4a79ed4709bce26963466699fafea687246b1074c91d9002
c4bd1a"
signature = "a9e3a078815b3f7c9d2a9310a5a5b6da193214cb6be6ef77dbbc8fac958
ce26bec96ded9334aa0d56dc37992906b6a7d6ead4a7dafea18d3514ea4
206f9a93b225debe99b8628ccad921d9253e39561c"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "2"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
SK = "60e55110f76883a13d030b2f6bd11883422d5abde717569fc0731f51237169fc"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
commitment_with_proof = "8bd94b05cd4e006145bc974cf5cdcc80e544a8c4624b0a7
f6a5509430c79be788be86536b725ea93dd0a035b4ef822
631dc4e8c1a02cc212cc9f914ecfab3470901d5d1573e4d
03653af76ebf3bd891a226635ac82ee6cc94bc201354713
65d2bb278e21eae8e71661ecd3f6301c7ba3"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message = "[ ]"
secret_prover_blind = "1b6f406b17aaf92dc7deb911c7cae49756a6623b5c385b5ae
6214d7e3d9597f7"
signer_blind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33a
baaa94e2"
Signature trace:
B = "b16f00f40d3a60700f7da8589b876ad722279de6e6c66dd2681a6855a3d71f2
976802972a4e7bcfa88e1f2e44387d9eb"
domain = "69ab8c6eb9481bee9c3cf60dfb9d3f539023e8c6e78c6568d0913ea046
752a2b"
signature = "b3e48d4f916c372e330b3727d14f1543cd5de4285e6c3b90692bc842e0c
c1f4eed563726df615fbd77427975222d196664d8733cf38ac4c57efe85
a055290cde0cd08680309218db9e04f3299985e814"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
SK = "60e55110f76883a13d030b2f6bd11883422d5abde717569fc0731f51237169fc"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20
249afb4abd37589"
signer_blind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33a
baaa94e2"
Signature trace:
B = "ab6c841535ba75d568e913d716cf2920624044c5cd99cfbebb564d5c0654a9b
bc3c458cc3c51349ece6ec40223f7e2a5"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
SK = "60e55110f76883a13d030b2f6bd11883422d5abde717569fc0731f51237169fc"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message_1 = "5982967821da3c5983496214df36aa5e58de6fa25314af4cf
4c00400779f08c3"
committed_message_2 = "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
committed_message_3 = "835889a40744813a892eff9deb1edaeb"
committed_message_4 = "e1ca9729410dc6ba"
committed_message_5 = ""
secret_prover_blind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20
249afb4abd37589"
signer_blind = "null"
Signature trace:
B = "8444fca0a990ab19c0c7c7cd93ed31406e5dde17c16f1333c2e42284ddfb88e
062fed9fd2aa6ae6cc81e6b9a6251fcb6"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
signature = "91902b68ac869d0b250355be499fe555e292759de6cad9c28eec51d3f4b
b5f435238636538d347be44a4b33e0edbfd4d1bc5b0082b29eea3b3aed2
b718706a8d08ada2fe623279472fa5e4c571c44ebf"
¶
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
SK = "60e55110f76883a13d030b2f6bd11883422d5abde717569fc0731f51237169fc"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
commitment_with_proof = "null"
header = "11223344556677889900aabbccddeeff"
messages_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4
a45f02"
messages_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb07
5f9b80"
messages_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
messages_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
messages_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
messages_6 = "515ae153e22aae04ad16f759e07237b4"
messages_7 = "d183ddc6e2665aa4e2f088af"
messages_8 = "ac55fb33a75909ed"
messages_9 = "96012096"
messages_10 = ""
committed_message = "null"
secret_prover_blind = "null"
signer_blind = "null"
Signature trace:
B = "853ff87eda30796f5997ec3fb9fffcefa78b0b457ce9f2487b8afaa0ffa5098
053dc91a65e0b169d97f7b1123e80ab14"
domain = "160cf879138e86f8f6025c41ec94434432a315c33dc6b90c38f1b21ce1
01418c"
signature = "8c21175e0465339fd9b32aece83c43402b8b467baf3085028ecb5669e76
e093c0db878bfd4e6121b2b86260fd38f11ca37fc2f16f145ba600b240e
b96a40960f7aac7416f2390225e7166863db321b16"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "6"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ]"
disclosed_commitment_indexes = "[ 0, 1, 2, 3, 4 ]"
proverBlind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20249afb4a
bd37589"
signerBlind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33ab
aaa94e2"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
2: "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
3: "835889a40744813a892eff9deb1edaeb"
4: "e1ca9729410dc6ba"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
7: "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075f9b80"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
9: "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
11: "515ae153e22aae04ad16f759e07237b4"
12: "d183ddc6e2665aa4e2f088af"
13: "ac55fb33a75909ed"
14: "96012096"
15: ""
}
Proof trace:
T1 = "89bd19c0b8bd63be291e6d71ee1a035e4582782c46c4f69c07fcb351592ecc
680af505570a7c5f31e955fa031b30b196"
T2 = "8a4aecacff0b7e8f7d24289e154d0abff199f709814bc014c7782d922b05c0
284c9b14827a26f9f1db2cbaa91e9a5c90"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
// random scalars
r1 = "2cf2bd257845b6138247ad87cb387aee347a9104fd1090f92e3b7559e855b0
68"
r2 = "14f989abea9c9d0cbae6d72e2eb806ac7dbfcd08a8ed647ad5b8e16a83b94d
4a"
e~ = "07e5d7e2b504d3e3075617400781df19831fac0763602bc494b3fe40dcdefb
47"
r1~ = "35888226d06bd50f1901008bdf70b1472ad98304664828c6a0fa45b396cca
7d9"
r3~ = "21e5d2a43d0190ddee9319dab20ad1bfaacf7c12399ac384fe9bf1235c191
907"
// m_tilde_scalars
m~_1 = "6683a44c7e1b057c7ce5e99dca9d71a091441b6c23ad9bfd45ba23862f61
0cf7"
proof = "8b29fc429ae913cccb71f730fa61fd220a8ce673c6eb704106783b7e00a5fd5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"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "8"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ]"
disclosed_commitment_indexes = "[ 0, 2, 4 ]"
proverBlind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20249afb4a
bd37589"
signerBlind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33ab
aaa94e2"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
3: "835889a40744813a892eff9deb1edaeb"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
7: "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075f9b80"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
9: "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
11: "515ae153e22aae04ad16f759e07237b4"
12: "d183ddc6e2665aa4e2f088af"
13: "ac55fb33a75909ed"
14: "96012096"
15: ""
}
Proof trace:
T1 = "802a8579d430dfb6256f3ab6bac9aa6ca87a2d24586c88b6b5f2713f114f22a
41ca940464b892d67599281d20b733a4f"
T2 = "a2edae923e082379a452a0ce552008e94ec31ac9b2e77b70a08d31bcc617bc9
6e787f8e0b0cefa7e0d070e5a58b63e8c"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e96
dbd02"
// random scalars
r1 = "5a113c961c5d21bd78b50c3079ea482f5e861c20be37899d26e2ba565ea6709
3"
r2 = "1ce7fcf7fc75bffdf3cd0a284a5cd4acf6be87df552fa937f246a38e8c03af0
b"
e~ = "286458907bcd8e3fc535ed9575531919d1942a907ef8ed10360e292fca5ad0b
b"
r1~ = "40caa7858d917197f007c87ea7e80f638db1313b0e3d46612bb2e73798bb24
c8"
r3~ = "6d30be5b88e8cb333e4872bdf0c4d7cffe4540eddf03eafaae3d4cb1f3ad1c
da"
// m_tilde_scalars
m~_1 = "342ddc1b4e04cef472c764f5bda8afae4b189e78ffcbb519075a83e640c01
00c"
m~_2 = "51608282827ece21a8ed20b774e2ff129353416006317c16e409e1a925540
345"
m~_3 = "0c1ff555f2b0f53e8859aff2947b22b1ef9d2be2c65621d8f6aa3252340fc
af2"
proof = "91b42b089d23d096669b0cc5cfb238490eb0bd668d32d8092ac38ca526cc8da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"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "11"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "[ 0, 1, 2, 3, 4 ]"
proverBlind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20249afb4a
bd37589"
signerBlind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33ab
aaa94e2"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
2: "a75d8b634891af92282cc81a675972d1929d3149863c1fc0"
3: "835889a40744813a892eff9deb1edaeb"
4: "e1ca9729410dc6ba"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
12: "d183ddc6e2665aa4e2f088af"
14: "96012096"
}
Proof trace:
T1 = "825523bddbdaa2a3bd3b7ec869c6287807e1a585d611400805be9f96f1d3f0
2fe650a5406e27da815f8ca938f0d75e8f"
T2 = "8e9f246ed76f512b974ee52512e32b2b347da58ad0c0a881d4d40d62d33234
43fe911387fdc22e0fc8af6e01115ce97c"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
// random scalars
r1 = "034d543fdd164520876e558a77c102d4ad8bc99bf82ebe74590481473df2df
56"
r2 = "4a8334929ba48d36eb4ebc7f8bfa701b4d3f30ef25bc01e2a45ef9611c1603
7f"
e~ = "19726feed8e0e5ff22e4f5de19713977beceb12c3e85c1f3fb41cfe4a7237d
1a"
r1~ = "73012dc2f14039c8de5853b26baab7b51280a3f41425416d78a1a91fbaae9
bf2"
r3~ = "68263029bdc322a3d6460758135205dec58957ff3e5397276a2f0ffdc738d
5e4"
// m_tilde_scalars
m~_1 = "52638b8d190f9fd439188b22c903507cfe5282296c2c9f605f1ef714afc1
4062"
m~_2 = "2cbc33e381cf6ae09dbb6f1d08e3ea93a5aa03c4a6574fd2fa2e879dc4de
eca9"
m~_3 = "1ec36e6be1c702255d9aa4d590014b2b5de2f07d290c9551b66977cde157
094b"
m~_4 = "5491612228a993693c79c11ae169dad9be4116a704ae9ed333ef96e39863
73a0"
m~_5 = "6f4d920974d33c1e08c86b7f4b6bb7c58a5c0289d8d706a92d4855125cce
db70"
m~_6 = "279717a2b1e1d34cccfddfe9c8e3729f6e92e28197a09459c6dcd56e3920
a0d7"
proof = "97154dab37939b7b94dc0b3e699c248fc2511e9e246c8ba1ef82777a293588c
4a80d24539c547b059b9e2a8e5b94dac78ed7c60601ce7843cc18a7119927cc
109dc152152d3131d10bd04b140127ec7d5c6a631665e58850b847ea221ac9e
1a3b549e5bc46d81c842c65b32c533e0222aafbbee4e7009cea9f03c5840332
295c4e58620cfe666706363c190e1398d4190c6556cfc9ddf20c0f62ecd18c2
d24678655f33312a2677f01a75894fc8977c01fa19d20f9771f4a3ca6f6e6c0
ba00b085bc9264c1f343e0509f1f44bf8a2ff624c45dd583626002101db0b05
3f9e3a162b1abd6b1dae6683ceaa3c0e4ea696256260ea1eca9712c353fc326
6d156a8f53b1911ee2fb54d0ac9e47cb4d6d20e93d42e3c80d6954565ba2e84
a48141858ce9c2f9499b4065c5206ac8ea70ed1bc21b5e9cf868a8bf94f4f61
7d316562b2ebefbcfd3825975013c834babea0fbc662407c6d35185e29d86f9
518bb1cd530c97a9f0c49ad26b20add7ddd8eb2166b3bff20c58d47fa72d04d
12bde322ca29aaeb07936a82655529d26f360a5b18015ddb3ea266abf629e3e
4c7e86425c90f481078b1b111410078fff5909b30b5cf641301a24e923b5958
950fd24c2d32cce7860a5c7e6c733c503da28eebff28c7"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "13"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "[ 0, 2, 4 ]"
proverBlind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20249afb4a
bd37589"
signerBlind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33ab
aaa94e2"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
3: "835889a40744813a892eff9deb1edaeb"
5: ""
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
12: "d183ddc6e2665aa4e2f088af"
14: "96012096"
}
Proof trace:
T1 = "af17d9d3db5a0dc69ac9bb0af43c1634202e2b6bd82cb92f8547ed9084453d
a96d3b660d3ec69c0ea7684cb339711aa6"
T2 = "95b4d41cf08975b312fe3dc1c74fe474b7ae1c71d62d061a3f52ec366d1879
d550d251ac1b229978203ca627e41602d6"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
// random scalars
r1 = "6fe2700deae18571f365d5b549a03eca3a19414532982cdb173e6442f8488a
82"
r2 = "4cc007c238298166e67bcbc8332435b27f39879b75ab00ed5e6863f6296051
a4"
e~ = "53f3c5e5ff89fb20a89d7fffa1198b13744d1ae78457119e5bb3da42d77bfe
56"
r1~ = "14e6c0d53eba55936c1f1ff11d9775fde7bc366d1859cdbd9ec9f65510a19
b02"
r3~ = "0a3c38367bd4f42d8b44d988580b40ad1c929a3844fd92e0d2c2a72479621
8b4"
// m_tilde_scalars
m~_1 = "4e27cd534e2d06c2af769760a2651010d8f2495066c4a4bbf33778f558c7
2b09"
m~_2 = "2ea785a49f1b29d7f79323d5e369e3598665c6e6ed1352797dcdd20b249d
58fe"
m~_3 = "438393d39c51a4efe0bf3b53acf17a7b26724ad7de58ff8bd5fdf9dea0f5
675e"
m~_4 = "01d9d79da4918a57bd628cd625cba37cb3a278b419e04f5880c6cbc77c90
5c2f"
m~_5 = "525ec7e60016e00e8e1d039d245bd7c44c4dbff8f566deb9e902d10819ed
c0b5"
m~_6 = "1a65097b4ef6145d0ca4c8257e193afe8245c85a3cc934b1a28c876c7d65
809f"
m~_7 = "5f3a2f4d08763ca6a6685aebb3eeb66a0887c750698b44ac17b7bed8ac3a
1fd6"
m~_8 = "4c583e5e4fc913aa71989afc50cfd8c2024d64df96ed12c7ef82d50ed4d8
bb1b"
proof = "86511a727d3930032106cbabd68480c8893cac0698ce156ff7060eb3a9a0d05
78e9c80b3a248948ece27c871b281ca9da29e15b5e254a4ce4df998a3b83ec8
daee50a35867fc4a545b550718b24385c086c8ce95fb569b9d5b08afc1a63d6
a3eb89b61dbac567a7ccfd9fb1462e806170dd885b719b64690025989b696cc
50ca7aa625f373f7f3ddb99a01cdc3f1e2442663dc0600cb09ab26066b933f3
a6a82f214309be31cc02362bb548e5eef4a04669197a372cb6937a00450c115
675d3e026a33af2ec80705a7517995a22661d21c9e4c0b464e798eca9203301
04a4c760074342f38b0372a70473904086465606803d9dc77606cf00c3832b5
34de13653f33a4723045bee32990a553c5e1d0ce70190e8e458a33ec62fe9b3
424e46bf77fe26a2969b74f5a242c4697a286f15057226bd9ab05335e6b2458
4bd477179e7623e3b6047c26c1b8e57dace080e114110d126537d9dc2eeb4ec
611083a79bce67c29696700f66f86ad4bcb6875d2f664098709700baf0beead
805f9f374a178edea6172a315f4d38aa02271afdd0f55f580b870d6a813b4e5
b7bc0530dace5dc600bdfd1134986e5aaff4108a608865a196f610cbc403857
73bdb5dead610078adcd4bc4fe2c83f28c355429982d2570269168d71f46d49
9e124dbadf5f61456cb969b2814b00f61bc87e5cb166e7c40163f0c0124d1bf
fc9941c3e805d37b1a7cffd15f39ca98e145a9c62158ac11"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "16"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "[ ]"
proverBlind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20249afb4a
bd37589"
signerBlind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33ab
aaa94e2"
(disclosed_msgs, disclosed_idxs) = {
6: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
8: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
10: "496694774c5604ab1b2544eababcf0f53278ff50"
12: "d183ddc6e2665aa4e2f088af"
14: "96012096"
}
Proof trace:
T1 = "a74e62b1b62be055210ca1873779df176bf1dedc71f7afd872832c91757788
29ca93bfb8cde254faca98a6eeb801b0f4"
T2 = "af369820104576933b3f8741a5c2253b629200f2528522ffe5f602d18f1999
d7d67bbb1e75367d65e050815a8153b2bc"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
// random scalars
r1 = "143f08e576583f264b72129ca9892b9c688e13087ed3d9509f85c43120eb79
ad"
r2 = "0217e712a7b1f6b5e65590f3f440f9d9ed25b76e065294fc728b866dbf4ef1
48"
e~ = "33b25342e7badf42d6b56c2d2db9a20fbd96b87ff39d8cd471142f32098849
44"
r1~ = "097f8d774312e72fd4f29f2d5d9d317b3f12942cdb9b2e9be3d191afe5cb8
b2b"
r3~ = "5a77c4f0644db0007295cf51a6a31457573800802640c2b1cdf28e8ec2cf6
a9e"
// m_tilde_scalars
m~_1 = "0766852f1fa8f06c12dd87e3bb6f85162d2fcd7af8e9d14521b521dde5ff
8705"
m~_2 = "65afb4d1a56075f316f72d2aa86fb9a8379a6ea1d47be68e55eeeb6cd176
f0d9"
m~_3 = "04a0b83f6d79bb19a9230a7f3cfbe70a81371490dee785cb0a206a462f94
41ec"
m~_4 = "4168e396ab4deb71c39e12e10ee26d8c0b8b56b136e78b64abdf0baabdb4
aa4f"
m~_5 = "241cceaf36d43c7f1d56264ac98e7c35fcdfb5d77022334224fa05e43ab7
2e23"
m~_6 = "59f396acf1d81dff23ea10d92dd718a0928fcd4f90585352b9f628df4904
808c"
m~_7 = "057f3655600aaf1efe069fd15d1a8ed4f6b122fd3a54b9b2d0db6b7edf7c
bfac"
m~_8 = "2ddb9f0733eefa0c47edbe47f55601711d2a1b3d13c6f07747a4f6a7f940
5fb3"
m~_9 = "30d19e2d1625799e21b7dc2b8cc08376863b7b1370aafac151216ecd5698
5814"
m~_10 = "6f5c1c1071faced0bbdfb5e382ca6a0c62adf679128361ba48f890aca65
fb340"
m~_11 = "496c5273ff17a2219473e75c203a4ee1210d43a3f31bbf18dbd262862e0
73bea"
proof = "a3e58b26112de65d6e6bbeaa662ccad8a2222fabc49fb792fef994681e5424e
795e8556d565efd94048507701b7182f782f8697e748f3fa9a75bb87b44beba
a16c730d97453f91db189851ad5695c02741b245ce212cf5b86fe83c6cf6f6d
0d1937c9ec0e1f8fea1bd6b259ad52c28bdf3b6f8990804037d096030786dd4
609c1c729e0b29286ec2cd53470bc202128814b9ac512da494b0bead3c7d345
e3f8aa557db59404bf2e7d9409c9c9a412c4b5fc92c9ba3dd9b2198905879f1
3ba2090bfac0a78faf7ce19174bfb16266c9383f5e12dd1456b533d7878c7bb
2813174df9bbe7b3ece410e4a8890d9fe7775f410e48d35b0e0e656c6ada917
6ec8a41bdac4b4d6031410078b2a5a8e8f90cdc430e551c1a94b5353d071cf9
45ae03d204f347905e167340bfe6f42a566b7cc793cd692ba74a2442aa95c96
7976d734714e17a98c50f067da5c0c2cfef91100ef6c97e9ebabfad141878c7
3af82d6a3b36d25baf0e72b7391baef0f220d73c6442c09915de3ed89717d19
e5375684f03efb1c8eb65db1049446b420c2c682855703f84f5781cd0bcf944
d6c13e883ea03365311256b918e1279067b42cccd99f902a69db49e53c1df89
b13cd9ab98c90dfbb1f6ac7a3645505fa04d593dca5f1703ef8b71b78aa134c
e1a8e819ba6dd5caac56909870d7eb948b903c7e0d977444df59a158af54eaa
3779c575436186fa6804cbe16397ef3759e35f254eda037e237c6a506319bec
da29e32cad64a3a941209e92ea9d7e55dd5cf6c7d25747990675eb271b8aa0d
3a38111a9ee488f849188e2b7cce5355d79ae2b4e8b1d055583b62cd581bb9b
6a4c31b194408959d06d1995f2094f27943d29e819a52bb91ed"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "18"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ ]"
disclosed_commitment_indexes = "[ 0, 2, 4 ]"
proverBlind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20249afb4a
bd37589"
signerBlind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33ab
aaa94e2"
(disclosed_msgs, disclosed_idxs) = {
1: "5982967821da3c5983496214df36aa5e58de6fa25314af4cf4c00400779f08c3"
3: "835889a40744813a892eff9deb1edaeb"
5: ""
}
Proof trace:
T1 = "a7cc44212d02317c8e185a6d55eb311daa108ba6150fbab4198a2026cc27b8
970530b9e3b1964f1ed6bae468a73b8640"
T2 = "b9c9fcd27848b714a9d520daae856c93d1e560ae865040fe3a16e1055a83b7
149685518faf4acd0a5f41892707962377"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
// random scalars
r1 = "23d8b41f82e80a32c4606bf7198b6a85bfdcbb9a87773a54e668aa6cc50f4b
60"
r2 = "259cb8451e183911fd32701689c8da084a351cbc878edabb5c65892f5566cb
ee"
e~ = "0750d611202174343211411eb9aeb18d6b09057c51e9f9524cf1ec29a845a4
c9"
r1~ = "519d28834203f545ce2e917b1428e59f4ca3e716351c2f03b9884bf3b84ee
5d9"
r3~ = "664fd86f51bd56079f1f58e8f29881ca6881f9022b267a0842eb9bd66d8ff
116"
// m_tilde_scalars
m~_1 = "35c21b4641053b0e351cecc6b4f7aa9687771ea67785ba51ddb13ee3d661
6344"
m~_2 = "2dec7bd3fcd718500184d41d750642b55d21ea63b494bdf41011dca9d707
5b57"
m~_3 = "277ca0dcb0183675a981bfa22e2ad09c8a61b23761575078374a9df40cb6
3237"
m~_4 = "3376f31a419eb425ae5375029f0f1caba349467ff477c30aa6a577ffbabc
162b"
m~_6 = "68b417316ece357d32bd0e94f5211a900abf5888ec25ad7762d40413d45a
6ff5"
m~_5 = "22808132ab0fea4b85a2b6621abc8f2e78b65f3417db2e8350bec0a5d02f
12f7"
m~_8 = "1f45ce8d90d44399aafe97bd024636747766b670004c366af6b19dfd211f
dae9"
m~_7 = "668d12f5ef2c391c0dc06f1f2c1451d710c743311cd213c268bd7b410853
00d5"
m~_9 = "304b07fecf8dcc052c29b4d52934a031d4abdad430c4bd3ccc65028d4e26
da8f"
m~_10 = "02d05a55bcfe243c268154cc03f548ffa461f84c4087c7bbb6284e4e07f
fee53"
m~_11 = "3e20f9d1709e50cf709530e4e267f544eda9c4b9e214e4b133c20cda847
7ffe9"
m~_12 = "6e41035b050e5ea1f97bc975eb5a63447470bc24639a7f63269e8b3f5d8
f94a3"
m~_13 = "31dad9cf8ab3482296a766c4c6e2a97b2ad9e83cf8c83755940736235be
a6e0e"
proof = "b3c858ca8b1193a759acfcbc985345103384565e42b5523443031879f2bc757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"
¶
Mocked RNG parameters for commitment:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_COMMIT_MOCK_RANDO
M_SCALARS_DST_"
count = "7"
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "21"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "8707ce71651e7fadbdd39cd88e83255629aacd969186eae
fe95ea27935ab54af325220bb410af7f4389f85adc63054
8a02ff284a86147a4fc93da14be0c8f2c8df53b0057f71a
dee985b3b72bc759c2642187bd6cdc9f9e78f4d44b7fea7
cb41563058647bc49614cdbb30b8f88264112e4b9aed884
9609ab34eed40a83fa095d7ed156e9f89e7bb64bec73cd0
2ccd8814aa43b6f46cf2b5684125fbc25c0285aa525dc3a
ba6f21a597f7b5a424a014c5162983082c2d63ff500fc06
b5200423fb647bf67815bb9baf76d5a8ccb665ba120fff6
8b6fd180f4b4c43fb437d68cff8eeac230a47d331b4a72f
124957042e4664bae34f486b5c33d1120eaa676e6e302ed
1f79739b75e074baa702beb7939"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "ad7169408a137b7365c6f156d5011b72e57e027a7326dc4fb95128099af
692fe7b1f7208b98ccbf717dcde22a611d2543ebd9679292532d6cd9559
75365fe5a260336f1329509e3e1fbce1bd2d9b5ef6"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ ]"
disclosed_commitment_indexes = "[ ]"
proverBlind = "4fba5396baa36b2fde81d46a9b9ee89c425dbc5e1ffd65c20249afb4a
bd37589"
signerBlind = "10e75ca49d242390896d9dd943b97ff23b8cb780bf27df185f51b33ab
aaa94e2"
(disclosed_msgs, disclosed_idxs) = {
}
Proof trace:
T1 = "842def1bd17fc544219d01f8e0a483519302fce802da67d13cd2f82bf97097
6692d3895a53311d996190cfe97620763a"
T2 = "a0e4a3c8b4d296d32edcd8f788d003e20697f70e3f992dd1b4efedc69717ee
cd2e05cc95558641e5fb5814a77de35090"
domain = "386bb1c7c4d1e3b95686cd66ad21ba8302f9f87290cc800a79c910f0e9
6dbd02"
// random scalars
r1 = "60d345d6f2bf3d7b6734145a0a1c84731771d9fb8f2caa849dc33a3e1ed429
06"
r2 = "5fd44fc64975d153f17a73ce413b86211acf63e62494ae73a0865f068588fb
02"
e~ = "6e3fdd342aa6c154fd11ba738e191c54f9877522f4648b466eb4ee1d301780
bb"
r1~ = "3da42b3641758dc3d8bce1ced15d1fd1d291bfd533d11373248082eca6d45
d9c"
r3~ = "01be275b265a083b2b8a1ba7110576e28cfcad346717c512c3311ca403168
120"
// m_tilde_scalars
m~_1 = "67ff540238565851a1f98c6357507be2da16884e44ae26fe4d0a0a860753
2fbe"
m~_2 = "5de3cb769cc629a9ab21fe29bb7acc06cd5df979826fabe26b78cc9ab67a
32f9"
m~_3 = "1a14acb3666d2d123db8d19ec473dd980cb1100532be1abda1b941668b43
ff28"
m~_4 = "4f03cb50f6a25f1f7f277682ab5965a772ac0b24e9ad2f1a7b42a047d8d7
adc6"
m~_5 = "11ef78647f2fbdc57f8d29cab816584920596bbd3813d2ee7df7f44b2461
7f33"
m~_6 = "4d7fb091d8f42be6fc0fc0401cc5ffbf0da7aad8951a451f26abf5820eec
e429"
m~_7 = "03b576c0e1b8063af7f9acc91784cb062920820e9b2d4baf11d55777d11e
2946"
m~_8 = "5c8053e4347ad1c5f600a7d1d5aef448dc0fbbad6204430486c65e7216c1
8a73"
m~_9 = "4b81ebb73b19c698f62d0fda7505452e97382b09bbe7821ef40fb1f3b3f2
6172"
m~_10 = "1ab69f6373dcf9d87b75f2e140a34345a92f7952a44436832036bf6bc4f
b3b75"
m~_11 = "0f0059e68095e5edccc546ac5312234ed1d6b1ca65c4b13f77dc1b7bae4
623a2"
m~_12 = "1372682d7f0522cf87aa4805f43d493c2beb7784fe9875712480a5bec63
a8b69"
m~_13 = "366a39b41f91f2f6faee881f06c1077e9c65257fc75587353880f6406ff
828f0"
m~_14 = "4eac85d64994ff0b48690a25055eb62f0f0b4a89095c54fc1b08fb7ba0e
90eae"
m~_15 = "475da477f48d661e2271eefd16d7437a64f6ec7a4cda8deaacdc9c62754
89fe2"
m~_16 = "3a9be520243abe976b50d5ad343692ac99e28d3d11e4e9a5cd458316d09
7ce36"
proof = "83ca9b4dc4a514497c22f78274a1d53414e5e5bc325f6c606386e033140416d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"
¶
Mocked RNG parameters for the signature:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_SIGNATURE_MOCK_RA
NDOM_SCALARS_DST_"
count = "1"
Mocked RNG parameters for the proof:
dst = "BBS_BLS12381G1_XMD:SHA-256_SSWU_RO_H2G_HM2S_PROOF_MOCK_RANDOM
_SCALARS_DST_"
count = "11"
message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a
45f02"
message_2 = "c344136d9ab02da4dd5908bbba913ae6f58c2cc844b802a6f811f5fb075
f9b80"
message_3 = "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
message_4 = "77fe97eb97a1ebe2e81e4e3597a3ee740a66e9ef2412472c"
message_5 = "496694774c5604ab1b2544eababcf0f53278ff50"
message_6 = "515ae153e22aae04ad16f759e07237b4"
message_7 = "d183ddc6e2665aa4e2f088af"
message_8 = "ac55fb33a75909ed"
message_9 = "96012096"
message_10 = ""
committed_message_1 = "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310
a1debdda4a45f02"
committed_message_2 = "089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debd
da4a45f02"
committed_message_3 = "7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f0
2"
committed_message_4 = "fac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
committed_message_5 = ""
commitment_with_proof = "null"
PK = "a820f230f6ae38503b86c70dc50b61c58a77e45c39ab25c0652bbaa8fa136f2851
bd4781c9dcde39fc9d1d52c9e60268061e7d7632171d91aa8d460acee0e96f1e7c
4cfb12d3ff9ab5d5dc91c277db75c845d649ef3c4f63aebc364cd55ded0c"
signature = "8c21175e0465339fd9b32aece83c43402b8b467baf3085028ecb5669e76
e093c0db878bfd4e6121b2b86260fd38f11ca37fc2f16f145ba600b240e
b96a40960f7aac7416f2390225e7166863db321b16"
header = "11223344556677889900aabbccddeeff"
ph = "bed231d880675ed101ead304512e043ade9958dd0241ea70b4b3957fba941501"
disclosed_indexes = "[ 0, 2, 4, 6, 8 ]"
disclosed_commitment_indexes = "null"
proverBlind = "null"
signerBlind = "null"
(disclosed_msgs, disclosed_idxs) = {
0: "9872ad089e452c7b6e283dfac2a80d58e8d0ff71cc4d5e310a1debdda4a45f02"
2: "7372e9daa5ed31e6cd5c825eac1b855e84476a1d94932aa348e07b73"
4: "496694774c5604ab1b2544eababcf0f53278ff50"
6: "d183ddc6e2665aa4e2f088af"
8: "96012096"
}
Proof trace:
T1 = "a554c36a5ee97c631ca428a68cec15146107beabafddeb466b7b6de310db0a
80c2ac11c7beb457029b4127b73281944c"
T2 = "a61f7dd16540060c811ac7d7586939e86cd1867c367d186e37b67f5b61be6c
d6fb3eac56bcf06f254399cf2a82d499a6"
domain = "160cf879138e86f8f6025c41ec94434432a315c33dc6b90c38f1b21ce1
01418c"
// random scalars
r1 = "034d543fdd164520876e558a77c102d4ad8bc99bf82ebe74590481473df2df
56"
r2 = "4a8334929ba48d36eb4ebc7f8bfa701b4d3f30ef25bc01e2a45ef9611c1603
7f"
e~ = "19726feed8e0e5ff22e4f5de19713977beceb12c3e85c1f3fb41cfe4a7237d
1a"
r1~ = "73012dc2f14039c8de5853b26baab7b51280a3f41425416d78a1a91fbaae9
bf2"
r3~ = "68263029bdc322a3d6460758135205dec58957ff3e5397276a2f0ffdc738d
5e4"
// m_tilde_scalars
m~_1 = "52638b8d190f9fd439188b22c903507cfe5282296c2c9f605f1ef714afc1
4062"
m~_2 = "2cbc33e381cf6ae09dbb6f1d08e3ea93a5aa03c4a6574fd2fa2e879dc4de
eca9"
m~_3 = "1ec36e6be1c702255d9aa4d590014b2b5de2f07d290c9551b66977cde157
094b"
m~_4 = "5491612228a993693c79c11ae169dad9be4116a704ae9ed333ef96e39863
73a0"
m~_5 = "6f4d920974d33c1e08c86b7f4b6bb7c58a5c0289d8d706a92d4855125cce
db70"
proof = "b52167f9cee8792582213798dc6909be7ac4a9084750b68d31abcc0c1231cc8
70e2b4c06e4799f2913d95fd2b84434a3b1392df3fe62719647cbf081f0677d
f748bf49a072551cfbee0a8d8772fb7b32208213ae3ba24c2ac8d2cc55aba99
b7cb5d7b5546131fa21e6fe6b6715b81532d18ecc63908ac25dc2fd3b4dd054
600ac6b2f82d05bef0e898d9b90f89df2aea62b346bbdeffe56401e3869fecf
66086f1a94b7d12d96737fbcc131aaafe0fdd602536c489001cc775398558e6
78e9f67c36233ced8c104d99f66a70cb4fd1f3524242535cef2ac8b4c357822
aca9c95284a7d825ece0a961b813b917312c0271b4d3ffa3244f0be87c8ec8d
dfa575c1dc23d25347f51d20b24b950a956ead3e3ee755d9171ff136d3e464c
acb53464acef7085aeee0c7556d576e4e81734d460a0905a0ef594d82f08d3d
1d791e3278ddb784653f3a5c3fb789470fdc3f768c56007aab7709a1b82fd3c
14c60778c15f662d30920dab48034fd703e70793a8204f34235f5fb7fe38959
b58e11a539beb9e1e6e16aad50d7a59d3c7ae33e30594995eebf1985ce95298
5b23287b454c89fc72b7a63829dc95fd2aa5bc68a146a"
¶
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