Subject: Million Message Attack draft

From: Eric Rescorla <[email-masked]>
Date: Sat, 17 Mar 2001 21:07:52 -0800

Now that RSA is once again going to be a (the?) mandatory CMS
cipher, there's been some concern about whether it was possible
to mount a Million Message attack on CMS. The following draft
describes the situation and the appropriate countermeasures
(if any). 
 
I'll be submitting this as an I-D but I wanted to get it out before
Minneapolis (barely).

-Ekr

INTERNET-DRAFT                                               E. Rescorla
<draft-ietf-smime-pkcs1-01.txt>                              RTFM, Inc.
                                    (March 2000 (Expires September 2001)

              Preventing the Million Message Attack on CMS

Status of this Memo

   This document is an Internet-Draft and is in full conformance with
   all provisions of Section 10 of RFC2026.  Internet-Drafts are working
   documents of the Internet Engineering Task Force (IETF), its areas,
   and its working groups.  Note that other groups may also distribute
   working documents as Internet-Drafts.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference mate-
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   ftp.isi.edu (US West Coast).

1.  Introduction

   When data is encrypted using RSA it must be padded out to the length
   of the modulus--typically 512 to 2048 bits.  he most popular tech-
   nique for doing this is described in [PKCS-1]. However, in 1998 Ble-
   ichenbacher described an adaptive chosen ciphertext attack on SSL
   [MMA]. This attack, called the Million Message Attack, allowed the
   recovery of a single PKCS-1 encrypted block, provided that the
   attacker could convince the receiver to act as a particular kind of
   oracle. The MMA is also possible against [CMS]. The CMS implementa-
   tions most likely to be targets for the MMA are automated servers
   such as mailing list agents, which will automatically respond to a
   large number of messages. This document describes a strategy for
   resisting such attacks.

2.  Overview of PKCS-1

   The first stage in RSA encryption is to map the message to be
   encrypted (in CMS a symmetric Content Encryption Key (CEK)) into an
   integer of the same order as (but less than) the RSA modulus of the
   recipient's public key (typically somewhere between 512 and 2048
   bits). PKCS-1 describes the most common procedure for this transfor-
   mation.

Rescorla                                                         [Page 1]Internet-Draft     Security Considerations Guidelines     

   We start with an "encryption block" of the same length as the modu-
   lus. The rightmost bits of the string are set to the message to be
   encrypted.  The first two bytes are a zero byte and a "block type"
   byte. For encryption the block type is 2. The remaining bytes are
   used as padding. The padding is constructed by generating a series of
   non-zero random bytes. The last padding byte is zero, which allows
   the padding to be distinguished from the message.

     |--------------------------------------------------------|
     | 0 | 2 | Nonzero random bytes | 0 |      Message        |
     |--------------------------------------------------------|

   Once the block has been formatted, the sender must then convert the
   block into an integer. This is done by treating the block as an inte-
   ger in big-endian form. Thus, the resulting number is less than the
   modulus (because the first byte is zero), but of more or less the
   same order (because the second byte is 2).

   In CMS, the message is always a randomly generated symmetric content
   encryption key (CEK). Depending on the cipher being used it might be
   anywhere from 64 to 256 bytes.

   There must be at least 8 bytes of non-random. The padding prevents an
   attacker from verifying guesses about the encrypted message.  Imagine
   that the attacker wishes to determine whether or not two RSA-
   encrypted keys are the same. Because there are at least 2^64 differ-
   ent padding value with high probability two encryptions of the same
   message will be different. The padding also prevents the attacker
   from verifying guessed CEKs by trial-encrypting them with the recipi-
   ent's RSA key since he must try each potential pad for every guess.
   Note that a lower cost attack would be to exhaustively search the CEK
   space by trial-decrypting the content and examining the plaintext to
   see if it appears reasonable.

2.1.  The Million Message Attack

   The purpose of the Million Message Attack (MMA) is to recover a sin-
   gle plaintext given the ciphertext. The attacker first captures the
   ciphertext in transit and then uses the recipient as an oracle to
   recover the plaintext by sending transformed versions of the cipher-
   text and observing the recipient's response.

   Call the ciphertext C. The attacker then generates a series of inte-
   gers S and computes C'=C(S^e) mod n. Upon decryption, C' produces a
   corresponding plaintext M'. Most M's will appear to be garbage but
   some M's (about one in 2^16) will have the correct first two bytes 00
   02 and thus appear to be correctly PKCS-1 formatted. The attack pro-
   ceeds by finding a sequence of values S such that the resulting M' is

Rescorla                                                         [Page 2]Internet-Draft     Security Considerations Guidelines     

   correctly PKCS-1 formatted. This information can be used to discover
   M. Operationally, this attack usually requires about 2^20 messages
   and responses. Details can be found in [MMA].

2.2.  Applicability

   Since the MMA requires so many messages, it must be mounted against a
   victim who is willing to process a large number of messages. In prac-
   tice, no human is willing to read this many messages and so the MMA
   can only be mounted against an automated victim.

   The MMA also requires that the attacker be able to distinguish cases
   where M' was PKCS-1 formatted from cases where it was not.  In the
   case of CMS the attacker will be sending CMS messages with M' replac-
   ing the wrapped CEK. Thus, there are five possibilities:

   1. M' is improperly formatted.
   2. M' is properly formatted but the CEK is prima facie bogus
   (wrong length, etc.)
   3. M' is properly formatted and the CEK appears OK. A signature
   or MAC is present so integrity checking fails.
   4. M' is properly formatted and no integrity check is applied.
   In this case there is some possibility (approximately 1/8) that
   the CBC padding block will verify correctly. The message will
   appear OK at the CMS level but will be bogus at the application
   level.
   5. M' is properly formatted and the resulting CEK is correct.
   This is extremely improbable but not impossible.

   The MMA requires the attacker to be able to distinguish case 1 from
   cases 2-4. (He can always distinguish case 5, of course). This might
   happen if the victim returned different errors for each case. The
   attacker might also be able to distinguish these cases based on tim-
   ing--decrypting the message and verifying the signature takes some
   time.  If the victim responds uniformly to all four errors then no
   attack is possible.

2.3.  Countermeasures

2.3.1.  Careful Checking

   Even without countermeasures, sufficiently careful checking can go
   quite a long way to mitigating the success of the MMA.  If the
   receiving implementation also checks the length of the CEK and the
   parity bits (if available) AND responds identically to all such
   errors, the chances of a given M' being correctly formatted are sub-
   stantially decreased. This increases the number of probe messages

Rescorla                                                         [Page 3]Internet-Draft     Security Considerations Guidelines     

   required to recover M. However, this sort of checking only increases
   the workfactor and does not eliminate the attack entirely because
   some messages will still be correctly formatted up to the point of
   keylength. However, the combination of all three kinds of checking
   (padding, length, parity bits) increases the number of messages to
   the point where the attack is impractical.

2.3.2.  Random Filling

   The simplest countermeasure is to treat misformatted messages as if
   they were correctly PKCS-1 formatted. When the victim detects an
   incorrectly formatted message, instead of returning an error he sub-
   stitutes a randomly generated message. In CMS, since the message is
   always a wrapped content encryption key (CEK) the victm should simply
   substitute a randomly generated CEK of appropriate length and con-
   tinue. Eventually this will result in a decryption or signature veri-
   fication error but this is exactly what would have happened if M'
   happened to be correctly formatted. Note that the timing behavior
   will also identical.

   In a layered implementation it's quite possible that the PKCS-1 check
   occurs at a point in the code where the length of the expected CEK is
   not known. In that case the implementation must ensure that bad
   PKCS-1 padding and ok-looking PKCS-1 padding with an incorrect length
   CEK behave the same. An easy way to do this is to also randomize CEKs
   that are of the wrong length or otherwise improperly formatted.

   Note: It is a mistake to use a fixed CEK because the attacker could
   then produce a CMS message encrypted with that CEK. This message
   would decrypt correctly, thus allowing the attacker to determine that
   the PKCS-1 formatting was incorrect.  In fact, the randomly generated
   CEK should be cryptographically random, thus preventing the attacker
   from guessing the next "random" CEK to be used.

2.3.3.  OAEP

   Optimal Asymmetric Encryption Padding (OAEP) [OAEP, PKCS1v2] is
   another technique for padding a message into an RSA encryption block.
   Implementations using OAEP are not susceptible to the MMA. However,
   OAEP is incompatible with PKCS-1. Implementations of S/MIME and CMS
   must therefore continue to use PKCS-1 for the foreseable future.

2.4.  Security Considerations

   This entire document describes how to avoid a certain class of
   attacks when performing PKCS-1 decryption with RSA.

Rescorla                                                         [Page 4]Internet-Draft     Security Considerations Guidelines     

References
   [PKCS-1]
   [MMA]
   [CMS]

Author's Address
Eric Rescorla <[email-masked]>
RTFM, Inc.
2439 Alvin Drive
Mountain View, CA 94043
Phone: (650) 314-0116

Rescorla                                                         [Page 5]Internet-Draft     Security Considerations Guidelines     

                           Table of Contents

1. Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . .   1
2. Overview of PKCS-1  . . . . . . . . . . . . . . . . . . . . . . .   1
2.1. The Million Message Attack  . . . . . . . . . . . . . . . . . .   2
2.2. Applicability . . . . . . . . . . . . . . . . . . . . . . . . .   3
2.3. Countermeasures . . . . . . . . . . . . . . . . . . . . . . . .   3
2.3.1. Careful Checking  . . . . . . . . . . . . . . . . . . . . . .   3
2.3.2. Random Filling  . . . . . . . . . . . . . . . . . . . . . . .   4
2.3.3. OAEP  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
2.4. Security Considerations . . . . . . . . . . . . . . . . . . . .   4
2.4. References  . . . . . . . . . . . . . . . . . . . . . . . . . .   5
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . .   5