Subject: [Cfrg] ECDSA_CFRG theorems: quick summary

From: Dan Brown <[email-masked]>
Date: Wed, 22 Jul 2015 15:00:02 +0000

Hi CFRG,

Kenny asked me today (I think paraphrasing DJB) to support the security
claims for ECDSA_CFRG in my presentation.  

Some of these security claims were presented as formal theorems.  

As a preliminary step, I'll briefly touch on some of these, with plans to
further elaborate later.

1.      The theorems with dates earlier than 2015 are from my existing
publications with that date.  

2.      The theorems with other people's names belong to other people.  

3.      The 2015 theorem on Slides 8 is relatively obvious.

4.      The 2015 theorems on Slide 9  support deletion-resistance, are
security claims for Schnorr signatures, including EdDSA variants.

5.      The first 2015 theorem on Slide 24 is informally proved in my
original ECDSA proposal.  It follows by virtue of the fact that an
ECDSA_CFRG signature can be converted into an ECDSA signature (allowing for
a curve and hash adjustment).  It concerns signer-absent forgery, so all one
needs is verifiers.

6.      The second 2015 theorem on Slide 24 regards a rather contrived
construction, which I will discuss in a separate email.

Best regards,

Daniel Brown

Research In Motion Limited