Subject: Re: [bitcoindev] Re: DahLIAS: Discrete Logarithm-Based Interactive Aggregate Signatures

From: Jonas Nick <[email-masked]>
Date: Wed, 30 Apr 2025 07:59:15 +0000

Thanks for your comments.

 > That side note reminds me of my first question: would it not be appropriate
 > to include a proof of the zero knowledgeness property of the scheme, and
 > not only the soundness? I can kind of accept the answer "it's trivial"
 > based on the structure of the partial sig components (s_k = r_k1 + br_k2 +
 > c_k x_k) being "identical" to baseline Schnorr?

That partial signatures do not leak information about the secret key x_k is
implied by the security theorem for DahLIAS: If information would leak, the
adversary could use that to win the unforgeability game. However, the adversary
doesn't win the game unless the adversary solves the DL problem or finds a
collision in hash function Hnon.

 > The side note also raises this point: would it be a good idea to explicitly
 > write down ways in which the usage of the scheme/structure can, and cannot,
 > be optimised for the single-party case?

This is a very interesting point, probably out of scope for the paper. A
single-party signer, given secret keys xi, ..., xn for public keys X1, ..., Xn
can draw r at random, compute R := r*G and then set s := r + c1*x1 + ... +
cn*xn. So this would only require a single group multiplication.

 > On that last point about "proof of knowledge of R", I suddenly realised
 > it's not a viable suggestion: of course it defends against key subtraction
 > attacks, but does not defend at all against the ability to grind nonces
 > adversarially in a Wagner type attack

We believe Appendix B provides a helpful characterization of "Wagner-style"
vulnerabilities. Roughly speaking, it shows that schemes where the adversary can
ask the signer to produce a partial signature s = r + c*x or s' = r + c'*x such
that c != c' then the scheme is vulnerable. In your "proof of knowledge of R
idea", the adversary can choose to provide either R2 or R2' in a signing
request, which would result in the same "effective nonce" r being used be the
signer but different challenges c and c'.

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