Subject: Re: [Bitcoin-development] The relationship between Proof-of-Publication and Anti-Replay Oracles

From: Adam Back <[email-masked]>
Date: Sun, 21 Dec 2014 10:01:37 +0000

On 20 December 2014 at 14:48, Peter Todd <[email-masked]> wrote:
> We need the following primitives operating on message m, pubkey p, and a
> valid signature sig1 for m, p:
>
>     AntiReplaySign(m, p, sig1) -> sig2
>     VerifyAntiReplaySig(m, p, sig2) -> True or False
>
> Additionally once AntiReplaySign() has been used once for a given pubkey
> it is impossible to re-run the primitive on a different message m'. This
> is of course impossible to implement with math alone, but we can
> implement it with a trusted third party.

Well while you cant prevent it you could render it insecure enabling
miners to take funds.

That could work via a one-show signature; normal ECDSA being address
a=H(Q), public key Q=dG, R=kG, r=R.x, s=(H(m)+rd)/k, signature (r,s),
verify: a=?H(Q) and sR=?H(m)G+rQ one-show being: a=H(Q,R), verify
being: a=?H(Q,R) and sR=?H(m)G+rQ.  Now that is unsafe to double-spend
by design as only that specific R is usable and as we know reusing R
with different messages leaks the private key because: s=(H(m)+rd)/k
and s'=(H(m')+rd)/k implies sk=H(m)+rd and s'k=H(m')+rd so
k=(H(m)-H(m'))/(s'-s), and d=(sk-H(m))/r.

Adam