From: Erik Aronesty <erik@q32•com>
To: Gregory Maxwell <greg@xiph•org>
Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists•linuxfoundation.org>
Subject: Re: [bitcoin-dev] Multiparty signatures
Date: Mon, 9 Jul 2018 13:59:23 -0400 [thread overview]
Message-ID: <CAJowKgL0b3RT7XwRTF+ohoJCyZAW-ZJ+-8Lijj_s1rqqxgU7VQ@mail.gmail.com> (raw)
In-Reply-To: <CAAS2fgRrkzq6Fa5T_-YDwLDkwi30LpDtMObMEBE+Fmmj0LJpBw@mail.gmail.com>
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- Adaptive r choice shouldn't be possible since r is derived from the
original threshold prf and it's not possible for a party to have any
adaptive impact on the value of r
- I'm guess I don't see how an attacker can use adaptive key choice in
this context either. Any modification of the key should be useless
AH!
I forgot to include some assumptions. The important part here is that
each party only has a share of the private key and publishes a share of the
public key.
This hopefully should preclude any sort of adaptive key attack.
From scratch:
1. Has a public g^x'
2. Computes and broadcasts g^k' ... where k' is a random number
3. Computes r = g^k using lagrange interpolation (see
http://crypto.stanford.edu/~dabo/papers/homprf.pdf)
4. Computes H(r || M), as per standard schnorr
5. Computes s' = k' - xe , as per standard schnorr .. except k' is a "share"
6. Publish (s', e, g^x')
Verification:
With m of n share-signatures:
1. Interpolation on m of n s' shares to get s
2. Interpolation on m of n g^x' shares to get g^x
3. Standard schnorr verification
The actual public key of the "set of signers" is interpolated.
On Mon, Jul 9, 2018 at 12:58 PM, Gregory Maxwell <greg@xiph•org> wrote:
> On Mon, Jul 9, 2018 at 4:33 PM, Erik Aronesty <erik@q32•com> wrote:
> >>> with security assumptions that match the original Schnorr construction
> more closely,
> >> More closely than what?
> > More closely than musig.
>
> Musig is instructions on using the original schnorr construction for
> multiparty signing which is secure against participants adaptively
> choosing their keys, which is something the naive scheme of just
> interpolating keys and shares is vulnerable to. It works as
> preprocessing on the keys, then you continue on with the naive
> protocol. The verifier (e.g. network consensus rules) is the same.
>
> Now that you're back to using a cryptographic hash, I think what
> you're suggesting is "use naive interpolation of schnorr signatures"
> -- which you can do, including with the verifier proposed in the BIP,
> but doing that alone is insecure against adaptive key choice (and
> potentially adaptive R choice, depending on specifics which aren't
> clear enough to me in your description). In particular, although it
> seems surprising picking your interpolation locations with the hash of
> each key isn't sufficient to prevent cancellation attacks due to the
> remarkable power of wagner's algorithm.
>
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next prev parent reply other threads:[~2018-07-09 17:59 UTC|newest]
Thread overview: 26+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-07-08 14:19 Erik Aronesty
2018-07-08 15:16 ` Tim Ruffing
2018-07-08 18:23 ` Erik Aronesty
2018-07-08 21:01 ` Gregory Maxwell
2018-07-09 0:27 ` Erik Aronesty
2018-07-09 2:33 ` Pieter Wuille
2018-07-09 4:29 ` Erik Aronesty
2018-07-09 4:39 ` Pieter Wuille
[not found] ` <CAJowKg+=7nS4gNmtc8a4-2cu1uCOPqxjfchFwDVqUciKNMUYWQ@mail.gmail.com>
2018-07-09 15:02 ` Erik Aronesty
2018-07-09 15:57 ` Dan Robinson
2018-07-09 15:59 ` Gregory Maxwell
2018-07-09 16:33 ` Erik Aronesty
2018-07-09 16:58 ` Gregory Maxwell
2018-07-09 17:59 ` Erik Aronesty [this message]
2018-07-10 11:46 ` Erik Aronesty
2018-07-11 10:35 ` Adam Back
2018-07-11 14:45 ` Erik Aronesty
2018-07-19 12:16 ` Erik Aronesty
2018-07-19 12:24 ` Erik Aronesty
2018-07-19 13:11 ` Russell O'Connor
2018-07-20 16:25 ` Erik Aronesty
2018-07-20 17:34 ` Erik Aronesty
2018-07-20 20:18 ` Erik Aronesty
2018-07-26 2:05 ` Erik Aronesty
2018-07-09 16:21 ` Gregory Maxwell
2018-07-09 2:29 ` Pieter Wuille
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