[bitcoin-dev] BIP 340 updates: even pubkeys, more secure nonce generation

[Lloyd Fournier]

Hi Pieter,

Let me put change (1) into my own words. We are already computing affine
coordinates since we store public keys as the affine x-coordinate. It is
faster to compute is_even(y) than is_quadratic_residue(y) so we get a speed
up here during keypair generation. In the verification algorithm, we do the
following for the public key  x_only => affine + negate if not is_even(y)
=> jacobian. The minor slowdown in verification comes from the extra
evenness check and possible negation which we didn't have to be done in the
previous version. This seems like a reasonable change if it makes things
easier for existing code bases and infrastructure.

With change (2), I feel like including this auxiliary random data is
overkill for the spec. For me, the main point of the spec is the
verification algorithm which actually affects consensus. Providing a note
that non-deterministic signatures are preferable in many cases and here's
exactly how you should do that (hash then xor with private key) is
valuable. In the end, people will want several variations of the signing
algorithm anyway (e.g. pass in public key with secret key) so I think
specifying the most minimal way to produce a signature securely is the most
useful thing for this document.

I feel similarly about hashing the public key to get the nonce. A note in
the alternative signing section that "if you pass the public key into
`sign` along with the secret key then you should do hash(bytes(d) ||
bytes(P) || m)" would suffice for me.

Despite only being included in the alternative signing section, I it would
be nice to have a few of test vectors for these alternative methods anyway.
Perhaps they even deserve their own BIP?

Cheers,

LL


On Mon, Feb 24, 2020 at 3:26 PM Pieter Wuille via bitcoin-dev <
bitcoin-dev at lists.linuxfoundation.org> wrote:

> Hello list,
>
> Despite saying earlier that I expected no further semantical changes
> to BIP 340-342, I've just opened
> https://github.com/bitcoin/bips/pull/893 to make a number of small
> changes that I believe are still worth making.
>
> 1. Even public keys
>
> Only one change affects the validation rules: the Y coordinate of
> 32-byte public keys is changed from implicitly square to implicitly
> even. This makes signing slightly faster (in the microsecond range),
> though also verification negligibly slower (in the nanosecond range).
> It also simplifies integration with existing key generation
> infrastructure. For example BIP32 produces public keys with known
> even/oddness, but squaredness would need to be computed separately.
> Similar arguments hold for PSBT and probably many other things.
>
> Note that the Y coordinate of the internal R point in the signature
> remains implicitly square: for R the squaredness gives an actual
> performance gain at validation time, but this is not true for public
> keys. Conversely, for public keys integration with existing
> infrastructure matters, but R points are purely internal.
>
> This affects BIP 340 and 341.
>
> 2. Nonce generation
>
> All other semantical changes are around more secure nonce generation
> in BIP 340, dealing with various failure cases:
>
> * Since the public key signed for is included in the signature
> challenge hash, implementers will likely be eager to use precomputed
> values for these (otherwise an additional EC multiplication is
> necessary at signing time). If that public key data happens to be
> gathered from untrusted sources, it can lead to trivial leakage of the
> private key - something that Greg Maxwell started a discussion about
> on the moderncrypto curves list:
> https://moderncrypto.org/mail-archive/curves/2020/001012.html. We
> believe it should therefore be best practice to include the public key
> also in the nonce generation, which largely mitigates this problem.
>
> * To protect against fault injection attacks it is recommended to
> include actual signing-time randomness into the nonce generation
> process. This was mentioned already, but the update elaborates much
> more about this, and integrates this randomness into the standard
> signing process.
>
> * To protect against differential power analysis, a different way of
> mixing in this randomness is used (masking the private key completely
> with randomness before continuing, rather than hashing them together,
> which is known in the literature to be vulnerable to DPA in some
> scenarios).
>
> 3. New tagged hash tags
>
> To make sure that any code written for the earlier BIP text fails
> consistently, the tags used in the tagged hashes in BIP 340 are
> changed as well.
>
> What do people think?
>
> --
> Pieter
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> bitcoin-dev at lists.linuxfoundation.org
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>
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