• David Leon Gil's avatar
    crypto/ecdsa: make Sign safe with broken entropy sources · a8049f58
    David Leon Gil authored
    ECDSA is unsafe to use if an entropy source produces predictable
    output for the ephemeral nonces. E.g., [Nguyen]. A simple
    countermeasure is to hash the secret key, the message, and
    entropy together to seed a CSPRNG, from which the ephemeral key
    is derived.
    
    Fixes #9452
    
    --
    
    This is a minimalist (in terms of patch size) solution, though
    not the most parsimonious in its use of primitives:
    
       - csprng_key = ChopMD-256(SHA2-512(priv.D||entropy||hash))
       - reader = AES-256-CTR(k=csprng_key)
    
    This, however, provides at most 128-bit collision-resistance,
    so that Adv will have a term related to the number of messages
    signed that is significantly worse than plain ECDSA. This does
    not seem to be of any practical importance.
    
    ChopMD-256(SHA2-512(x)) is used, rather than SHA2-256(x), for
    two sets of reasons:
    
    *Practical:* SHA2-512 has a larger state and 16 more rounds; it
    is likely non-generically stronger than SHA2-256. And, AFAIK,
    cryptanalysis backs this up. (E.g., [Biryukov] gives a
    distinguisher on 47-round SHA2-256 with cost < 2^85.) This is
    well below a reasonable security-strength target.
    
    *Theoretical:* [Coron] and [Chang] show that Chop-MD(F(x)) is
    indifferentiable from a random oracle for slightly beyond the
    birthday barrier. It seems likely that this makes a generic
    security proof that this construction remains UF-CMA is
    possible in the indifferentiability framework.
    
    --
    
    Many thanks to Payman Mohassel for reviewing this construction;
    any mistakes are mine, however. And, as he notes, reusing the
    private key in this way means that the generic-group (non-RO)
    proof of ECDSA's security given in [Brown] no longer directly
    applies.
    
    --
    
    [Brown]: http://www.cacr.math.uwaterloo.ca/techreports/2000/corr2000-54.ps
    "Brown. The exact security of ECDSA. 2000"
    
    [Coron]: https://www.cs.nyu.edu/~puniya/papers/merkle.pdf
    "Coron et al. Merkle-Damgard revisited. 2005"
    
    [Chang]: https://www.iacr.org/archive/fse2008/50860436/50860436.pdf
    "Chang and Nandi. Improved indifferentiability security analysis
    of chopMD hash function. 2008"
    
    [Biryukov]: http://www.iacr.org/archive/asiacrypt2011/70730269/70730269.pdf
    "Biryukov et al. Second-order differential collisions for reduced
    SHA-256. 2011"
    
    [Nguyen]: ftp://ftp.di.ens.fr/pub/users/pnguyen/PubECDSA.ps
    "Nguyen and Shparlinski. The insecurity of the elliptic curve
    digital signature algorithm with partially known nonces. 2003"
    
    New tests:
    
      TestNonceSafety: Check that signatures are safe even with a
        broken entropy source.
    
      TestINDCCA: Check that signatures remain non-deterministic
        with a functional entropy source.
    
    Updated "golden" KATs in crypto/tls/testdata that use ECDSA suites.
    
    Change-Id: I55337a2fbec2e42a36ce719bd2184793682d678a
    Reviewed-on: https://go-review.googlesource.com/3340Reviewed-by: 's avatarAdam Langley <agl@golang.org>
    a8049f58
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