This partially fixes a bug where, on x86_64, BN_mod_exp_mont_consttime would sometimes return m, the modulus, when it should have returned zero. Thanks to Guido Vranken for reporting it. It is only a partial fix because the same bug also exists in the "rsaz" codepath. That will be fixed in the subsequent CL. (See the commented out test.) The bug only affects zero outputs (with non-zero inputs), so we believe it has no security impact on our cryptographic functions. BoringSSL calls BN_mod_exp_mont_consttime in the following cases: - RSA private key operations - Primality testing, raising the witness to the odd part of p-1 - DSA keygen and key import, pub = g^priv (mod p) - DSA signing, r = g^k (mod p) - DH keygen, pub = g^priv (mod p) - Diffie-Hellman, secret = peer^priv (mod p) It is not possible in the RSA private key operation, provided p and q are primes. If using CRT, we are working modulo a prime, so zero output with non-zero input is impossible. If not using CRT, we work mod n. While there are nilpotent values mod n, none of them hit zero by exponentiating. (Both p and q would need to divide the input, which means n divides the input.) In primality testing, this can only be hit when the input was composite. But as the rest of the loop cannot then hit 1, we'll correctly report it as composite anyway. DSA and DH work modulo a prime, where this case cannot happen. Analysis: This bug is the result of sloppiness with the looser bounds from "almost Montgomery multiplication", described in https://eprint.iacr.org/2011/239. Prior to upstream's ec9cc70f72454b8d4a84247c86159613cee83b81, I believe x86_64-mont5.pl implemented standard Montgomery reduction (the left half of figure 3 in the paper). Though it did not document this, ec9cc70f7245 changed it to implement the "almost" variant (the right half of the figure.) The difference is that, rather than subtracting if T >= m, it subtracts if T >= R. In code, it is the difference between something like our bn_reduce_once, vs. subtracting based only on T's carry bit. (Interestingly, the .Lmul_enter branch of bn_mul_mont_gather5 seems to still implement normal reduction, but the .Lmul4x_enter branch is an almost reduction.) That means none of the intermediate values here are bounded by m. They are only bounded by R. Accordingly, Figure 2 in the paper ends with step 10: REDUCE h modulo m. BN_mod_exp_mont_consttime is missing this step. The bn_from_montgomery call only implements step 9, AMM(h, 1). (x86_64-mont5.pl's bn_from_montgomery only implements an almost reduction.) The impact depends on how unreduced AMM(h, 1) can be. Remark 1 of the paper discusses this, but is ambiguous about the scope of its 2^(n-1) < m < 2^n precondition. The m+1 bound appears to be unconditional: Montgomery reduction ultimately adds some 0 <= Y < m*R to T, to get a multiple of R, and then divides by R. The output, pre-subtraction, is thus less than m + T/R. MM works because T < mR => T' < m + mR/R = 2m. A single subtraction of m if T' >= m gives T'' < m. AMM works because T < R^2 => T' < m + R^2/R = m + R. A single subtraction of m if T' >= R gives T'' < R. See also Lemma 1, Section 3 and Section 4 of the paper, though their formulation is more complicated to capture the word-by-word algorithm. It's ultimately the same adjustment to T. But in AMM(h, 1), T = h*1 = h < R, so AMM(h, 1) < m + R/R = m + 1. That is, AMM(h, 1) <= m. So the only case when AMM(h, 1) isn't fully reduced is if it outputs m. Thus, our limited impact. Indeed, Remark 1 mentions step 10 isn't necessary because m is a prime and the inputs are non-zero. But that doesn't apply here because BN_mod_exp_mont_consttime may be called elsewhere. Fix: To fix this, we could add the missing step 10, but a full division would not be constant-time. The analysis above says it could be a single subtraction, bn_reduce_once, but then we could integrate it into the subtraction already in plain Montgomery reduction, implemented by uppercase BN_from_montgomery. h*1 = h < R <= m*R, so we are within bounds. Thus, we delete lowercase bn_from_montgomery altogether, and have the mont5 path use the same BN_from_montgomery ending as the non-mont5 path. This only impacts the final step of the whole exponentiation and has no measurable perf impact. In doing so, add comments describing these looser bounds. This includes one subtlety that BN_mod_exp_mont_consttime actually mixes bn_mul_mont (MM) with bn_mul_mont_gather5/bn_power5 (AMM). But this is fine because MM is AMM-compatible; when passed AMM's looser inputs, it will still produce a correct looser output. Ideally we'd drop the "almost" reduction and stick to the more straightforward bounds. As this only impacts the final subtraction in each reduction, I would be surprised if it actually had a real performance impact. But this would involve deeper change to x86_64-mont5.pl, so I haven't tried this yet. I believe this is basically the same bug as https://github.com/golang/go/issues/13907 from Go. Change-Id: I06f879777bb2ef181e9da7632ec858582e2afa38 Reviewed-on: https://boringssl-review.googlesource.com/c/boringssl/+/52825 Commit-Queue: David Benjamin <davidben@google.com> Reviewed-by: Adam Langley <agl@google.com>chromium-5359
David Benjamin
3 years ago
committed by
Boringssl LUCI CQ
parent
a8b1633d1c
commit
13c9d5c69d
5 changed files with 126 additions and 243 deletions
Loading…
Reference in new issue