David Benjamin 76e98c4351 Always end BN_mod_exp_mont_consttime with normal Montgomery reduction.
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>
2023-09-15 17:01:39 -07:00
2023-09-03 15:32:26 -07:00
2022-11-03 10:30:09 -07:00
2020-11-05 15:43:17 -08:00
2023-09-03 16:03:25 -07:00
2022-10-19 23:49:17 -07:00
2023-09-03 13:49:57 -07:00
2019-04-10 09:33:38 -10:00
2023-09-03 13:49:57 -07:00

THE SOFTWARE IS PROVIDED "AS IS" AND BRIAN SMITH AND THE AUTHORS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL BRIAN SMITH OR THE AUTHORS BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

ring

ring is focused on the implementation, testing, and optimization of a core set of cryptographic operations exposed via an easy-to-use (and hard-to-misuse) API. ring exposes a Rust API and is written in a hybrid of Rust, C, and assembly language.

Particular attention is being paid to making it easy to build and integrate ring into applications and higher-level frameworks, and to ensuring that ring works optimally on small devices, and eventually microcontrollers, to support Internet of Things (IoT) applications.

Most of the C and assembly language code in ring comes from BoringSSL, and BoringSSL is derived from OpenSSL. ring merges changes from BoringSSL regularly. Also, several changes that were developed for ring have been contributed to and integrated into BoringSSL.

Documentation

See the documentation at https://docs.rs/ring/latest/ring/.

See BUILDING.md for instructions on how to build it. These instructions are especially important for cross-compiling and for building on Windows when not building from crates.io, as there are build prerequisites that need to be installed.

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ring's benchmarks are located in the benches folder of this repository. Because there is lots of platform-specific code in ring, and because ring chooses dynamically at runtime which optimized implementation of each crypto primitive to use, it is very difficult to publish a useful single set of benchmarks; instead, you are highly encouraged to run the benchmarks yourselves on your target hardware.

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