This uses the full binary GCD algorithm, where all four of A, B, C, and
D must be retained. (BN_mod_inverse_odd implements the odd number
version which only needs A and C.) It is patterned after the version
in the Handbook of Applied Cryptography, but tweaked so the coefficients
are non-negative and bounded.
Median of 29 RSA keygens: 0m0.225s -> 0m0.220s
(Accuracy beyond 0.1s is questionable.)
Bug: 238
Change-Id: I6dc13524ea7c8ac1072592857880ddf141d87526
Reviewed-on: https://boringssl-review.googlesource.com/26370
Reviewed-by: Adam Langley <alangley@gmail.com>
RSA key generation requires computing a GCD (p-1 and q-1 are relatively
prime with e) and an LCM (the Carmichael totient). I haven't made BN_gcd
itself constant-time here to save having to implement
bn_lshift_secret_shift, since the two necessary operations can be served
by bn_rshift_secret_shift, already added for Rabin-Miller. However, the
guts of BN_gcd are replaced. Otherwise, the new functions are only
connected to tests for now, they'll be used in subsequent CLs.
To support LCM, there is also now a constant-time division function.
This does not replace BN_div because bn_div_consttime is some 40x slower
than BN_div. That penalty is fine for RSA keygen because that operation
is not bottlenecked on division, so we prefer simplicity over
performance.
Median of 29 RSA keygens: 0m0.212s -> 0m0.225s
(Accuracy beyond 0.1s is questionable.)
Bug: 238
Change-Id: Idbfbfa6e7f5a3b8782ce227fa130417b3702cf97
Reviewed-on: https://boringssl-review.googlesource.com/26369
Reviewed-by: Adam Langley <alangley@gmail.com>
Expose the constant-time abs_sub functions from the fixed Karatsuba code
in BIGNUM form for RSA to call into. RSA key generation involves
checking if |p - q| is above some lower bound.
BN_sub internally branches on which of p or q is bigger. For any given
iteration, this is not secret---one of p or q is necessarily the larger,
and whether we happened to pick the larger or smaller first is
irrelevant. Accordingly, there is no need to perform the p/q swap at the
end in constant-time.
However, this stage of the algorithm picks p first, sticks with it, and
then computes |p - q| for various q candidates. The distribution of
comparisons leaks information about p. The leak is unlikely to be
problematic, but plug it anyway.
Median of 29 RSA keygens: 0m0.210s -> 0m0.212s
(Accuracy beyond 0.1s is questionable.)
Bug: 238
Change-Id: I024b4e51b364f5ca2bcb419a0393e7be13249aec
Reviewed-on: https://boringssl-review.googlesource.com/26368
Reviewed-by: Adam Langley <alangley@gmail.com>
RSA key generation currently does the GCD check before the primality
test, in hopes of discarding things invalid by other means before
running the expensive primality check.
However, GCD is about to get a bit more expensive to clear the timing
leak, and the trial division part of primality testing is quite fast.
Thus, split that portion out via a new bn_is_obviously_composite and
call it before GCD.
Median of 29 RSA keygens: 0m0.252s -> 0m0.207s
(Accuracy beyond 0.1s is questionable.)
Bug: 238
Change-Id: I3999771fb73cca16797cab9332d14c4ebeb02046
Reviewed-on: https://boringssl-review.googlesource.com/26366
Reviewed-by: Adam Langley <alangley@gmail.com>
I'm not sure why I separated "fixed" and "quick_ctx" names. That's
annoying and doesn't generalize well to, say, adding a bn_div_consttime
function for RSA keygen.
Change-Id: I751d52b30e079de2f0d37a952de380fbf2c1e6b7
Reviewed-on: https://boringssl-review.googlesource.com/26364
Commit-Queue: David Benjamin <davidben@google.com>
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Rabin-Miller requires selecting a random number from 2 to |w|-1.
This is done by picking an N-bit number and discarding out-of-range
values. This leaks information about |w|, so apply blinding. Rather than
discard bad values, adjust them to be in range.
Though not uniformly selected, these adjusted values
are still usable as Rabin-Miller checks.
Rabin-Miller is already probabilistic, so we could reach the desired
confidence levels by just suitably increasing the iteration count.
However, to align with FIPS 186-4, we use a more pessimal analysis: we
do not count the non-uniform values towards the iteration count. As a
result, this function is more complex and has more timing risk than
necessary.
We count both total iterations and uniform ones and iterate until we've
reached at least |BN_PRIME_CHECKS_BLINDED| and |iterations|,
respectively. If the latter is large enough, it will be the limiting
factor with high probability and we won't leak information.
Note this blinding does not impact most calls when picking primes
because composites are rejected early. Only the two secret primes see
extra work. So while this does make the BNTest.PrimeChecking test take
about 2x longer to run on debug mode, RSA key generation time is fine.
Another, perhaps simpler, option here would have to run
bn_rand_range_words to the full 100 count, select an arbitrary
successful try, and declare failure of the entire keygen process (as we
do already) if all tries failed. I went with the option in this CL
because I happened to come up with it first, and because the failure
probability decreases much faster. Additionally, the option in this CL
does not affect composite numbers, while the alternate would. This gives
a smaller multiplier on our entropy draw. We also continue to use the
"wasted" work for stronger assurance on primality. FIPS' numbers are
remarkably low, considering the increase has negligible cost.
Thanks to Nathan Benjamin for helping me explore the failure rate as the
target count and blinding count change.
Now we're down to the rest of RSA keygen, which will require all the
operations we've traditionally just avoided in constant-time code!
Median of 29 RSA keygens: 0m0.169s -> 0m0.298s
(Accuracy beyond 0.1s is questionable. The runs at subsequent test- and
rename-only CLs were 0m0.217s, 0m0.245s, 0m0.244s, 0m0.247s.)
Bug: 238
Change-Id: Id6406c3020f2585b86946eb17df64ac42f30ebab
Reviewed-on: https://boringssl-review.googlesource.com/25890
Commit-Queue: Adam Langley <agl@google.com>
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(This is actually slightly silly as |a|'s probability distribution falls
off exponentially, but it's easy enough to do right.)
Instead, we run the loop to the end. This is still performant because we
can, as before, return early on composite numbers. Only two calls
actually run to the end. Moreover, running to the end has comparable
cost to BN_mod_exp_mont_consttime.
Median time goes from 0.140s to 0.231s. That cost some, but we're still
faster than the original implementation.
We're down to one more leak, which is that the BN_rand_range_ex call
does not hide |w1|. That one may only be solved probabilistically...
Median of 29 RSA keygens: 0m0.123s -> 0m0.145s
(Accuracy beyond 0.1s is questionable.)
Bug: 238
Change-Id: I4847cb0053118c572d2dd5f855388b5199fa6ce2
Reviewed-on: https://boringssl-review.googlesource.com/25888
Reviewed-by: Adam Langley <agl@google.com>
Compilers use a variant of Barrett reduction to divide by constants,
which conveniently also avoids problematic operations on the secret
numerator. Implement the variant as described here:
http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html
Repurpose this to implement a constant-time BN_mod_word replacement.
It's even much faster! I've gone ahead and replaced the other
BN_mod_word calls on the primes table.
That should give plenty of budget for the other changes. (I am assuming
that a regression is okay, as RSA keygen is not performance-sensitive,
but that I should avoid anything too dramatic.)
Proof of correctness: https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v
Median of 29 RSA keygens: 0m0.621s -> 0m0.123s
(Accuracy beyond 0.1s is questionable, though this particular
improvement is quite solid.)
Bug: 238
Change-Id: I67fa36ffe522365b13feb503c687b20d91e72932
Reviewed-on: https://boringssl-review.googlesource.com/25887
Reviewed-by: Adam Langley <agl@google.com>
The extra details in Enhanced Rabin-Miller are only used in
RSA_check_key_fips, on the public RSA modulus, which the static linker
will drop in most of our consumers anyway. Implement normal Rabin-Miller
for RSA keygen and use Montgomery reduction so it runs in constant-time.
Note that we only need to avoid leaking information about the input if
it's a large prime. If the number ends up composite, or we find it in
our table of small primes, we can return immediately.
The leaks not addressed by this CL are:
- The difficulty of selecting |b| leaks information about |w|.
- The distribution of whether step 4.4 runs leaks information about w.
- We leak |a| (the largest power of two which divides w) everywhere.
- BN_mod_word in the trial division is not constant-time.
These will be resolved in follow-up changes.
Median of 29 RSA keygens: 0m0.521 -> 0m0.621s
(Accuracy beyond 0.1s is questionable.)
Bug: 238
Change-Id: I0cf0ff22079732a0a3ababfe352bb4327e95b879
Reviewed-on: https://boringssl-review.googlesource.com/25886
Reviewed-by: Adam Langley <agl@google.com>
Primality testing checks for small words in random places.
Median of 29 RSA keygens: 0m0.811s -> 0m0.521s
(Accuracy beyond 0.1s is questionable, and this "speed up" is certainly
noise.)
Bug: 238
Change-Id: Ie5efab7291302a42ac6e283d25da0c094d8577e7
Reviewed-on: https://boringssl-review.googlesource.com/25885
Reviewed-by: Adam Langley <agl@google.com>
There are a number of random subtractions in RSA key generation. Add a
fixed-width version.
Median of 29 RSA keygens: 0m0.859s -> 0m0.811s
(Accuracy beyond 0.1s is questionable.)
Bug: 238
Change-Id: I9fa0771b95a438fd7d2635fd77a332146ccc96d9
Reviewed-on: https://boringssl-review.googlesource.com/25884
Commit-Queue: Adam Langley <agl@google.com>
Reviewed-by: Adam Langley <agl@google.com>
These are composite numbers whose composite witnesses aren't in the
first however many prime numbers, so deterministically checking small
numbers may not work.
We don't check composite witnesses deterministically but these are
probably decent tests. (Not sure how else to find composites with
scarce witnesses, but these seemed decent candidates.)
Change-Id: I23dcb7ba603a64c1f7d1e9a16942e7c29c76da51
Reviewed-on: https://boringssl-review.googlesource.com/26645
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These were randomly generated.
Change-Id: I532afdaf469e6c80e518dae3a75547ff7cb0948f
Reviewed-on: https://boringssl-review.googlesource.com/26065
Reviewed-by: Steven Valdez <svaldez@google.com>
Commit-Queue: David Benjamin <davidben@google.com>
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This clearly was supposed to be a return 1. See
https://github.com/openssl/openssl/issues/5537 for details.
(Additionally, now that our BIGNUMs may be non-minimal, this function
violates the rule that BIGNUM functions should not depend on widths. We
should use w >= bn_minimal_width(a) to retain the original behavior. But
the original behavior is nuts, so let's just fix it.)
Update-Note: BN_mask_bits no longer reports failure in some cases. These
cases were platform-dependent and not useful, and code search confirms
nothing was relying on it.
Change-Id: I31b1c2de6c5de9432c17ec3c714a5626594ee03c
Reviewed-on: https://boringssl-review.googlesource.com/26464
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This isn't strictly necessary now that BIGNUMs are safe, but we get to
rely on type-system annotations from EC_SCALAR. Additionally,
EC_POINT_mul depends on BN_div, while the EC_SCALAR version does not.
Change-Id: I75e6967f3d35aef17278b94862f4e506baff5c23
Reviewed-on: https://boringssl-review.googlesource.com/26424
Reviewed-by: Steven Valdez <svaldez@google.com>
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Better commit such details to comments before I forget them.
Change-Id: Ie36332235c692f4369413b4340a742b5ad895ce1
Reviewed-on: https://boringssl-review.googlesource.com/25984
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This was done by OpenSSL with the kind permission of Intel. This change
is imported from upstream's commit
dcf6e50f48e6bab92dcd2dacb27fc17c0de34199.
Change-Id: Ie8d3b700cd527a6e8cf66e0728051b2acd8cc6b9
Reviewed-on: https://boringssl-review.googlesource.com/25588
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These files are otherwise up-to-date with OpenSSL master as of
50ea9d2b3521467a11559be41dcf05ee05feabd6, modulo a couple of spelling
fixes which I've imported.
I've also reverted the same-line label and instruction patch to
x86_64-mont*.pl. The new delocate parser handles that fine.
Change-Id: Ife35c671a8104c3cc2fb6c5a03127376fccc4402
Reviewed-on: https://boringssl-review.googlesource.com/25644
Reviewed-by: Adam Langley <agl@google.com>
Change-Id: I5fc029ceddfa60b2ccc97c138b94c1826f6d75fa
Reviewed-on: https://boringssl-review.googlesource.com/25844
Reviewed-by: David Benjamin <davidben@google.com>
Commit-Queue: David Benjamin <davidben@google.com>
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This allows a BIGNUM consumer to avoid messing around with bn->d and
bn->top/width.
Bug: 232
Change-Id: I134cf412fef24eb404ff66c84831b4591d921a17
Reviewed-on: https://boringssl-review.googlesource.com/25484
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This is a bit easier to read than BN_less_than_consttime when we must do
>= or <=, about as much work to compute, and lots of code calls BN_cmp
on secret data. This also, by extension, makes BN_cmp_word
constant-time.
BN_equal_consttime is probably a little more efficient and is perfectly
readable, so leave that one around.
Change-Id: Id2e07fe312f01cb6fd10a1306dcbf6397990cf13
Reviewed-on: https://boringssl-review.googlesource.com/25444
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The loop and the outermost special-cases are basically the same.
Change-Id: I5e3ca60ad9a04efa66b479eebf8c3637a11cdceb
Reviewed-on: https://boringssl-review.googlesource.com/25406
Commit-Queue: David Benjamin <davidben@google.com>
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Same mistake as bn_mul_recursive.
Change-Id: I2374d37e5da61c82ccb1ad79da55597fa3f10640
Reviewed-on: https://boringssl-review.googlesource.com/25405
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This follows similar lines as the previous cleanups and fixes the
documentation of the preconditions.
And with that, RSA private key operations, provided p and q have the
same bit length, should be constant time, as far as I know. (Though I'm
sure I've missed something.)
bn_cmp_part_words and bn_cmp_words are no longer used and deleted.
Bug: 234
Change-Id: Iceefa39f57e466c214794c69b335c4d2c81f5577
Reviewed-on: https://boringssl-review.googlesource.com/25404
Commit-Queue: David Benjamin <davidben@google.com>
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The power of two computations here were extremely confusing and one of
the comments mixed && and ||. Remove the cached k = j + j value.
Optimizing the j*8, j*8, j*2, and j*4 multiplications is the compiler's
job. If it doesn't manage it, it was only a couple shifts anyway.
With that fixed, it becomes easier to tell that rr was actaully
allocated twice as large as necessary. I suspect rr is also
incorrectly-allocated in the bn_mul_part_recursive case, but I'll wait
until I've checked that function over first. (The array size
documentation on the other bn_{mul,sqr}_recursive functions have had
mistakes before.)
Change-Id: I298400b988e3bd108d01d6a7c8a5b262ddf81feb
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I left the input length as int because the calling convention passes
these messy deltas around. This micro-optimization is almost certainly
pointless, but bn_sub_part_words is written in assembly, so I've left it
alone for now. The documented preconditions were also all completely
wrong, so I've fixed them. We actually only call them for even tighter
bounds (one of dna or dnb is 0 and the other is 0 or -1), at least
outside bn_mul_part_recursive which I still need to read through.
This leaves bn_mul_part_recursive, which is reachable for RSA keys which
are not a power of two in bit width.
The first iteration of this had an uncaught bug, so I added a few more
aggressive tests generated with:
A = 0x...
B = 0x...
# Chop off 0, 1 and > 1 word for both 32 and 64-bit.
for i in (0, 1, 2, 4):
for j in (0, 1, 2, 4):
a = A >> (32*i)
b = B >> (32*j)
p = a * b
print "Product = %x" % p
print "A = %x" % a
print "B = %x" % b
print
Bug: 234
Change-Id: I72848d992637c0390cdd3c4f81cb919393b59eb8
Reviewed-on: https://boringssl-review.googlesource.com/25344
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We still need BN_mul and, in particular, bn_mul_recursive will either
require bn_abs_sub_words be generalized or that we add a parallel
bn_abs_sub_part_words, but start with the easy one.
While I'm here, simplify the i and j mess in here. It's patterned after
the multiplication one, but can be much simpler.
Bug: 234
Change-Id: If936099d53304f2512262a1cbffb6c28ae30ccee
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There is no more need for the "constant-time" reading beyond bn->top. We
can write the bytes out naively because RSA computations no longer call
bn_correct_top/bn_set_minimal_width.
Specifically, the final computation is a BN_mod_mul_montgomery to remove
the blinding, and that keeps the sizes correct.
Bug: 237
Change-Id: I6e90d81c323b644e179d899f411479ea16deab98
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This is to be used in constant-time RSA CRT.
Bug: 233
Change-Id: Ibade5792324dc6aba38cab6971d255d41fb5eb91
Reviewed-on: https://boringssl-review.googlesource.com/25286
Commit-Queue: David Benjamin <davidben@google.com>
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Use the now constant-time modular arithmetic functions.
Bug: 236
Change-Id: I4567d67bfe62ca82ec295f2233d1a6c9b131e5d2
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As the EC code will ultimately want to use these in "words" form by way
of EC_FELEM, and because it's much easier, I've implement these as
low-level words-based functions that require all inputs have the same
width. The BIGNUM versions which RSA and, for now, EC calls are
implemented on top of that.
Unfortunately, doing such things in constant-time and accounting for
undersized inputs requires some scratch space, and these functions don't
take BN_CTX. So I've added internal bn_mod_*_quick_ctx functions that
take a BN_CTX and the old functions now allocate a bit unnecessarily.
RSA only needs lshift (for BN_MONT_CTX) and sub (for CRT), but the
generic EC code wants add as well.
The generic EC code isn't even remotely constant-time, and I hope to
ultimately use stack-allocated EC_FELEMs, so I've made the actual
implementations here implemented in "words", which is much simpler
anyway due to not having to take care of widths.
I've also gone ahead and switched the EC code to these functions,
largely as a test of their performance (an earlier iteration made the EC
code noticeably slower). These operations are otherwise not
performance-critical in RSA.
The conversion from BIGNUM to BIGNUM+BN_CTX should be dropped by the
static linker already, and the unused BIGNUM+BN_CTX functions will fall
off when EC_FELEM happens.
Update-Note: BN_mod_*_quick bounce on malloc a bit now, but they're not
really used externally. The one caller I found was wpa_supplicant
which bounces on malloc already. They appear to be implementing
compressed coordinates by hand? We may be able to convince them to
call EC_POINT_set_compressed_coordinates_GFp.
Bug: 233, 236
Change-Id: I2bf361e9c089e0211b97d95523dbc06f1168e12b
Reviewed-on: https://boringssl-review.googlesource.com/25261
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The fallback functions still themselves leak, but I've left TODOs there.
This only affects BN_mod_mul_montgomery on platforms where we don't use
the bn_mul_mont assembly, but BN_mul additionally affects the final
multiplication in RSA CRT.
Bug: 232
Change-Id: Ia1ae16162c38e10c056b76d6b2afbed67f1a5e16
Reviewed-on: https://boringssl-review.googlesource.com/25260
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Functions that deserialize from bytes and Montgomery multiplication have
no reason to minimize their inputs.
Bug: 232
Change-Id: I121cc9b388033d684057b9df4ad0c08364849f58
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This has no behavior change, but it has a semantic one. This CL is an
assertion that all BIGNUM functions tolerate non-minimal BIGNUMs now.
Specifically:
- Functions that do not touch top/width are assumed to not care.
- Functions that do touch top/width will be changed by this CL. These
should be checked in review that they tolerate non-minimal BIGNUMs.
Subsequent CLs will start adjusting the widths that BIGNUM functions
output, to fix timing leaks.
Bug: 232
Change-Id: I3a2b41b071f2174452f8d3801bce5c78947bb8f7
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These actually work as-is, but BN_bn2hex allocates more memory than
necessary, and we may as well skip the unnecessary words where we can.
Also add a test for this.
Bug: 232
Change-Id: Ie271fe9f3901d00dd5c3d7d63c1776de81a10ec7
Reviewed-on: https://boringssl-review.googlesource.com/25304
Commit-Queue: David Benjamin <davidben@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
Reviewed-by: Adam Langley <agl@google.com>
Test this by re-running bn_tests.txt tests a lot. For the most part,
this was done by scattering bn_minimal_width or bn_correct_top calls as
needed. We'll incrementally tease apart the functions that need to act
on non-minimal BIGNUMs in constant-time.
BN_sqr was switched to call bn_correct_top at the end, rather than
sample bn_minimal_width, in anticipation of later splitting it into
BN_sqr (for calculators) and BN_sqr_fixed (for BN_mod_mul_montgomery).
BN_div_word also uses bn_correct_top because it calls BN_lshift so
officially shouldn't rely on BN_lshift returning something
minimal-width, though I expect we'd want to split off a BN_lshift_fixed
than change that anyway?
The shifts sample bn_minimal_width rather than bn_correct_top because
they all seem to try to be very clever around the bit width. If we need
constant-time versions of them, we can adjust them later.
Bug: 232
Change-Id: Ie17b39034a713542dbe906cf8954c0c5483c7db7
Reviewed-on: https://boringssl-review.googlesource.com/25255
Commit-Queue: David Benjamin <davidben@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
Reviewed-by: Adam Langley <agl@google.com>
These empty states aren't any use to either caller or implementor.
Change-Id: If0b748afeeb79e4a1386182e61c5b5ecf838de62
Reviewed-on: https://boringssl-review.googlesource.com/25254
Reviewed-by: Adam Langley <agl@google.com>
Checking the excess words for zero doesn't need to be in constant time,
but it's free. BN_bn2bin_padded is a little silly as read_word_padded
only exists to work around bn->top being minimal. Once non-minimal
BIGNUMs are turned on and the RSA code works right, we can simplify
BN_bn2bin_padded.
Bug: 232
Change-Id: Ib81e30ca1e5a8ea90ab3278bf4ded219bac481ac
Reviewed-on: https://boringssl-review.googlesource.com/25253
Reviewed-by: Adam Langley <agl@google.com>
One less to worry about.
Bug: 232
Change-Id: Ib7d38e18fee02590088d76363e17f774cfefa59b
Reviewed-on: https://boringssl-review.googlesource.com/25252
Reviewed-by: Adam Langley <agl@google.com>
Saves a bit of work, and we get a width sanity-check.
Bug: 232
Change-Id: I1c6bc376c9d8aaf60a078fdc39f35b6f44a688c6
Reviewed-on: https://boringssl-review.googlesource.com/25251
Reviewed-by: Adam Langley <agl@google.com>
Give a non-minimal modulus, there are two possible values of R we might
pick: 2^(BN_BITS2 * width) or 2^(BN_BITS2 * bn_minimal_width).
Potentially secret moduli would make the former attractive and things
might even work, but our only secret moduli (RSA) have public bit
widths. It's more cases to test and the usual BIGNUM invariant is that
widths do not affect numerical output.
Thus, settle on minimizing mont->N for now. With the top explicitly made
minimal, computing |lgBigR| is also a little simpler.
This CL also abstracts out the < R check in the RSA code, and implements
it in a width-agnostic way.
Bug: 232
Change-Id: I354643df30530db7866bb7820e34241d7614f3c2
Reviewed-on: https://boringssl-review.googlesource.com/25250
Reviewed-by: Adam Langley <agl@google.com>
These functions already require their inputs to be reduced mod N (or, in
some cases, bounded by R or N*R), so negative numbers are nonsense. The
code still attempted to account for them by working on the absolute
value and fiddling with the sign bit. (The output would be in range (-N,
N) instead of [0, N).)
This complicates relaxing bn_correct_top because bn_correct_top is also
used to prevent storing a negative zero. Instead, just reject negative
inputs.
Upgrade-Note: These functions are public API, so some callers may
notice. Code search suggests there is only one caller outside
BoringSSL, and it looks fine.
Bug: 232
Change-Id: Ieba3acbb36b0ff6b72b8ed2b14882ec9b88e4665
Reviewed-on: https://boringssl-review.googlesource.com/25249
Reviewed-by: Adam Langley <agl@google.com>
This matches bn_mod_mul_montgomery_small and removes a bit of
unnecessary stuttering.
Change-Id: Ife249c6e8754aef23c144dbfdea5daaf7ed9f48a
Reviewed-on: https://boringssl-review.googlesource.com/25248
Reviewed-by: Adam Langley <agl@google.com>
This cuts down on a duplicated place where we mess with bn->top. It also
also better abstracts away what determines the value of R.
(I ordered this wrong and rebasing will be annoying. Specifically, the
question is what happens if the modulus is non-minimal. In
https://boringssl-review.googlesource.com/c/boringssl/+/25250/, R will
be determined by the stored width of mont->N, so we want to use mont's
copy of the modulus. Though, one way or another, the important part is
that it's inside the Montgomery abstraction.)
Bug: 232
Change-Id: I74212e094c8a47f396b87982039e49048a130916
Reviewed-on: https://boringssl-review.googlesource.com/25247
Reviewed-by: Adam Langley <agl@google.com>
This is actually a bit more complicated (the mismatching widths cases
will never actually happen in RSA), but it's easier to think about and
removes more width-sensitive logic.
Bug: 232
Change-Id: I85fe6e706be1f7d14ffaf587958e930f47f85b3c
Reviewed-on: https://boringssl-review.googlesource.com/25246
Reviewed-by: Adam Langley <agl@google.com>
This makes it easier going to and from non-minimal BIGNUMs and words
without worrying about the widths which are ultimately to become less
friendly.
Bug: 232
Change-Id: Ia57cb29164c560b600573c27b112ad9375a86aad
Reviewed-on: https://boringssl-review.googlesource.com/25245
Reviewed-by: Adam Langley <agl@google.com>
