This commit improves the performance of ECDSA signature verification
(over NIST P-256 curve) for x86 platforms. The speedup is by a factor of 1.15x.
It does so by:
1) Leveraging the fact that the verification does not need
to run in constant time. To this end, we implemented:
a) the function ecp_nistz256_points_mul_public in a similar way to
the current ecp_nistz256_points_mul function by removing its constant
time features.
b) the Binary Extended Euclidean Algorithm (BEEU) in x86 assembly to
replace the current modular inverse function used for the inversion.
2) The last step in the ECDSA_verify function compares the (x) affine
coordinate with the signature (r) value. Converting x from the Jacobian's
representation to the affine coordinate requires to perform one inversions
(x_affine = x * z^(-2)). We save this inversion and speed up the computations
by instead bringing r to x (r_jacobian = r*z^2) which is faster.
The measured results are:
Before (on a Kaby Lake desktop with gcc-5):
Did 26000 ECDSA P-224 signing operations in 1002372us (25938.5 ops/sec)
Did 11000 ECDSA P-224 verify operations in 1043821us (10538.2 ops/sec)
Did 55000 ECDSA P-256 signing operations in 1017560us (54050.9 ops/sec)
Did 17000 ECDSA P-256 verify operations in 1051280us (16170.8 ops/sec)
After (on a Kaby Lake desktop with gcc-5):
Did 27000 ECDSA P-224 signing operations in 1011287us (26698.7 ops/sec)
Did 11640 ECDSA P-224 verify operations in 1076698us (10810.8 ops/sec)
Did 55000 ECDSA P-256 signing operations in 1016880us (54087.0 ops/sec)
Did 20000 ECDSA P-256 verify operations in 1038736us (19254.2 ops/sec)
Before (on a Skylake server platform with gcc-5):
Did 25000 ECDSA P-224 signing operations in 1021651us (24470.2 ops/sec)
Did 10373 ECDSA P-224 verify operations in 1046563us (9911.5 ops/sec)
Did 50000 ECDSA P-256 signing operations in 1002774us (49861.7 ops/sec)
Did 15000 ECDSA P-256 verify operations in 1006471us (14903.6 ops/sec)
After (on a Skylake server platform with gcc-5):
Did 25000 ECDSA P-224 signing operations in 1020958us (24486.8 ops/sec)
Did 10373 ECDSA P-224 verify operations in 1046359us (9913.4 ops/sec)
Did 50000 ECDSA P-256 signing operations in 1003996us (49801.0 ops/sec)
Did 18000 ECDSA P-256 verify operations in 1021604us (17619.4 ops/sec)
Developers and authors:
***************************************************************************
Nir Drucker (1,2), Shay Gueron (1,2)
(1) Amazon Web Services Inc.
(2) University of Haifa, Israel
***************************************************************************
Change-Id: Idd42a7bc40626bce974ea000b61fdb5bad33851c
Reviewed-on: https://boringssl-review.googlesource.com/c/31304
Commit-Queue: Adam Langley <agl@google.com>
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Reviewed-by: David Benjamin <davidben@google.com>
Reviewed-by: Adam Langley <agl@google.com>
EC_POINT is split into the existing public EC_POINT (where the caller is
sanity-checked about group mismatches) and the low-level EC_RAW_POINT
(which, like EC_FELEM and EC_SCALAR, assume that is your problem and is
a plain old struct). Having both EC_POINT and EC_RAW_POINT is a little
silly, but we're going to want different type signatures for functions
which return void anyway (my plan is to lift a non-BIGNUM
get_affine_coordinates up through the ECDSA and ECDH code), so I think
it's fine.
This wasn't strictly necessary, but wnaf.c is a lot tidier now. Perf is
a wash; once we get up to this layer, it's only 8 entries in the table
so not particularly interesting.
Bug: 239
Change-Id: I8ace749393d359f42649a5bb0734597bb7c07a2e
Reviewed-on: https://boringssl-review.googlesource.com/27706
Commit-Queue: David Benjamin <davidben@google.com>
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This introduces EC_FELEM, which is analogous to EC_SCALAR. It is used
for EC_POINT's representation in the generic EC_METHOD, as well as
random operations on tuned EC_METHODs that still are implemented
genericly.
Unlike EC_SCALAR, EC_FELEM's exact representation is awkwardly specific
to the EC_METHOD, analogous to how the old values were BIGNUMs but may
or may not have been in Montgomery form. This is kind of a nuisance, but
no more than before. (If p224-64.c were easily convertable to Montgomery
form, we could say |EC_FELEM| is always in Montgomery form. If we
exposed the internal add and double implementations in each of the
curves, we could give |EC_POINT| an |EC_METHOD|-specific representation
and |EC_FELEM| is purely a |EC_GFp_mont_method| type. I'll leave this
for later.)
The generic add and doubling formulas are aligned with the formulas
proved in fiat-crypto. Those only applied to a = -3, so I've proved a
generic one in https://github.com/mit-plv/fiat-crypto/pull/356, in case
someone uses a custom curve. The new formulas are verified,
constant-time, and swap a multiply for a square. As expressed in
fiat-crypto they do use more temporaries, but this seems to be fine with
stack-allocated EC_FELEMs. (We can try to help the compiler later,
but benchamrks below suggest this isn't necessary.)
Unlike BIGNUM, EC_FELEM can be stack-allocated. It also captures the
bounds in the type system and, in particular, that the width is correct,
which will make it easier to select a point in constant-time in the
future. (Indeed the old code did not always have the correct width. Its
point formula involved halving and implemented this in variable time and
variable width.)
Before:
Did 77274 ECDH P-256 operations in 10046087us (7692.0 ops/sec)
Did 5959 ECDH P-384 operations in 10031701us (594.0 ops/sec)
Did 10815 ECDSA P-384 signing operations in 10087892us (1072.1 ops/sec)
Did 8976 ECDSA P-384 verify operations in 10071038us (891.3 ops/sec)
Did 2600 ECDH P-521 operations in 10091688us (257.6 ops/sec)
Did 4590 ECDSA P-521 signing operations in 10055195us (456.5 ops/sec)
Did 3811 ECDSA P-521 verify operations in 10003574us (381.0 ops/sec)
After:
Did 77736 ECDH P-256 operations in 10029858us (7750.5 ops/sec) [+0.8%]
Did 7519 ECDH P-384 operations in 10068076us (746.8 ops/sec) [+25.7%]
Did 13335 ECDSA P-384 signing operations in 10029962us (1329.5 ops/sec) [+24.0%]
Did 11021 ECDSA P-384 verify operations in 10088600us (1092.4 ops/sec) [+22.6%]
Did 2912 ECDH P-521 operations in 10001325us (291.2 ops/sec) [+13.0%]
Did 5150 ECDSA P-521 signing operations in 10027462us (513.6 ops/sec) [+12.5%]
Did 4264 ECDSA P-521 verify operations in 10069694us (423.4 ops/sec) [+11.1%]
This more than pays for removing points_make_affine previously and even
speeds up ECDH P-256 slightly. (The point-on-curve check uses the
generic code.)
Next is to push the stack-allocating up to ec_wNAF_mul, followed by a
constant-time single-point multiplication.
Bug: 239
Change-Id: I44a2dff7c52522e491d0f8cffff64c4ab5cd353c
Reviewed-on: https://boringssl-review.googlesource.com/27668
Reviewed-by: Adam Langley <agl@google.com>
This is adapted from upstream's
eb7916960bf50f436593abe3d5f2e0592d291017.
This gives a 22% win for ECDSA signing. (Upstream cites 30-40%, but they
are unnecessarily using BN_mod_exp_mont_consttime in their generic path.
The exponent is public. I expect part of their 30-40% is just offsetting
this.)
Did 506000 ECDSA P-256 signing operations in 25044595us (20204.0 ops/sec)
Did 170506 ECDSA P-256 verify operations in 25033567us (6811.1 ops/sec)
Did 618000 ECDSA P-256 signing operations in 25031294us (24689.1 ops/sec)
Did 182240 ECDSA P-256 verify operations in 25006918us (7287.6 ops/sec)
Most of the performance win appears to be from the assembly operations
and not the addition chain. I have a CL to graft the addition chain onto
the C implementation, but it did not show measurable improvement in
ECDSA verify. ECDSA sign gets 2-4% faster, but we're more concerned
about ECDSA verify in the OPENSSL_SMALL builds.
Change-Id: Ide166f98b146c025f7f80ed7906336c16818540a
Reviewed-on: https://boringssl-review.googlesource.com/27593
Reviewed-by: Adam Langley <alangley@gmail.com>
This introduces a hook for the OpenSSL assembly.
Change-Id: I35e0588f0ed5bed375b12f738d16c9f46ceedeea
Reviewed-on: https://boringssl-review.googlesource.com/27592
Reviewed-by: Adam Langley <alangley@gmail.com>
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
Commit-Queue: David Benjamin <davidben@google.com>
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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>
The fiat-crypto-generated code uses the Montgomery form implementation
strategy, for both 32-bit and 64-bit code.
64-bit throughput seems slower, but the difference is smaller than noise between repetitions (-2%?)
32-bit throughput has decreased significantly for ECDH (-40%). I am
attributing this to the change from varibale-time scalar multiplication
to constant-time scalar multiplication. Due to the same bottleneck,
ECDSA verification still uses the old code (otherwise there would have
been a 60% throughput decrease). On the other hand, ECDSA signing
throughput has increased slightly (+10%), perhaps due to the use of a
precomputed table of multiples of the base point.
64-bit benchmarks (Google Cloud Haswell):
with this change:
Did 9126 ECDH P-256 operations in 1009572us (9039.5 ops/sec)
Did 23000 ECDSA P-256 signing operations in 1039832us (22119.0 ops/sec)
Did 8820 ECDSA P-256 verify operations in 1024242us (8611.2 ops/sec)
master (40e8c921ca):
Did 9340 ECDH P-256 operations in 1017975us (9175.1 ops/sec)
Did 23000 ECDSA P-256 signing operations in 1039820us (22119.2 ops/sec)
Did 8688 ECDSA P-256 verify operations in 1021108us (8508.4 ops/sec)
benchmarks on ARMv7 (LG Nexus 4):
with this change:
Did 150 ECDH P-256 operations in 1029726us (145.7 ops/sec)
Did 506 ECDSA P-256 signing operations in 1065192us (475.0 ops/sec)
Did 363 ECDSA P-256 verify operations in 1033298us (351.3 ops/sec)
master (2fce1beda0):
Did 245 ECDH P-256 operations in 1017518us (240.8 ops/sec)
Did 473 ECDSA P-256 signing operations in 1086281us (435.4 ops/sec)
Did 360 ECDSA P-256 verify operations in 1003846us (358.6 ops/sec)
64-bit tables converted as follows:
import re, sys, math
p = 2**256 - 2**224 + 2**192 + 2**96 - 1
R = 2**256
def convert(t):
x0, s1, x1, s2, x2, s3, x3 = t.groups()
v = int(x0, 0) + 2**64 * (int(x1, 0) + 2**64*(int(x2,0) + 2**64*(int(x3, 0)) ))
w = v*R%p
y0 = hex(w%(2**64))
y1 = hex((w>>64)%(2**64))
y2 = hex((w>>(2*64))%(2**64))
y3 = hex((w>>(3*64))%(2**64))
ww = int(y0, 0) + 2**64 * (int(y1, 0) + 2**64*(int(y2,0) + 2**64*(int(y3, 0)) ))
if ww != v*R%p:
print(x0,x1,x2,x3)
print(hex(v))
print(y0,y1,y2,y3)
print(hex(w))
print(hex(ww))
assert 0
return '{'+y0+s1+y1+s2+y2+s3+y3+'}'
fe_re = re.compile('{'+r'(\s*,\s*)'.join(r'(\d+|0x[abcdefABCDEF0123456789]+)' for i in range(4)) + '}')
print (re.sub(fe_re, convert, sys.stdin.read()).rstrip('\n'))
32-bit tables converted from 64-bit tables
Change-Id: I52d6e5504fcb6ca2e8b0ee13727f4500c80c1799
Reviewed-on: https://boringssl-review.googlesource.com/23244
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Reviewed-by: Adam Langley <agl@google.com>
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None of the asymmetric crypto we inherented from OpenSSL is
constant-time because of BIGNUM. BIGNUM chops leading zeros off the
front of everything, so we end up leaking information about the first
word, in theory. BIGNUM functions additionally tend to take the full
range of inputs and then call into BN_nnmod at various points.
All our secret values should be acted on in constant-time, but k in
ECDSA is a particularly sensitive value. So, ecdsa_sign_setup, in an
attempt to mitigate the BIGNUM leaks, would add a couple copies of the
order.
This does not work at all. k is used to compute two values: k^-1 and kG.
The first operation when computing k^-1 is to call BN_nnmod if k is out
of range. The entry point to our tuned constant-time curve
implementations is to call BN_nnmod if the scalar has too many bits,
which this causes. The result is both corrections are immediately undone
but cause us to do more variable-time work in the meantime.
Replace all these computations around k with the word-based functions
added in the various preceding CLs. In doing so, replace the BN_mod_mul
calls (which internally call BN_nnmod) with Montgomery reduction. We can
avoid taking k^-1 out of Montgomery form, which combines nicely with
Brian Smith's trick in 3426d10119. Along
the way, we avoid some unnecessary mallocs.
BIGNUM still affects the private key itself, as well as the EC_POINTs.
But this should hopefully be much better now. Also it's 10% faster:
Before:
Did 15000 ECDSA P-224 signing operations in 1069117us (14030.3 ops/sec)
Did 18000 ECDSA P-256 signing operations in 1053908us (17079.3 ops/sec)
Did 1078 ECDSA P-384 signing operations in 1087853us (990.9 ops/sec)
Did 473 ECDSA P-521 signing operations in 1069835us (442.1 ops/sec)
After:
Did 16000 ECDSA P-224 signing operations in 1064799us (15026.3 ops/sec)
Did 19000 ECDSA P-256 signing operations in 1007839us (18852.2 ops/sec)
Did 1078 ECDSA P-384 signing operations in 1079413us (998.7 ops/sec)
Did 484 ECDSA P-521 signing operations in 1083616us (446.7 ops/sec)
Change-Id: I2a25e90fc99dac13c0616d0ea45e125a4bd8cca1
Reviewed-on: https://boringssl-review.googlesource.com/23075
Reviewed-by: Adam Langley <agl@google.com>
I really need to resurrect the CL to make them entirely static
(https://crbug.com/boringssl/20), but, in the meantime, to make
replacing the EC_METHOD pointer in EC_POINT with EC_GROUP not
*completely* insane, make them refcounted.
OpenSSL did not do this because their EC_GROUPs are mutable
(EC_GROUP_set_asn1_flag and EC_GROUP_set_point_conversion_form). Ours
are immutable but for the two-function dance around custom curves (more
of OpenSSL's habit of making their objects too complex), which is good
enough to refcount.
Change-Id: I3650993737a97da0ddcf0e5fb7a15876e724cadc
Reviewed-on: https://boringssl-review.googlesource.com/22244
Reviewed-by: Adam Langley <agl@google.com>
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crypto/{asn1,x509,x509v3,pem} were skipped as they are still OpenSSL
style.
Change-Id: I3cd9a60e1cb483a981aca325041f3fbce294247c
Reviewed-on: https://boringssl-review.googlesource.com/19504
Reviewed-by: Adam Langley <agl@google.com>
Commit-Queue: David Benjamin <davidben@google.com>
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The names in the P-224 code collided with the P-256 code and thus many
of the functions and constants in the P-224 code have been prefixed.
Change-Id: I6bcd304640c539d0483d129d5eaf1702894929a8
Reviewed-on: https://boringssl-review.googlesource.com/15847
Reviewed-by: David Benjamin <davidben@google.com>
Commit-Queue: David Benjamin <davidben@google.com>
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