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>
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