e089eecc1e group: Further simply gej_add_ge (Tim Ruffing)
ac71020ebe group: Save a normalize_to_zero in gej_add_ge (Tim Ruffing)
Pull request description:
As discovered by sipa in #1033.
See commit message for reasoning but note that the infinity handling will be replaced in the second commit again.
ACKs for top commit:
sipa:
ACK e089eecc1e
apoelstra:
ACK e089eecc1e
Tree-SHA512: fb1b5742e73dd8b2172b4d3e2852490cfd626e8673b72274d281fa34b04e9368a186895fb9cd232429c22b14011df136f4c09bdc7332beef2b3657f7f2798d66
The code currently switches to the alternative formula for lambda only if (R,M)
= (0,0) but the alternative formula works whenever M = 0: Specifically, M = 0
implies y1 = -y2. If x1 = x2, then a = -b this is the r = infinity case that we
handle separately. If x1 != x2, then the denominator in the alternative formula
is non-zero, so this formula is well-defined.
One needs to carefully check that the infinity assignment is still correct
because now the definition of m_alt at this point in the code has changed. But
this is true:
Case y1 = -y2:
Then degenerate = true and infinity = ((x1 - x2)Z == 0) & ~a->infinity .
a->infinity is handled separately.
And if ~a->infinity, then Z = Z1 != 0,
so infinity = (x1 - x2 == 0) = (a == -b) by case condition.
Case y1 != -y2:
Then degenerate = false and infinity = ((y1 + y2)Z == 0) & ~a->infinity .
a->infinity is handled separately.
And if ~a->infinity, then Z = Z1 != 0,
so infinity = (y1 + y2 == 0) = false by case condition.
Co-Authored-By: Pieter Wuille <pieter@wuille.net>
e848c3799c Update sage files for new formulae (Peter Dettman)
d64bb5d4f3 Add fe_half tests for worst-case inputs (Peter Dettman)
4eb8b932ff Further improve doubling formula using fe_half (Peter Dettman)
557b31fac3 Doubling formula using fe_half (Pieter Wuille)
2cbb4b1a42 Run more iterations of run_field_misc (Pieter Wuille)
9cc5c257ed Add test for secp256k1_fe_half (Pieter Wuille)
925f78d55e Add _fe_half and use in _gej_add_ge (Peter Dettman)
Pull request description:
- Trades 1 _half for 3 _mul_int and 2 _normalize_weak
Gives around 2-3% faster signing and ECDH, depending on compiler/platform.
ACKs for top commit:
sipa:
utACK e848c3799c
jonasnick:
ACK e848c3799c
real-or-random:
ACK e848c3799c
Tree-SHA512: 81a6c93b3d983f1b48ec8e8b6f262ba914215045a95415147f41ee6e85296aa4d0cbbad9f370cdf475571447baad861d2cc8e0b04a71202d48959cb8a098f584
