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Effective affine addition in EC multiplication

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* Make secp256k1_gej_add_var and secp256k1_gej_double return the
  Z ratio to go from a.z to r.z.
* Use these Z ratios to speed up batch point conversion to affine
  coordinates, and to speed up batch conversion of points to a
  common Z coordinate.
* Add a point addition function that takes a point with a known
  Z inverse.
* Due to secp256k1's endomorphism, all additions in the EC
  multiplication code can work on affine coordinate (with an
  implicit common Z coordinate), correcting the Z coordinate of
  the result afterwards.

Refactoring by Pieter Wuille:
* Move more global-z logic into the group code.
* Separate code for computing the odd multiples from the code to bring it
  to either storage or globalz format.
* Rename functions.
* Make all addition operations return Z ratios, and test them.
* Make the zr table format compatible with future batch chaining
  (the first entry in zr becomes the ratio between the input and the
  first output).

Original idea and code by Peter Dettman.
This commit is contained in:
Peter Dettman
2014-11-04 19:16:55 +07:00
committed by Pieter Wuille
parent 22f60a6280
commit 4f9791abba
6 changed files with 339 additions and 95 deletions
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8
src/ecmult_gen_impl.h
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@@ -54,18 +54,18 @@ static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context_t *c
/* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
precj[j*16] = numsbase;
for (i = 1; i < 16; i++) {
secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
}
/* Multiply gbase by 16. */
for (i = 0; i < 4; i++) {
secp256k1_gej_double_var(&gbase, &gbase);
secp256k1_gej_double_var(&gbase, &gbase, NULL);
}
/* Multiply numbase by 2. */
secp256k1_gej_double_var(&numsbase, &numsbase);
secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
if (j == 62) {
/* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
secp256k1_gej_neg(&numsbase, &numsbase);
secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej);
secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
}
}
secp256k1_ge_set_all_gej_var(1024, prec, precj);