Radix-2^51 support #4
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This probably isn't constant time because of the Z1==Z2 check. If it should be, we can drop that first part (and there is still a speed increase from removing the two FieldElement.invert() calls).
Sign/verify tests fail, but all other tests pass. The problem is probably in ScalarOps somewhere.
…with long The test fails (likely because all longs are signed in Java)
The only BigInteger operations used are and(), or() and shift[Left|Right]() (but it is possible that these are not constant time?)
Before: 0.534 each sign, 2.3272 each verify, 2.8612 s+v After: 0.5888 each sign, 2.3566 each verify, 2.9454 s+v Sign uses reduce() twice, verify uses it once. Therefore the ref10 version is about 28us slower than the BigInteger version. Basically negligible, so the important factor to determine is whether the BigInteger operations used are constant time. If we can't get the ref10 version to be constant time, we may as well use the BigInteger version.
Most FieldElement implementations (in particular, the ref10 implementation) don't have a generic pow() method, and instead will have I hard-coded.
Before black magic: 0.5548 each sign, 2.4118 each verify, 2.9666 s+v After black magic: 0.1572 each sign, 0.2798 each verify, 0.437 s+v
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This pull request refactors the existing BigInteger implementation so all BigInteger-specific code is in a single subpackage. The Ed25519-specific radix-2^51 implementation from ref10 is then implemented, resulting in a considerable speed boost (signing is about 3.5x faster, verifying is about 8.5x faster).