RFR: 8294731: Improve multiplicative inverse for secp256r1 implementation [v2]

[Xue-Lei Andrew Fan]

> Hi,
> 
> May I have this patch reviewed?
> 
> This is one of a few steps to improve the EC performance. The multiplicative inverse implementation could be improved for better performance. 
> 
> For secp256r1 prime p, the current  multiplicative inverse impl needs 256 square and 128 multiplication.  With the path, the operation needs 256 square and 37 multiplication.
> 
> For secp256r1 order n, the current  multiplicative inverse impl needs 256 square and 169 multiplication. With the patch, the operation needs  256 square and 94 multiplication.
> 
> Here is the benchmark numbers before the patch applied:
> 
> Benchmark        (messageLength)   Mode  Cnt     Score    Error  Units
> Signatures.sign               64  thrpt   15  1412.644 ±  5.529  ops/s
> Signatures.sign              512  thrpt   15  1407.711 ± 14.118  ops/s
> Signatures.sign             2048  thrpt   15  1415.674 ±  6.965  ops/s
> Signatures.sign            16384  thrpt   15  1395.582 ± 12.689  ops/s
> 
> 
> And the following are the benchmarking after the patch applied.
> 
> Benchmark        (messageLength)   Mode  Cnt     Score    Error  Units
> Signatures.sign               64  thrpt   15  1459.527 ± 10.160  ops/s
> Signatures.sign              512  thrpt   15  1450.707 ± 15.554  ops/s
> Signatures.sign             2048  thrpt   15  1453.490 ±  5.362  ops/s
> Signatures.sign            16384  thrpt   15  1437.364 ±  8.291  ops/s
> 
> 
> It looks like the performance improvement is no significant enough for now.  But it may be 2+ times more in numbers when the scalar multiplication implementation is improved in a follow-up enhancement in another pull request.
> 
> Enhancement for other curves will be considered in separate pull requests.
> 
> Thanks,
> Xuelei

Xue-Lei Andrew Fan has updated the pull request incrementally with one additional commit since the last revision:

  more performance improvement

-------------

Changes:
  - all: https://git.openjdk.org/jdk/pull/10544/files
  - new: https://git.openjdk.org/jdk/pull/10544/files/1da02c5e..b9bf0269

Webrevs:
 - full: https://webrevs.openjdk.org/?repo=jdk&pr=10544&range=01
 - incr: https://webrevs.openjdk.org/?repo=jdk&pr=10544&range=00-01

  Stats: 5 lines in 1 file changed: 0 ins; 0 del; 5 mod
  Patch: https://git.openjdk.org/jdk/pull/10544.diff
  Fetch: git fetch https://git.openjdk.org/jdk pull/10544/head:pull/10544

PR: https://git.openjdk.org/jdk/pull/10544