RFR: 8295011: EC point multiplication improvement for secp256r1 [v3]

[Daniel Jeliński]

On Fri, 28 Oct 2022 14:39:34 GMT, Xue-Lei Andrew Fan <xuelei at openjdk.org> wrote:

>> src/jdk.crypto.ec/share/classes/sun/security/ec/ECOperations.java line 628:
>> 
>>> 626:                             ProjectivePoint.Mutable m =
>>> 627:                                     multiplier.pointMultiply(s);
>>> 628:                             points[d][w] = m.setValue(m.asAffine()).fixed();
>> 
>> Did you try using AffinePoints instead of ProjectivePoints? Sum with AffinePoints is supposed to be a bit faster, wonder if the improvement is worthwhile.
>> 
>> Also, unless you switch to affine points, just use `m.fixed()`.
>
>> Did you try using AffinePoints instead of ProjectivePoints?
> 
> Yes.  See [JDK-8295763](https://bugs.openjdk.org/browse/JDK-8295763).  Unfortunately, the mixed point addition formulas used in JDK implementation does not support additional of neutral point. It may be doable again if the formulas get changed in the future.
> 
>> Also, unless you switch to affine points, just use m.fixed().
> 
> Yes, the change to AffinePoints is mainly for checking in the following block.  BTW, the class loading is slow, hard-coded tables should be used in a coming update very soon.

ah... right. The neutral point, aka point at infinity (0:1:0) cannot be represented in affine space. Thanks for checking.

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PR: https://git.openjdk.org/jdk/pull/10893