secp256k1: Add field func to determine when >= P-N. #2093
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matheusd
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dajohi
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This introduces the ability to determine if a specialized field value is greater than or equal to the field prime minus the group order in constant time. It is also significantly faster than performing the calculation via big integers since it would require a conversion from the specialized type in practice. Comprehensive tests with 100% coverage and benchmarks are included. For now, this merely introduces the method without modifying any of the code to make use of it, but it will be useful when working with signatures and public key recovery in the future. The following benchmark shows a comparison between determining the condition via the new specialized method and via generic big ints: benchmark old ns/op new ns/op delta -------------------------------------------------------------------- BenchmarkIsGtOrEqPrimeMinusOrder 123 10.6 -91.38% benchmark old allocs new allocs delta -------------------------------------------------------------------- BenchmarkIsGtOrEqPrimeMinusOrder 2 0 -100.00% benchmark old bytes new bytes delta -------------------------------------------------------------------- BenchmarkIsGtOrEqPrimeMinusOrder 96 0 -100.00%
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This is rebased on #2087.
This introduces the ability to determine if a specialized field value is greater than or equal to the field prime minus the group order in constant time. It is also significantly faster than performing the calculation via big integers since it would require a conversion from the specialized type in practice.
Comprehensive tests with 100% coverage and benchmarks are included.
For now, this merely introduces the method without modifying any of the code to make use of it, but it will be useful when working with signatures and public key recovery in the future.
The following benchmark shows a comparison between determining the condition via the new specialized method and via generic big ints: