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Better-performing “25519” elliptic-curve cryptography


Automated reasoning and optimizations specific to CPU microarchitectures improve both performance and assurance of correct implementation.

In this post, we explore different aspects of our work, including the process for proving correctness via automated reasoning, microarchitecture ( μ arch) optimization techniques, the special considerations for constant-time code, and the quantification of performance gains. For Arm64 μ archs, such as AWS Graviton 3 with improved integer multipliers, we use relatively straightforward schoolbook multiplication, which turns out to give good performance. The reason is that, on these μ archs, 64x64-bit multiplication producing a 128-bit result has substantially lower throughput relative to other operations, making the number size at which Karatsuba optimization becomes worthwhile much smaller.

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