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microsoft / PQCrypto-SIDH

SIDH Library is a fast and portable software library that implements state-of-the-art supersingular isogeny cryptographic schemes. The chosen parameters aim to provide security against attackers running a large-scale quantum computer, and security against classical algorithms.
MIT License
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Consider integrating https://eprint.iacr.org/2017/1015 #6

Closed eternaleye closed 6 years ago

eternaleye commented 6 years ago

A Faster Software Implementation of the Supersingular Isogeny Diffie-Hellman Key Exchange Protocol

Armando Faz-Hernández and Julio López and Eduardo Ochoa-Jiménez and Francisco Rodríguez-Henríquez

Abstract: Since its introduction by Jao and De Feo in 2011, the supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol has positioned itself as a promising candidate for post-quantum cryptography. One salient feature of the SIDH protocol is that it requires exceptionally short key sizes. However, the latency associated to SIDH is higher than the ones reported for other post-quantum cryptosystem proposals. Aiming to accelerate the SIDH runtime performance, we present in this work several algorithmic optimizations targeting both elliptic-curve and field arithmetic operations. We introduce in the context of the SIDH protocol a more efficient approach for calculating the elliptic curve operation P + [k]Q. Our strategy achieves a factor 1.4 speedup compared with the popular variable-three-point ladder algorithm regularly used in the SIDH shared secret phase. Moreover, profiting from pre-computation techniques our algorithm yields a factor 1.7 acceleration for the computation of this operation in the SIDH key generation phase. We also present an optimized evaluation of the point tripling formula, and discuss several algorithmic and implementation techniques that lead to faster field arithmetic computations. A software implementation of the above improvements on an Intel Skylake Core i7-6700 processor gives a factor 1.33 speedup against the state-of-the-art software implementation of the SIDH protocol reported by Costello-Longa-Naehrig in CRYPTO 2016.

(emphasis mine)

dconnolly commented 6 years ago

These changes have been implemented in the fork of PQCrypto-SIDH by the authors of that paper: https://github.com/armfazh/flor-sidh-x64

patricklonga commented 6 years ago

Version 3.0 of the library incorporates the new algorithm for computing P + [k]Q due to Faz-Hernández, López, Ochoa-Jiménez and Rodríguez-Henríquez. It also incorporates a faster tripling formula due to Costello and Hisil that has (virtually) the same cost as the formula presented in the paper above.