Cryptology ePrint Archive: Report 2016/413

Efficient algorithms for supersingular isogeny Diffie-Hellman

Craig Costello and Patrick Longa and Michael Naehrig

Abstract: We propose a new suite of algorithms that significantly improve the performance of supersingular isogeny Diffie-Hellman (SIDH) key exchange. Subsequently, we present a full-fledged implementation of SIDH that is geared towards the 128-bit quantum and 192-bit classical security levels. Our library is the first constant-time SIDH implementation and is up to 2.9 times faster than the previous best (non-constant-time) SIDH software. The high speeds in this paper are driven by compact, inversion-free point and isogeny arithmetic and fast SIDH-tailored field arithmetic: on an Intel Haswell processor, generating ephemeral public keys takes 46 million cycles for Alice and 54 million cycles for Bob, while computing the shared secret takes 44 million and 52 million cycles, respectively. The size of public keys is only 564 bytes, which is significantly smaller than most of the popular post-quantum key exchange alternatives. Ultimately, the size and speed of our software illustrates the strong potential of SIDH as a post-quantum key exchange candidate and we hope that these results encourage a wider cryptanalytic effort.

Category / Keywords: Post-quantum cryptography, Diffie-Hellman key exchange, supersingular elliptic curves, isogenies, SIDH

Original Publication (with minor differences): IACR-CRYPTO-2016

Date: received 26 Apr 2016, last revised 16 Sep 2019

Contact author: craigco at microsoft com

Available format(s): PDF | BibTeX Citation

Version: 20190917:000416 (All versions of this report)

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