## Cryptology ePrint Archive: Report 2016/229

Key Compression for Isogeny-Based Cryptosystems

Reza Azarderakhsh, David Jao, Kassem Kalach, Brian Koziel, and Christopher Leonardi

Abstract: We present a method for key compression in quantum-resistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no effect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each $j$-invariant, and representing elements on the curve as linear combinations with respect to a canonical choice of basis. This method of compressing public information can be applied to numerous isogeny-based protocols, such as key exchange, zero-knowledge identification, and public-key encryption. We performed personal computer and ARM implementations of the key exchange with compression and decompression in C and provided timing results, showing the computational cost of key compression and decompression at various security levels. Our results show that isogeny-based cryptosystems achieve by far the smallest possible key sizes among all existing families of post-quantum cryptosystems at practical security levels; e.g. 3073-bit public keys at the quantum 128-bit security level, comparable to (non-quantum) RSA key sizes.

Category / Keywords: elliptic curves, isogenies, key compression, post-quantum cryptography

Original Publication (in the same form): AsiaPKC2016

Date: received 1 Mar 2016, last revised 15 Apr 2016

Contact author: rxaeec at rit edu

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2016/229

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