Cryptology ePrint Archive: Report 2020/417

Optimal strategies for CSIDH

Jesús-Javier Chi-Domínguez and Francisco Rodríguez-Henríquez

Abstract: Since its proposal in Asiacrypt 2018, the commutative isogeny-based key exchange protocol (CSIDH) has spurred considerable attention to improving its performance and re-evaluating its classical and quantum security guarantees. In this paper we discuss how the optimal strategies employed by the Supersingular Isogeny Diffie-Hellman (SIDH) key agreement protocol can be naturally extended to CSIDH. Furthermore, we report a software library that achieves moderate but noticeable performance speedups when compared against state-of-the-art implementations of CSIDH-512, which is the most popular CSIDH instantiation. We also report an estimated number of field operations for larger instantiations of this protocol, namely, CSIDH-1024 and CSIDH-1792.

Category / Keywords: public-key cryptography / CSIDH, isogeny-based cryptography, post-quantum cryptography, key exchange

Date: received 13 Apr 2020, last revised 5 Aug 2020

Contact author: jesus chidominguez at tuni fi,francisco@cs cinvestav mx

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Version: 20200805:133716 (All versions of this report)

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