Accelerating the Couveignes Rostovtsev Stolbunov key exchange protocol

2018/04/26 by Jean Kieffer, Kieffer, Jean
Computer Science · #Chaos-based Image/Signal Encryption #Cryptographic Implementations and Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1804.10128

openalex publication_date 2018/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a key exchange protocol based on isogenies between ordinary elliptic curves over a finite field, first mentioned by Couveignes and investigated by Rostovtsev and Stolbunov. After presenting the fundamental notions about elliptic curves, we present the theory of complex multiplication which is the theoretical basis of this cryptosystem. Modular curves, which are an essential tool in the computations, are also introduced. We then present the protocol itself and original ideas to boost its practical performances. Finally, we discuss our implementation and practical results.

Citations

• A linear lower bound on the gonality of modular curves

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