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Mathematics > Number Theory

arXiv:1804.10128 (math)
[Submitted on 26 Apr 2018]

Title:Accelerating the Couveignes Rostovtsev Stolbunov key exchange protocol

Authors:Jean Kieffer
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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.
Comments: In French. Rapport de stage de Master 2 Mathématiques fondamentales, Université Paris VI
Subjects: Number Theory (math.NT); Cryptography and Security (cs.CR)
Cite as: arXiv:1804.10128 [math.NT]
  (or arXiv:1804.10128v1 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1804.10128

Submission history

From: Jean Kieffer [view email]
[v1] Thu, 26 Apr 2018 15:59:54 UTC (58 KB)
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