### PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES

Alexander Rostovtsev and Anton Stolbunov

##### Abstract

A new general mathematical problem, suitable for public-key cryptosystems, is proposed: morphism computation in a category of Abelian groups. In connection with elliptic curves over finite fields, the problem becomes the following: compute an isogeny (an algebraic homomorphism) between the elliptic curves given. The problem seems to be hard for solving with a quantum computer. ElGamal public-key encryption and Diffie-Hellman key agreement are proposed for an isogeny cryptosystem. The paper describes theoretical background and a public-key encryption technique, followed by security analysis and consideration of cryptosystem parameters selection. A demonstrative example of encryption is included as well.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
public-key cryptographyelliptic curve cryptosystemisogeny starisogeny cyclequantum computer
Contact author(s)
stolbunov @ list ru
History
2006-05-29: last of 3 revisions
See all versions
Short URL
https://ia.cr/2006/145

CC BY

BibTeX

@misc{cryptoeprint:2006/145,
author = {Alexander Rostovtsev and Anton Stolbunov},
title = {PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES},
howpublished = {Cryptology ePrint Archive, Paper 2006/145},
year = {2006},
note = {\url{https://eprint.iacr.org/2006/145}},
url = {https://eprint.iacr.org/2006/145}
}

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