Paper 2006/145

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.

Metadata
Available format(s)
PDF PS
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
2006-04-13: received
See all versions
Short URL
https://ia.cr/2006/145
License
Creative Commons Attribution
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},
      url = {https://eprint.iacr.org/2006/145}
}
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