PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES

Alexander Rostovtsev; Anton Stolbunov

Paper 2006/145 Original: eprint.iacr.org/2006/145 ↗

PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES

Alexander Rostovtsev

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
Category: Public-key cryptography
Publication info: Preprint.
History: 2006-05-29: last updated; 2006-04-13: published
Short URL: https://ia.cr/2006/145
License: https://creativecommons.org/licenses/by/4.0/

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}
}