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PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES

Authors:
Alexander Rostovtsev
Anton Stolbunov
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URL: http://eprint.iacr.org/2006/145
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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.
BibTeX
@misc{eprint-2006-21638,
  title={PUBLIC-KEY CRYPTOSYSTEM BASED ON ISOGENIES},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / public-key cryptography, elliptic curve cryptosystem, cryptosystem on isogenies of elliptic curves, isogeny star, isogeny cycle, quantum computer},
  url={http://eprint.iacr.org/2006/145},
  note={ stolbunov@list.ru 13297 received 13 Apr 2006, last revised 29 May 2006},
  author={Alexander Rostovtsev and Anton Stolbunov},
  year=2006
}