Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem

Abderrahmane Nitaj; Willy Susilo; Joseph Tonien

Paper 2019/1052 Original: eprint.iacr.org/2019/1052 ↗

Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem

Abderrahmane Nitaj

Willy Susilo

Joseph Tonien

Abstract

This paper presents two new improved attacks on the KMOV cryptosystem. KMOV is an encryption algorithm based on elliptic curves over the ring ${\mathbb{Z}}_N$ where $N=pq$ is a product of two large primes of equal bit size. The first attack uses the properties of the convergents of the continued fraction expansion of a specific value derived from the KMOV public key. The second attack is based on Coppersmith's method for finding small solutions of a multivariate polynomial modular equation. Both attacks improve the existing attacks on the KMOV cryptosystem.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2019-09-18: last updated; 2019-09-18: published
Short URL: https://ia.cr/2019/1052
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2019/1052,
      author = {Abderrahmane Nitaj and Willy Susilo and Joseph Tonien},
      title = {Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1052},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1052}
}