A New RSA Variant Based on Elliptic Curves

Maher Boudabra; Abderrahmane Nitaj

Paper 2023/1299

A New RSA Variant Based on Elliptic Curves

Maher Boudabra, Department of Computing and Mathematics, King Fahd University of Petroleum and Minerals, Saudi Arabia

Abderrahmane Nitaj

, Normandie Univ, UNICAEN, CNRS, LMNO, 14000 Caen, France

Abstract

We propose a new scheme based on ephemeral elliptic curves over the ring where is an RSA modulus with , , . The new scheme is a variant of both the RSA and the KMOV cryptosystems. The scheme can be used for both signature and encryption. We study the security of the new scheme and show that is immune against factorization attacks, discrete logarithm problem attacks, sum of two squares attacks, sum of four squares attacks, isomorphism attacks, and homomorphism attacks. Moreover, we show that the private exponents can be much smaller than the ordinary exponents for RSA and KMOV, which makes the decryption phase in the new scheme more efficient.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. MDPI Cryptography 2023
DOI: doi.org/10.3390/ cryptography7030037
Keywords: Public key Cryptography RSA KMOV Elliptic curves Continued fractions Coppersmith's method.
Contact author(s): maher boudabra @ kfupm edu sa
abderrahmane nitaj @ unicaen fr
History: 2023-09-02: approved; 2023-08-31: received; See all versions
Short URL: https://ia.cr/2023/1299
License: CC0

BibTeX

@misc{cryptoeprint:2023/1299,
      author = {Maher Boudabra and Abderrahmane Nitaj},
      title = {A New {RSA} Variant Based on Elliptic Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1299},
      year = {2023},
      doi = {doi.org/10.3390/ cryptography7030037},
      url = {https://eprint.iacr.org/2023/1299}
}