A New Public Key Cryptosystem Based on the Cubic Pell Curve

Michel Seck; Abderrahmane Nitaj

Paper 2024/385

A New Public Key Cryptosystem Based on the Cubic Pell Curve

Michel Seck

, Ecole Polytechnique de Thies, LTISI, Senegal

Abderrahmane Nitaj

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

Abstract

Since its invention in 1978 by Rivest, Shamir and Adleman, the public key cryptosystem RSA has become a widely popular and a widely useful scheme in cryptography. Its security is related to the difficulty of factoring large integers which are the product of two large prime numbers. For various reasons, several variants of RSA have been proposed, and some have different arithmetics such as elliptic and singular cubic curves. In 2018, Murru and Saettone proposed another variant of RSA based on the cubic Pell curve with a modulus of the form . In this paper, we present a new public key cryptosystem based on the arithmetic of the cubic Pell curve with a modulus of the form . Its security is based on the hardness of factoring composite integers, and on Rabin's trapdoor one way function. In the new scheme, the arithmetic operations are performed on a cubic Pell curve which is known only to the sender and the recipient of a plaintext.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. NuTMiC 2024
DOI: 10.1007/978-3-031-82380-0_8
Keywords: Public Key Cryptography Cubic Pell curve RSA KMOV Rabin’s trapdoor
Contact author(s): mseck @ ept sn
abderrahmane nitaj @ unicaen fr
History: 2025-02-22: revised; 2024-03-01: received; See all versions
Short URL: https://ia.cr/2024/385
License: CC BY

BibTeX

@misc{cryptoeprint:2024/385,
      author = {Michel Seck and Abderrahmane Nitaj},
      title = {A New Public Key Cryptosystem Based on the Cubic Pell Curve},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/385},
      year = {2024},
      doi = {10.1007/978-3-031-82380-0_8},
      url = {https://eprint.iacr.org/2024/385}
}