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A New RSA Variant Based on Elliptic Curves
Version 1
: Received: 1 June 2023 / Approved: 1 June 2023 / Online: 1 June 2023 (15:37:57 CEST)
A peer-reviewed article of this Preprint also exists.
Boudabra, M.; Nitaj, A. A New RSA Variant Based on Elliptic Curves. Cryptography 2023, 7, 37. Boudabra, M.; Nitaj, A. A New RSA Variant Based on Elliptic Curves. Cryptography 2023, 7, 37.
Abstract
We propose a new scheme based on ephemeral elliptic curves over the ring Z/nZ where n=pq is an RSA modulus with p=up^2+vp^2, q=uq^2+vq^2, up≡uq≡3(mod4). 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.
Keywords
Public key Cryptography; RSA; KMOV; Demytko’s scheme; Elliptic curves; Continued fractions; Coppersmith’s method.
Subject
Computer Science and Mathematics, Information Systems
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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