Paper 2021/1632
Cryptanalysis of RSA Variants with Primes Sharing Most Significant Bits
Meryem Cherkaoui-Semmouni, Abderrahmane Nitaj, Willy Susilo, and Joseph Tonien
Abstract
We consider four variants of the RSA cryptosystem with an RSA modulus $N=pq$ where the public exponent $e$ and the private exponent $d$ satisfy an equation of the form $ed-k\left(p^2-1\right)\left(q^2-1\right)=1$. We show that, if the prime numbers $p$ and $q$ share most significant bits, that is, if the prime difference $|p-q|$ is sufficiently small, then one can solve the equation for larger values of $d$, and factor the RSA modulus, which makes the systems insecure.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Information Security Conference ISC 2021
- DOI
- 10.1007/978-3-030-91356-4_3
- Keywords
- RSA variantsContinued fractionsCoppersmith's methodLattice reduction
- Contact author(s)
- abderrahmane nitaj @ unicaen fr
- History
- 2021-12-17: received
- Short URL
- https://ia.cr/2021/1632
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1632,
author = {Meryem Cherkaoui-Semmouni and Abderrahmane Nitaj and Willy Susilo and Joseph Tonien},
title = {Cryptanalysis of {RSA} Variants with Primes Sharing Most Significant Bits},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1632},
year = {2021},
doi = {10.1007/978-3-030-91356-4_3},
url = {https://eprint.iacr.org/2021/1632}
}
