Paper 2017/1076
A generalized attack on RSA type cryptosystems
Martin Bunder and Abderrahmane Nitaj and Willy Susilo and Joseph Tonien
Abstract
Let $N=pq$ be an RSA modulus with unknown factorization. Some variants of the RSA cryptosystem, such as LUC, RSA with Gaussian primes and RSA type schemes based on singular elliptic curves use a public key $e$ and a private key $d$ satisfying an equation of the form $ed- k\left(p^2-1\right)\left(q^2-1\right)=1$. In this paper, we consider the general equation $ex-\left(p^2-1\right)\left(q^2-1\right)y=z$ and present a new attack that finds the prime factors $p$ and $q$ in the case that $x$, $y$ and $z$ satisfy a specific condition. The attack combines the continued fraction algorithm and Coppersmith's technique and can be seen as a generalization of the attacks of Wiener and Blömer-May on RSA.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- RSACryptanalysisCoppersmith's methodContinued fractionsFactorization
- Contact author(s)
- abderrahmane nitaj @ unicaen fr
- History
- 2017-11-10: received
- Short URL
- https://ia.cr/2017/1076
- License
-
CC BY