Paper 2014/549
New Attacks on the RSA Cryptosystem
Abderrahmane Nitaj, Muhammad Rezal Kamel Ariffin, Dieaa I. Nassr, and Hatem M. Bahig
Abstract
This paper presents three new attacks on the RSA cryptosystem. The first two attacks work when k RSA public keys (Ni, ei) are such that there exist k relations of the shape eix-yi\phi(Ni)=zi or of the shape eixi-y\phi(Ni)=zi where Ni = piqi, \phi(Ni)=(pi-1)(qi-1) and the parameters x, xi, y, yi, zi are suitably small in terms of the prime factors of the moduli. We show that our attacks enable us to simultaneously factor the k RSA moduli Ni. The third attack works when the prime factors p and q of the modulus N = pq share an amount of their least significant bits (LSBs) in the presence of two decryption exponents d1 and d2 sharing an amount of their most significant bits (MSBs). The three attacks improve the bounds of some former attacks that make RSA insecure.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. AFRICACRYPT2014
- DOI
- 10.1007/978-3-319-06734-6_12
- Keywords
- RSACryptanalysisFactorizationLLL algorithmSimultaneous diophantine approximationsCoppersmith's method
- Contact author(s)
- rezal @ upm edu my
- History
- 2014-07-18: received
- Short URL
- https://ia.cr/2014/549
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2014/549,
author = {Abderrahmane Nitaj and Muhammad Rezal Kamel Ariffin and Dieaa I. Nassr and Hatem M. Bahig},
title = {New Attacks on the {RSA} Cryptosystem},
howpublished = {Cryptology {ePrint} Archive, Paper 2014/549},
year = {2014},
doi = {10.1007/978-3-319-06734-6_12},
url = {https://eprint.iacr.org/2014/549}
}
