Publication Type

Journal Article

Version

publishedVersion

Publication Date

2-2021

Abstract

RSA is a well known standard algorithm used by modern computers to encrypt and decrypt messages. In some applications, to save the decryption time, it is desirable to have a short secret key d compared to the modulus N. The first significant attack that breaks RSA with short secret key given by Wiener in 1990 is based on the continued fraction technique and it works with d < 1/4 root 18 N-.(25). A decade later, in 2000, Boneh and Durfee presented an improved attack based on lattice technique which works with d < N-.(292). Until this day, Boneh-Durfee attack remain as the best attack on RSA with short secret key. In this paper, we revisit the continued fraction technique and propose a new attack on RSA. Our main result shows that when d < root t (2 root 2 + 8/3) N-.(75)/root e, where e is the public exponent and t is a chosen parameter, our attack can break the RSA with the running time of O(tlog (N)). Our attack is especially well suited for the case where e is much smaller than N. When e approximate to N, the Boneh-Durfee attack outperforms ours. As a result, we could simultaneously run both attacks, our new attack and the classical Boneh-Durfee attack as a backup.

Keywords

RSA, Wiener, Boneh-Durfee, Short key attack, Continued fractions

Discipline

Information Security | Theory and Algorithms

Research Areas

Information Systems and Management

Publication

Computer Standards and Interfaces

Volume

74

First Page

1

Last Page

6

ISSN

0920-5489

Identifier

10.1016/j.csi.2020.103470

Publisher

Elsevier

Additional URL

http://doi.org/10.1016/j.csi.2020.103470

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