Parallel implementation of Wiener's attack on RSA: Algorithm design and performance evaluation

Abstract

The robustness of the RSA cryptosystem is intrinsically tied to the choice of public and private keys. As pinpointed by M. Wiener, should the private decryption exponent, d, be improperly chosen-either disproportionately large or unduly small in relation to the public key n-an adversary could feasibly deduce the private keys within a practical time span. In this paper, the algorithm invented by Wiener is revisited and find a way to parallelize the attacking algorithm by using OpenMP. The algorithm is based on the proof made in Wieners article, that if d<1/3 n^(1/4), then the private key d is the denominator of one of the convergent of CF(e/n). Using a constant set of private keys (e,n), an extensive series of simulated attacks employing Wieners method was conducted on a laptop to determine the optimal thread count for executing the parallel algorithm. The results indicate that the algorithms execution speed can be enhanced by a factor of 1.5607 (rounded to five significant figures). Specifically, while the sequential version of the algorithm averaged a runtime of 3518939.04 nanoseconds, its parallel counterpart averaged 2240493.28 nanoseconds.