Continued fractions and RSA with small secret exponent
Cryptography and Security
2007-05-23 v1 Number Theory
Abstract
Extending the classical Legendre's result, we describe all solutions of the inequality |x - a/b| < c/b^2 in terms of convergents of continued fraction expansion of x. Namely, we show that a/b = (rp_{m+1} +- sp_m) / (rq_{m+1} +- sq_m) for some nonnegative integers m,r,s such that rs < 2c. As an application of this result, we describe a modification of Verheul and van Tilborg variant of Wiener's attack on RSA cryptosystem with small secret exponent.
Cite
@article{arxiv.cs/0402052,
title = {Continued fractions and RSA with small secret exponent},
author = {Andrej Dujella},
journal= {arXiv preprint arXiv:cs/0402052},
year = {2007}
}
Comments
11 pages, to appear in Tatra Mt. Math. Publ