Continued fractions and RSA with small secret exponent
Abstract
Description
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.
11 pages, to appear in Tatra Mt. Math. Publ
11 pages, to appear in Tatra Mt. Math. Publ