Continued fractions and RSA with small secret exponent

Details Continued fractions and RSA with small secret exponent Continued fractions and RSA with small secret exponent

2004-02-20

arxiv.org/abs/cs/0402052v1

Tatra Mt. Math. Publ. 29 (2004), 101-112.

Computer Science

Cryptography and Security

11 pages, to appear in Tatra Mt. Math. Publ

Scientific paper

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.

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