Continued fractions and RSA with small secret exponent
<|reference_start|>Continued fractions and RSA with small secret exponent: 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.<|reference_end|>
@article{dujella2004continued,
    title={Continued fractions and RSA with small secret exponent},
    author={Andrej Dujella},
    journal={Tatra Mt. Math. Publ. 29 (2004), 101-112.},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0402052},
    primaryClass={cs.CR math.NT}
}