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Continued fractions and RSA with small secret exponent | | Andrej Dujella
; | | Date: |
20 Feb 2004 | | Journal: | Tatra Mt. Math. Publ. 29 (2004), 101-112. | | Subject: | Cryptography and Security; Number Theory ACM-class: E.3 | cs.CR math.NT | | 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. | | Source: | arXiv, cs.CR/0402052 | | Services: | Forum | Review | PDF | Favorites | |
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