<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">Correction: the Mathematics Colloquium is on <b class="">Wednesday at 10:40.</b></div><div class=""><span class="">Kind regards,</span></div><div class=""><span class="">Michel.<br class=""></span><span class=""><br class=""></span><blockquote type="cite" class="">You are cordially invited to the Sabanci Mathematics Colloquium.<br class=""><br class="">Guest: Andrej Dujella<br class="">Title: Applications of Diophantine approximations algorithms in cryptanalysis of RSA<br class="">Room / Date / Time: FENS G055 / <b class="">27 Nov</b> / 10:40-11:30<br class=""><br class="">Abstract: To speed up the RSA decryption one may try to use small secret decryption<br class="">exponent d. The choice of a small d is especially interesting when there is a large<br class="">difference in computing power between two communicating devices. However,<br class="">in 1990, Wiener showed that if d < n^(1/4), where n = pq is the modulus of the<br class="">cryptosystem, then there exist a polynomial time attack on the RSA. He showed<br class="">that d is the denominator of some convergent p_m/q_m of the continued fraction<br class="">expansion of e/n, and therefore d can be computed efficiently from the public key (n,e).<br class="">In this talk, we will discuss similar attacks on RSA and its variants<br class="">which use results and algorithms from Diophantine approximations, such as<br class="">Worley's extension of the classical Legendre's theorem on continued fractions <br class="">and LLL-algorithm for computing short vectors in lattices. <br class=""><br class="">Bio: Andrej Dujella is professor at the University of Zagreb and Fellow of the Croatian Academy of Sciences and Arts. He received a PhD in mathematics from the University of Zagreb in 1996 and Doctor Honoris<br class="">Causa of University of Debrecen in 2017. His research interests include Diophantine equations, elliptic curves, polynomial root separation, and applications of Diophantine approximation to<br class="">cryptography. <br class=""><br class=""><br class="">Kind regards,<br class="">Michel Lavrauw</blockquote></div></body></html>