Attacks on RSA based on lattice reduction

This thesis aims to describe in detail the Coppersmith's algorithm for fin- ding small solutions to polynomial congruences which is based on lattice basis reduction. This algorithm is a cornerstone of several attacks on the most wi- despread asymmetric cryptosystem RSA, therefore, next aim of the thesis is a description of selected attacks. As an important and current example, we can mention so-called ROCA attack which factorizes RSA modulus whenever the pri- mes are specifically crafted. At the end of the thesis, we implement both the Coppersmith's algorithm and the ROCA and several measurements and experi- ments are done. From the resulting data, one can deduce how the running time of the algorithm is affected by different parameters or what are the ideal values for these parameters in various situations.