Lines Matching full:primes
3229 The system begins with with two primes $p$ and $q$ and their product $N = pq$. The order or \textit{Euler totient} of the
3241 Currently RSA is a difficult system to cryptanalyze provided that both primes are large and not close to each other.
4884 two phases. First it will perform trial division by the first few primes. Second it will perform eight rounds of the
4890 When making random primes the trial division step is in fact an optimized implementation of \textit{Implementation of Fast RSA Key Generation on Smart Cards}\footnote{Chenghuai Lu, Andre L. M. dos Santos and Francisco R. Pimentel}.
4891 In essence a table of machine-word sized residues are kept of a candidate modulo a set of primes. When the candidate
4897 instance, in RSA two primes $p$ and $q$ are required. The order of the multiplicative sub-group (modulo $pq$) is given
4900 the multi-prime RSA. Suppose $q = rs$ for two primes $r$ and $s$ then $\phi(pq) = (p - 1)(r - 1)(s - 1)$ which clearly is
