In electronic subscription and pay TV systems, data can be organized and encrypted using symmetric key algorithms according to predefined time periods and user privileges and then broadcast to users.â€¦ (More)

We present a detailed analysis of SQUFOF, Daniel Shanksâ€™ Square Form Factorization algorithm. We give the average time and space requirements for SQUFOF. We analyze the effect of multipliers, eitherâ€¦ (More)

This paper deals with variations of the Quadratic Sieve integer factoring algorithm. We describe what we believe is the rst implementation of the Hypercube Multiple Polynomial Quadratic Sieve withâ€¦ (More)

Much asymptotic analysis has been devoted to factoring algorithms. We present a practical analysis of the complexity of the elliptic curve algorithm, suggesting optimal parameter selection andâ€¦ (More)

The fractional parts of the Bernoulli numbers are dense in the interval (0, 1). For every positive integer k, the set of all m for which B 2. has the same fractional part as B 21 has positiveâ€¦ (More)

Ab s t r a c t We consi der the probl emof di st ri but i ng potent i al l y dangerous i nf ormat i on to a number of compet i ng part i es. As a prime exampl e, we f ocus on the i ssue of di st riâ€¦ (More)

We add to the heuristic and empirical evidence for a conjecture of Gillies about the distribution of the prime divisors of Mersenne numbers. We list some large prime divisors of Mersenne numbers Mpâ€¦ (More)