Correspondance du P. Marin Mersenne, ed. by PAUL TANNERY and CORNELIS DE WAARD, Volume III (1631-1633), 2nd ed., Paris, editions du Centre National de la Recherche Scientifique, 1969, pp. xiv, 660, illus., 120F. The correspondence of Mersenne (1588-1648) antedates and practically anticipates the monumental collections of scientific work given in the second part of the century in the Transaction...

We use the hyperelliptic curve C : y + xy = x + tx + x + t over the field F2[t]/(t 113 + t + 1) which was generated by Wouter Castryck, Katholieke Universiteit Leuven, Belgium. The choice of the finite field takes into account three aspects: Firstly, it allows for an order of the divisor class group of appropriate size for the desired security level. Secondly, the extension degree of F2 was cho...

We give an overview of two important families of divisibility sequences: the Lehmer–Pierce family (which generalise the Mersenne sequence) and the elliptic divisibility sequences. Recent computational work is described, as well as some of the mathematics behind these sequences.

For example, all the Fermat primes are evil while all the Mersenne primes > 3 are odious. Using direct calculations up to 10 we noticed that among the primes not exceeding n the evil primes are never in majority except for the cases n = 5 and n = 6. Moreover, in the considered limits the excess of the odious primes is not monotone but increases on the whole with records on primes 2, 13, 41, 67,...

Sequence generators obtained by linear recursions over the two-element field F2, i.e., F2-linear generators, are widely used as pseudorandom number generators. For example, the Mersenne Twister MT19937 is one of the most successful applications. An advantage of such generators is that we can assess them quickly by using theoretical criteria, such as the dimension of equidistribution with v-bit ...

Mersenne Twister (MT) is a widely-used fast pseudorandom number generator (PRNG) with a long period of 2 − 1, designed 10 years ago based on 32-bit operations. In this decade, CPUs for personal computers have acquired new features, such as Single Instruction Multiple Data (SIMD) operations (i.e., 128bit operations) and multi-stage pipelines. Here we propose a 128-bit based PRNG, named SIMD-orie...