Given a finite group G, let PG(s) be the probability that s randomly chosen elements generate G, and let H be a finite group with PG(s) = PH(s). We show that if the nonabelian composition factors of G and H are PSL(2, p) for some non-Mersenne prime p ≥ 5, then G and H have the same non-Frattini chief factors. Mathematics Subject Classification (2010). 20D06.

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...

Steganography over real-time streaming media is a novel and promising research subject. This paper performs steganography over a typical streaming media, Voice over IP (VoIP), and suggests a new covert communication scheme for interactive secret messages. To resist the statistical detection, a sophisticated compounded pseudorandom sequence, produced by a compounded pseudorandom number generator...

In this correspondence, we present a construction, in a closed form, for an optimal family of 2m binary sequences of period 2 1 with respect to Welch’s bound, whenever there exists a balanced binary sequence of period 2m 1 with ideal autocorrelation property using the trace function. This construction enables us to reinterpret a small set of Kasami and No sequences as a family constructed from ...

This paper describes a new method to speed up Fp-arithmetic for Barreto-Naehrig (BN) curves. We explore the characteristics of the modulus defined by BN curves and choose curve parameters such that Fp multiplication becomes more efficient. The proposed algorithm uses Montgomery reduction in a polynomial ring combined with a coefficient reduction phase using a pseudo-Mersenne number. With this a...

We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree of variables in various forms of redundancy-free boolean conjunctive normal forms (clause-sets). Let μvd(F ) ∈ N for a clause-set F denote the minimum variable-degree, the minimum of the number of occurrences of a variable. A central result is the upper bound σ(F ) + 1 ...