In this paper we propose a new protocol for Group Key Management. The protocol is based on the use of orthogonal systems in vector spaces. The main advantage in comparison to other existing multicast key management protocols consists in small communications overheads, i.e. length and number of messages to be sent, as well as key storage, especially with respect to a comparable security level. This makes the protocol especially attractive when the number of legitimate receivers is large.

Some Rabin signature schemes may be exposed to forgery; several variants are here described to counter this vulnerability. Blind Rabin signatures are also discussed.

An elementary approach is shown which derives the values of the Gauss sums over $\mathbb F_{p^r}$, $p$ odd, of a cubic character. New links between Gauss sums over different field extensions are shown in terms of factorizations of the Gauss sums themselv

Interesting properties of the partitions of a finite field 𝔽_q induced by the combination of involutions and trace maps are studied. The special features of involutions of the form , u being a fixed element of 𝔽_q, are exploited to generate pseudorandom numbers, the randomness resting on the uniform distribution of the images of zero-trace elements among the sets of non-zero trace elements of 𝔽_q.