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

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.

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