Group schemes of prime order

Algebraic structure of association schemes of prime order

Finite groups of prime order must be cyclic. It is natural to ask what about association schemes of prime order. In this paper, we will give an answer to this question. An association scheme of prime order is commutative, and its valencies of nontrivial relations and multiplicities of nontrivial irreducible characters are constant. Moreover, if we suppose that the minimal splitting field is an ...

Association schemes of prime order and their splitting fields

Extensions of the Representation Modules of a Prime Order Group

For the ring R of integers of a ramified extension of the field of p-adic numbers and a cyclic group G of prime order p we study the extensions of the additive groups of R-representations modules of G by the group G. Let T be the field of fractions of a principal ideal domain R, F a field which contains R, let G be a finite group and Γ a matrix R-representation of G. Let M be an RG-module, whic...

Group-arcs of Prime Power Order on Cubic Curves

This article continues the characterization of elliptic curves among sets in a finite plane which are met by lines in at most three points. The case treated here is that of sets of prime-power cardinality. 1 Notation GF (q) the finite field of q elements PG(2, q) the projective plane over GF (q) PG(1)(2, q) the set of lines in PG(2, q) P(X) the point of PG(2, q) with coordinate vector X PQ the ...

Identity based broadcast encryption with group of prime order

Identity Based Broadcast Encryption (IBBE) is a cryptographic primitive, which allows a center to transmit encrypted data over a broadcast channel to a large number of users such that only a select subset of privileged users can decrypt it. In this paper, based on bilinear groups, we propose a secure IBBE scheme with a constant-size system parameters, private keys and cipher texts. This constru...