Vector Finite Groups as Primitives for Fast Digital Signature Algorithms

Abstract

Using digital signature (DS) algorithms to perform electronic messages authentication is an issue of significant importance for geographical information systems. The most computationally efficient DS algorithms are based on elliptic curves (EC) over finite fields. However, for many practical applications more efficient DS algorithms are required. To satisfy such performance requirements a new type of the finite groups is proposed as primitive for DS schemes. The elements of the proposed groups are vectors defined over the ground finite field. The group operation is the vector multiplication defined with some basis vector multiplication tables the characteristic feature of which is the use of expansion coefficients. It has been shown that the vector groups possess the multidimensionyclic structure and in special cases the dimension of the cyclicity is μ = 1. In such special cases the vector finite fields (VFFs) are formed. The DS algorithms based on EC over VFFs provides performance significantly higher than the performance of the known EC-based algorithms. Fast DS algorithms based on computations in vector finite groups corresponding to the case μ ≥ 2have also been proposed. KeywordsDigital signatureVector finite groupsMultidimension cyclicityVector finite fieldsElliptic curves