Multiplication in a Galois Ring

Akleylek S., ÖZBUDAK F.

7th International Workshop on Signal Design and Its Applications in Communications (IWSDA), Bengaluru, India, 13 - 19 September 2015, pp.28-32 identifier

  • Publication Type: Conference Paper / Full Text
  • City: Bengaluru
  • Country: India
  • Page Numbers: pp.28-32
  • Keywords: Galois ring, subquadratic space complexity multiplication, Toeplitz matrix-vector multiplication, polynomial multiplication, sequential multiplier, CHINESE REMAINDER THEOREM, EXTENSION, FIELDS, CODES
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we focus on the efficient multiplication in a Galois ring of the size 4(n), where n is a positive integer. We consider to adapt the finite field multiplication methods to the Galois ring multiplication. We give the polynomial multiplication in the Galois ring as a Toeplitz matrix-vector multiplication design with a modification used in finite fields of characteristic two. By this method, we reduce the multiplication complexity. Note that the proposed approach can be easily generalized to Galois rings of arbitrary characteristic. To the best of our knowledge, this is the first study to have a subquadratic space complexity to multiply two elements in the Galois rings.