Multiplication in a Galois Ring

Date

2015-09-18

Author

AKLEYLEK, SEDAT
Özbudak, Ferruh

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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.

Subject Keywords

Sequential multiplier, Polynomial multiplication, Toeplitz matrix-vector multiplication, Subquadratic space complexity multiplication, Galois ring

URI

https://hdl.handle.net/11511/53661

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Department of Mathematics, Conference / Seminar

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Citation Formats

S. AKLEYLEK and F. Özbudak, “Multiplication in a Galois Ring,” 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53661.