Issue No. 11 - Nov. (2016 vol. 65)
ISSN: 0018-9340
pp: 3239-3250
Can Kizilkale , Department of Computer Science, University of California, Santa Barbara, CA
Omer Egecioglu , Department of Computer Science, University of California, Santa Barbara, CA
Cetin Kaya Koc , Department of Computer Science, University of California, Santa Barbara, CA
ABSTRACT
We introduce a matrix decomposition method and prove that multiplication in GF $(2^k)$ with a Type 1 optimal normal basis for can be performed using $k^2-1$ XOR gates irrespective of the choice of the irreducible polynomial generating the field. The previous results achieved this bound only with special irreducible polynomials. Furthermore, the decomposition method performs the multiplication operation using $1.5k(k-1)$ XOR gates for Type 2a and 2b optimal normal bases, which matches previous bounds.
INDEX TERMS
Logic gates, Matrix decomposition, Delays, Standards, Gaussian processes, Elliptic curve cryptography
CITATION
Can Kizilkale, Omer Egecioglu, Cetin Kaya Koc, "A Matrix Decomposition Method for Optimal Normal Basis Multiplication", IEEE Transactions on Computers, vol. 65, no. , pp. 3239-3250, Nov. 2016, doi:10.1109/TC.2016.2543228