A Matrix Decomposition Method for Optimal Normal Basis Multiplication

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 spe...

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Bibliographic Details
Published in:IEEE transactions on computers 2016-11, Vol.65 (11), p.3239-3250
Main Authors: Kizilkale, Can, Egecioglu, Omer, Koc, Cetin Kaya
Format: Article
Language:English
Subjects:
Cryptography
Delays
Elliptic curve cryptography
gaussian normal bases
Gaussian processes
Logic gates
Massey-Omura
Matrix decomposition
type 1
type 2a
type 2b normal bases
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Summary: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.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2016.2543228