IACR News item: 24 July 2015
Can K{\\i}z{\\i}lkale, \\\"{O}mer E\\v{g}ecio\\v{g}lu, \\c{C}etin Kaya Ko\\c{c}
ePrint Report
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.
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