Computer Arithmetic, IEEE Symposium on (1997)
Mar. 6, 1997 to Mar. 9, 1997
C. K. Koc , Oregon State University
T. Acar , Oregon State University
We present a new algorithm for computing a^e where a in GF(2^k) and e is a positive integer. The proposed algorithm is more suitable for implementation in software, and relies on the Montgomery multiplication in GF(2^k). The speed of the exponentiation algorithm largely depends on the availability of a fast method for multiplying two polynomials of length w defined over GF(2). The theoretical analysis and our experiments indicate that the proposed exponentiation method is at least 6 times faster than the exponentiation method using the standard multiplication when w=8. Furthermore, the availability of a 32-bit GF(2) polynomial multiplication instruction on the underlying processor would make the new exponentiation algorithm up to 37 times faster.
Galois field, polynomial arithmetic, Montgomery multiplication, squaring.
C. K. Koc, T. Acar, "Fast Software Exponentiation in GF(2^k)", Computer Arithmetic, IEEE Symposium on, vol. 00, no. , pp. 225, 1997, doi:10.1109/ARITH.1997.614899