Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Montgomery Multiplier and Squarer for a Class of Finite Fields
IEEE Transactions on Computers
A Scalable Architecture for Montgomery Multiplication
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
A Scalable Architecture for Modular Multiplication Based on Montgomery's Algorithm
IEEE Transactions on Computers
Montgomery multiplication and squaring algorithms in GF(2k)
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Optimizing robustness while generating shared secret safe primes
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
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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.