ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
Minimizing hamming weight based on 1's complement of binary numbers over GF(2m)
ICACT'10 Proceedings of the 12th international conference on Advanced communication technology
Modular arithmetic and fast algorithm designed for modern computer security applications
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part III
Cryptography with fast point multiplication by using ASCII codes and its implementation
International Journal of Communication Networks and Distributed Systems
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The multiplications of common multiplicands and exponentiations of large integers with a large modulus are the primary computation operations in several well-known public key crypt systems. The Hamming weight of the multiplier or the exponent plays an important role for thecomputation efficiency. By performing complements, the Hamming weight of an integer can be reduced. Based on this concept, we propose efficient algorithms for common-multiplicand multiplications (CMM) and exponentiations. In average case, it takes\frac{\kappa }{2} + 2 \times \log (\kappa ) + 5 k-bit additions to compute the CMM. For exponentiation, the proposed method takes \frac{{5\kappa }}{4} + 2 multiplications on average, but the pre-computation for a modular multiplicative inverse is required. Combining the riginal CMM, the number multiplications can further be reduced to \frac{{9\kappa }}{8} + 2.