The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A survey of fast exponentiation methods
Journal of Algorithms
Complexity and Fast Algorithms for Multiexponentiations
IEEE Transactions on Computers
Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Algorithms for Multi-Exponentiation Based on Complex Arithmetic
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Left-to-Right Optimal Signed-Binary Representation of a Pair of Integers
IEEE Transactions on Computers
Fast multi-computations with integer similarity strategy
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
A note on asynchronous multi-exponentiation algorithm using binary representation
Information Processing Letters
| Hi-index | 14.98 |
We propose a new strategy to improve the performance of multicomputations, such as computing xA + yBin an additive group or a^{x}b^{y}in a multiplicative group. This new strategy is called asynchronous strategy. In each iteration, it tries to compute partial results by pairing nearby zero and nonzero bits. The new strategy can be applied to any binary code of xand yto further reduce the computational cost. However, our experiments show that sparse signed-digit code can achieve minimum computational cost. The algorithms using the asynchronous strategy need only O(h)extra registers when they try to do computation with bits which are hpositions apart.