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
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Fast exponentiation with precomputation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Fast Multicomputation with Asynchronous Strategy
IEEE Transactions on Computers
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Multi-computations in finite groups, such as multiexponentiations and multi-scalar multiplications, are very important in ElGamal-like public key cryptosystems. Algorithms to improve multi-computations can be classified into two main categories: precomputing methods and recoding methods. The first one uses a table to store the precomputed values, and the second one finds a better binary signed-digit (BSD) representation. In this article, we propose a new integer similarity strategy for multi-computations. The proposed strategy can aid with precomputing methods or recoding methods to further improve the performance of multi-computations. Based on the integer similarity strategy, we propose two efficient algorithms to improve the performance for BSD sparse forms. The performance factor can be improved from 1.556 to 1.444 and to 1.407, respectively.