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
A common-multiplicand method to the Montgomery algorithm for speeding up exponentiation
Information Processing Letters
Complexity and Fast Algorithms for Multiexponentiations
IEEE Transactions on Computers
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Computer Arithmetic Algorithms
Computer Arithmetic Algorithms
Cryptography and Network Security: Principles and Practice
Cryptography and Network Security: Principles and Practice
Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
Modified Radix-2 Montgomery Modular Multiplication to Make It Faster and Simpler
ITCC '05 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume I - Volume 01
Information Sciences: an International Journal
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In this paper, an improved common-multiplicand-multiplication algorithm is proposed, utilizing the binary exponentiation method and minimal-signed-digit recoding technique for fast exponentiation. By adopting the recoding technique on the common signed-digit representations in the grouped exponent substrings, the proposed algorithm provides an efficient exponentiation method. The proposed algorithm achieves better performance in modern exponentiation methods by decreasing the overall computational complexity. In particular, the proposed method is very suitable for parallel processing systems to improve the efficiency of exponentiation operation.