A cryptographic library for the Motorola DSP56000
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A common-multiplicand method to the Montgomery algorithm for speeding up exponentiation
Information Processing Letters
Optimal Left-to-Right Binary Signed-Digit Recoding
IEEE Transactions on Computers - Special issue on computer arithmetic
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis
IEEE Transactions on Computers
High-Radix Montgomery Modular Exponentiation on Reconfigurable Hardware
IEEE Transactions on Computers
Computer Arithmetic: Principles, Architecture and Design
Computer Arithmetic: Principles, Architecture and Design
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
Enhanced Montgomery Multiplication
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Fast modular exponentiation of large numbers with large exponents
Journal of Systems Architecture: the EUROMICRO Journal
Fast Algorithms for Common-Multiplicand Multiplication and Exponentiation by Performing Complements
AINA '03 Proceedings of the 17th International Conference on Advanced Information Networking and Applications
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
Hardware Complexity of Modular Multiplication and Exponentiation
IEEE Transactions on Computers
Digital filter synthesis based on an algorithm to generate all minimal signed digit representations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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In this paper, a new parallel Montgomery binary exponentiation algorithm was proposed. This algorithm is based on the Montgomery modular reduction technique, binary method, common-multiplicand-multiplication (CMM) algorithm, and the canonical-signed-digit recoding (CSD) technique. By using the CMM algorithm of computing the common part from two modular multiplications, the same common part in two modular multiplications can be computed once rather twice, we can thus improve the efficiency of the binary exponentiation algorithm by decreasing the number of modular multiplications. Furthermore, by using the proposed parallel CMM-CSD Montgomery binary exponentiation algorithm, the total number of single-precision multiplications can be reduced by about 66.7% and 30% as compared with the original Montgomery algorithm and the Ha-Moon's improved Montgomery algorithm, respectively.