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
Cryptography and network security (2nd ed.): principles and practice
Cryptography and network security (2nd ed.): principles and practice
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
A Fast Algorithm for Multiplicative Inversion in GF(2m) Using Normal Basis
IEEE Transactions on Computers
Computer Arithmetic Algorithms
Computer Arithmetic Algorithms
Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
Efficient elliptic curve scalar multiplication algorithms resistant to power analysis
Information Sciences: an International Journal
Should one always use repeated squaring for modular exponentiation?
Information Processing Letters
Fast exponentiation based on common-multiplicand-multiplication and minimal-signed-digit techniques
International Journal of Computer Mathematics
New directions in cryptography
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
Information Sciences: an International Journal
Improving timing attack on RSA-CRT via error detection and correction strategy
Information Sciences: an International Journal
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The modular exponentiation is a common operation for scrambling secret data and is used by several public-key cryptosystems, such as the RSA scheme and DSS digital signature scheme. However, the calculations involved in modular exponentiation are time-consuming especially when performed in software. In this paper, we propose an efficient CMM-MSD Montgomery algorithm by utilizing the Montgomery modular reduction method, common-multiplicand-multiplication (CMM) method, and minimal-signed-digit (MSD) recoding technique for fast modular exponentiation. By using the technique of recording the common signed-digit representations in the grouped substrings of exponent, our algorithm can improve the efficiency of both the original CMM exponentiation algorithm and the Montgomery multiplication algorithm. The fast modular exponentiation algorithm developed in this paper can be easily implemented in general signed-digit computing machine, and is therefore well suited for parallel implementation to fast evaluating modular exponentiation. Moreover, by using the proposed CMM-MSD Montgomery algorithm, on average the total number of single-precision multiplications can be reduced by about 38.9% and 26.68% as compared with Dusse-Kaliski's Montgomery algorithm and Ha-Moon's Montgomery algorithm, respectively.