Proceedings on Advances in cryptology---CRYPTO '86
Exponentiating faster with addition chains
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
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
Comparison of three modular reduction functions
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Modular Exponentiation Using Recursive Sums of Residues
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Low-Weight Polynomial Form Integers for Efficient Modular Multiplication
IEEE Transactions on Computers
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A modular exponentiation is one of the most important operations in public-key cryptography. However, it takes much time because the modular exponentiation deals with very large operands as 512-bit integers. The modular exponentiation is composed of repetition of modular multiplications. Therefore, we can rcducc the execution time of it by reducing thc execution time of each modular multiplication. In this paper, we propose two fast modular multiplication algorithms. One is for modular multiplications between different integers, and the other is for modular squarings. These proposed algorithms require single-precision multiplications fewer than those of Montgomery modular multiplication algorithms by 1/2 and 1/3 times, respectively. Implementing on PC, proposed algorithms reduce execution times by 50% and 30% compared with Montgomery algorithms, respectively.