Algorithmics: theory & practice
Algorithmics: theory & practice
Hardware Implementation of Montgomery's Modular Multiplication Algorithm
IEEE Transactions on Computers
Modulo Reduction in Residue Number Systems
IEEE Transactions on Parallel and Distributed Systems
High-Radix Montgomery Modular Exponentiation on Reconfigurable Hardware
IEEE Transactions on Computers
An RNS Montgomery Modular Multiplication Algorithm
IEEE Transactions on Computers
The Chinese Remainder Theorem and its application in a high-speed RSA crypto chip
ACSAC '00 Proceedings of the 16th Annual Computer Security Applications Conference
Simplifying Quotient Determination in High-Radix Modular Multiplication
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Modular Multiplication and Base Extensions in Residue Number Systems
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
A Scalable Architecture for Modular Multiplication Based on Montgomery's Algorithm
IEEE Transactions on Computers
ICA3PP '09 Proceedings of the 9th International Conference on Algorithms and Architectures for Parallel Processing
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Large integer Modular Multiplication and Exponentiation (MM and ME) are the foundation of most publickey cryptosystems, specifically RSA, Diffie-Helleman, ElGamal and the Elliptic Curve Cryptosystems. Thus MM algorithms have been studied widely and extensively. Most of the work is based on the well known Montgomery Multiplication Method and its variants, which require standard multiplication operations. Despite their better complexity orders, Karatsuba and FFT algorithms seem to be rarely used for hardware implementation. In this paper, we review their hardware complexity and propose original implementations of MM and ME that become useful for 24-bit operators (Karatsuba algorithm) or 373-bit operators (FFT algorithm).