A Full RNS Implementation of RSA
IEEE Transactions on Computers
Hardware Complexity of Modular Multiplication and Exponentiation
IEEE Transactions on Computers
Exploiting the Power of GPUs for Asymmetric Cryptography
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Revisiting sum of residues modular multiplication
Journal of Electrical and Computer Engineering
Optimizing robustness while generating shared secret safe primes
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
The CRNS framework and its application to programmable and reconfigurable cryptography
ACM Transactions on Architecture and Code Optimization (TACO) - Special Issue on High-Performance Embedded Architectures and Compilers
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Abstract: We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an effect corresponding to a redundant high-radix implementation is achieved, due to the carry-free nature of residue arithmetic. The actual computation in the multiplication takes place in constant time, where the unit of time is a few simple residue operations. However, it is necessary twice to convert values from one residue system into another, operations which take {\cal O}(n) time on {\cal O}(n) processors, where n is the number of moduli in the RNS systems. Thus these conversions are the bottlenecks of the method, and any future improvements in RNS base conversions, or the use of particular residue systems, can immediately be applied.