# An RNS Montgomery modular multiplication algorithm

@article{Bajard1997AnRM, title={An RNS Montgomery modular multiplication algorithm}, author={Jean-Claude Bajard and Laurent-St{\'e}phane Didier and Peter Kornerup}, journal={Proceedings 13th IEEE Sympsoium on Computer Arithmetic}, year={1997}, pages={234-239} }

The authors present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to mixed radix, and is performed using a residue number system. By choosing the moduli of the RNS system reasonably large, and implementing the system an a ring of fairly simple processors, an effect corresponding to a redundant high-radix implementation is achieved. The algorithm call be implemented to run in O(n) time on O(n) processors, where n is the number of…

## 181 Citations

Montgomery Modular Multiplication inResidue

- Computer Science, Mathematics
- 2000

A new RNS modular multiplication for very large operands is presented, based on Montgomery's method adapted to residue arithmetic, which achieves an effect corresponding to a redundant high-radix implementation by choosing the moduli of the RNS system reasonably large.

Modular multiplication and base extensions in residue number systems

- Computer Science, MathematicsProceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001
- 2001

A new RNS modular multiplication for very large operands is presented, based on Montgomery's (1985) method adapted to residue arithmetic, which achieves an effect corresponding to a redundant high-radix implementation by choosing the moduli of the RNS system reasonably large.

An improved RNS Montgomery modular multiplier

- Computer Science, Mathematics2010 International Conference on Computer Application and System Modeling (ICCASM 2010)
- 2010

An improved RNS modular multiplication for large operands is presented, using Montgomery's method together with the Chinese Remainder Theorem, and is performed using a Residue Number System.

Improved RNS Montgomery Modular Multiplication with Residue Recovery

- Computer Science, Mathematics
- 2014

A new residue recovery method is proposed that directly employs binary system rather than mixed radix system to perform RNS modular multiplications, in which it is more efficient than parallel base conversion method.

Some improvements on RNS Montgomery modular multiplication

- Computer Science, MathematicsSPIE Optics + Photonics
- 2000

An algorithmic parallel algorithm is proposed for this translation from RNS to Mixed Radix, using a result that comes from an RNS division algorithm, and obtaining in a logarithmic time an approximation of the Mixed radix representation.

Montgomery modular multiplication and exponentiation in the residue number system

- Computer Science, MathematicsConference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020)
- 1999

A new sequential modular multiplication method suitable for smart cards is proposed which achieves the best known operation count for an all-modular-arithmetic approach in the residue number system (RNS).

Implementation of RSA Algorithm Based on RNS Montgomery Multiplication

- Computer ScienceCHES
- 2001

An implementation of RSA cryptosystem using the RNS Montgomery multiplication is described, and an implementation method using the Chinese Remainder Theorem (CRT) is presented.

Cox-Rower Architecture for Fast Parallel Montgomery Multiplication

- Computer Science, MathematicsEUROCRYPT
- 2000

The main contribution of this paper is to provide a new RNS base extension algorithm, which can be adapted to an existing standard radix interface of RSA cryptosystem.

An iterative modular multiplication algorithm in RNS

- Computer Science, MathematicsAppl. Math. Comput.
- 2005

Parallel Modular Multiplication Algorithm in Residue Number System

- Computer SciencePPAM
- 2003

A novel method for the parallelization of the modular multiplication algorithm in the Residue Number System (RNS) is presented, which only requires L moduli which is half the number needed in the previous algorithm.

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