# Analyzing and comparing Montgomery multiplication algorithms

@article{Ko1996AnalyzingAC, title={Analyzing and comparing Montgomery multiplication algorithms}, author={Çetin Kaya Koç and Tolga Acar and Burton S. Kaliski}, journal={IEEE Micro}, year={1996}, volume={16}, pages={26-33} }

Montgomery multiplication methods constitute the core of modular exponentiation, the most popular operation for encrypting and signing digital data in public-key cryptography. In this article, we study the operations involved in computing the Montgomery product, describe several high-speed, space-efficient algorithms for computing MonPro(a, b), and analyze their time and space requirements. Our focus is to collect several alternatives for Montgomery multiplication, three of which are new…

## 595 Citations

Achieving NTRU with Montgomery Multiplication

- Computer Science, MathematicsIEEE Trans. Computers
- 2003

The unified design is capable of supporting a majority of public-key cryptosystems such as NTRU, RSA, Diffie-Hellman key exchange, and elliptic curve schemes, among others, and is highly efficient in terms of area and speed.

Embedded Public-key Cryptosystems Via Enhanced Montgomery Multiplication

- Computer Science2007 IEEE International Symposium on Industrial Electronics
- 2007

The proposed approach improves on the basic FIPS formulation by removing sources of inefficiencies, and boosts the exploitation of the computing resources in digital hardware, and confirms both the method effectiveness in increasing efficiency and its general validity.

Performance analysis of Montgomery multiplier for public key cryptosystem

- Computer Science, Mathematics2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT)
- 2013

A 256-bit Modular multiplier using Montgomery Reduction Algorithm in VHDL is implemented using Montgomery reduction Algorithm for modular multiplication in RSA Cryptography and Elliptical Curve Cryptography.

Tripartite Modular Multiplication using Toom-Cook Multiplication

- Computer Science, Mathematics
- 2012

This paper presents an efficient modular multiplication algorithm for large integer that integrates with three existing algorithm, Barrett Algorithm and Montgomery algorithm for modular multiplication, Toom-Cook algorithm for multiplication and done in parallel way so that enhance the performance.

Modified Montgomery Modular Inversion with Reduced Number of Multiplications

- Mathematics, Computer ScienceTENCON 2006 - 2006 IEEE Region 10 Conference
- 2006

In this paper, a modified algorithm to compute Montgomery modular Inverse that requires less number of Montgomery modular multiplications compared to the best known methods in literature is proposed.…

Montgomery modular multiplication architecture for public key cryptosystems

- Computer Science, MathematicsIEEE Workshop onSignal Processing Systems, 2004. SIPS 2004.
- 2004

A novel hardware architecture of the coarsely integrated hybrid scanning (CIHS) algorithm which performs Montgomery modular multiplication, and to the authors' knowledge, these are the first performance figures for a hardware CIHS algorithm architecture to be reported in the literature.

Performance comparison of multipliers based on Square and Multiply and montgomery algorithms

- Computer Science, Mathematics2014 International Conference on Green Computing Communication and Electrical Engineering (ICGCCEE)
- 2014

A k - partition method for Montgomery multiplication is thoroughly studied and analysed, and another method for modular exponentiation - Square and Multiply method is implemented.

Design and Implementation of Fast Multiplication Algorithms in Public Key Cryptosystems for Smart Cards

- Computer Science, Mathematics
- 2003

Three different integer multiplication techniques, as used in conjunction with various public-key cryptographic algorithms as used a standard smart card, are investigated to obtain exact numerical results for standard multiplication algorithms used in industry.

Achieving NTRU with

- Computer Science, Mathematics
- 2003

A new unified architecture is proposed that utilizes the Montgomery Multiplication algorithm to perform a modular multiplication for both integers and binary polynomials and NTRU's polynomial multiplications.

High speed systolic Montgomery modular multipliers for RSA cryptosystems

- Computer Science, Mathematics
- 2006

A modified Montgomery modular multiplication algorithm is presented where the carry-save operations are split into two cycles so as to eliminate the generation of the data-dependent control signal from dominating the critical path.

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