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… 

Figures and Tables from this paper

Achieving NTRU with Montgomery Multiplication
TLDR
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
TLDR
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
  • Sandeep Kakde, G. Somulu, P. Zode
  • Computer Science, Mathematics
    2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT)
  • 2013
TLDR
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
TLDR
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
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
TLDR
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
  • P. Gokul, E. Prabhu, H. Mangalam
  • Computer Science, Mathematics
    2014 International Conference on Green Computing Communication and Electrical Engineering (ICGCCEE)
  • 2014
TLDR
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
TLDR
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
TLDR
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
TLDR
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.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 12 REFERENCES
Can Montgomery parasites be avoided? A design methodology based on key and cryptosystem modifications
TLDR
Except the advantage of halving the number of Montgomery multiplications, this strategy skips the precalculation (and the storage) of the constantN−2 modn and turns to be particularly efficient when a hardware device implementingMn(...,...) is the basic computational tool at one's command.
A Cryptographic Library for the Motorola DSP56000
TLDR
A cryptographic library for the Motorola DSP56000 that provides hardware speed yet software flexibility, and an algorithm for modular multiplication that interleaves multiplication with Montgomery modular reduction to give a very fast implementation of RSA.
Systolic Modular Multiplication
  • C. D. Walter
  • Computer Science, Mathematics
    IEEE Trans. Computers
  • 1993
TLDR
A systolic array for modular multiplication is presented using the ideally suited algorithm of P.L. Montgomery (1985), where its main use would be where many consecutive multiplications are done, as in RSA cryptosystems.
New directions in cryptography
TLDR
This paper suggests ways to solve currently open problems in cryptography, and discusses how the theories of communication and computation are beginning to provide the tools to solve cryptographic problems of long standing.
Modular multiplication without trial division
TLDR
A method for multiplying two integers modulo N while avoiding division by N, a representation of residue classes so as to speed modular multiplication without affecting the modular addition and subtraction algorithms.
A method for obtaining digital signatures and public-key cryptosystems
TLDR
An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key, soriers or other secure means are not needed to transmit keys.
The Art of Computer Programming
TLDR
The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Can Montgomery parasites be avoided? A design methodology based on key and cryptosystem modiications. Designs, Codes and Cryptography
  • Can Montgomery parasites be avoided? A design methodology based on key and cryptosystem modiications. Designs, Codes and Cryptography
  • 1995
The Z80180 and big-number arithmetic
  • Dr. Dobb's Journal,
  • 1993
The Z80180 and big-numberarithmetic. Dr. Dobb's Journal
  • The Z80180 and big-numberarithmetic. Dr. Dobb's Journal
  • 1993
...
1
2
...