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Design of Optimized Modular Multiplier Using Montgomery Algorithm for RSA Cryptosystem

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 150)

Abstract

Modular multiplication plays a vital role in RSA Cryptography and Elliptical Curve Cryptography. We have implemented a 256-bit Modular multiplier using Montgomery Reduction Algorithm in VHDL. The output of the Montgomery multiplier is Z = X*Y R−1 mod M. Our main aim is to calculate the area required for the modular multiplier using Montgomery reduction algorithm. It is a full-featured circuit including Carry save Adders, shift registers, multiplexers, parallel registers component and are too big to fit into a single Altera Stratix Device on the Field Programmable platform, so that we are unable to test them in real hardware. However, each sub-component was simulated in Model-Sim SE 6.0 and Altera Quartus II 8.0 and proved functionally correct.

Keywords

Montgomery algorithm RSA Cryptography Modular arithmetic 

References

  1. 1.
    Eldridge SE, Walter CD (1993) Hardware implementation of Montgomery’s modular multiplication algorithm. IEEE Trans Conzpzrt 42:693–699Google Scholar
  2. 2.
    Clerk Maxwell J (1892) A treatise on electricity and magnetism, vol 2, 3rd edn. Clarendon, Oxford, pp 68–73Google Scholar
  3. 3.
    Koc CK, Acar T, Kaliski B (1996) Analyzing and comparing Montgomery multiplication algorithms. IEEE Micro 16(3):26–33CrossRefGoogle Scholar
  4. 4.
    Blum T, Paar C (1999) Montgomery modular exponentiation on reconfigurable hardware. Proceedings of 14th symposium on computer arithmetic, pp 70–77Google Scholar
  5. 5.
    Bunimov V, Schimmler M (2004) Area-time optimal modular multiplication. Embedded Cryptographic Hardware: Methodologies and Architectures, 2004, ISBN: 1-59454-012-8Google Scholar
  6. 6.
    Lu J, Quan W. Implementing a 1024 bit RSA on FPGA. Reconfigurable Network GroupGoogle Scholar
  7. 7.
    Takagi N, Yajima S. Modular multiplication hardware algorithms with a redundant representation and their application to RSA cryptosystemGoogle Scholar
  8. 8.
    Bernal A, Guyot A (1998) Design of a modular multiplier based on Montgomery’s algorithm. Proceedings of the 13th international conference design of circuits and integrated systems (DCIS’98), Novemb 1998Google Scholar
  9. 9.
    Sutter GD, Deschamps J-P, Imaña J L (2010) Modular multiplication and exponentiation architectures for fast RSA cryptosystem based on digit serial computation. 0278-0046/$26.00 © 2010 IEEEGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Yeshwantrao Chavan College of EngineeringNagpurIndia

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