Parallel Memory Architecture for Elliptic Curve Cryptography over $$ \mathbb{G}\mathbb{F}{\left( p \right)} $$ Aimed at Efficient FPGA Implementation

  • Authors:
  • Ralf Laue;Sorin A. Huss

  • Affiliations:
  • Integrated Circuits and Systems Laboratory, Department of Computer Science, Technische Universität Darmstadt, Darmstadt, Germany;Integrated Circuits and Systems Laboratory, Department of Computer Science, Technische Universität Darmstadt, Darmstadt, Germany

  • Venue:
  • Journal of Signal Processing Systems
  • Year:
  • 2008

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Abstract

Parallelization of operations is of utmost importance for efficient implementation of Public Key Cryptography algorithms. Starting with a classification of parallelization methods at different abstraction levels of public key algorithms, we propose a novel memory architecture for elliptic curve implementations with multiple modular multiplier units. This architecture is well-suited for different point addition and doubling algorithms over $$ \mathbb{G}\mathbb{F}{\left( p \right)} $$ to be implemented on FPGAs. It allows the execution time to scale with the number of modular multipliers and exhibits nearly no overhead compared to the mere runtime of the multipliers. The advantages of this distributed memory architecture are demonstrated by means of two different point addition and doubling algorithms.