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Applications of Fast Truncated Multiplication in Cryptography

Abstract

Truncated multiplications compute truncated products, contiguous subsequences of the digits of integer products. For an n-digit multiplication algorithm of time complexity O(nα), with 1<α≤2, there is a truncated multiplication algorithm, which is constant times faster when computing a short enough truncated product. Applying these fast truncated multiplications, several cryptographic long integer arithmetic algorithms are improved, including integer reciprocals, divisions, Barrett and Montgomery multiplications, 2n-digit modular multiplication on hardware for n-digit half products. For example, Montgomery multiplication is performed in 2.6 Karatsuba multiplication time.

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Correspondence to Laszlo Hars.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hars, L. Applications of Fast Truncated Multiplication in Cryptography. J Embedded Systems 2007, 061721 (2006). https://doi.org/10.1155/2007/61721

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Keywords

  • Constant Time
  • Time Complexity
  • Multiplication Time
  • Multiplication Algorithm
  • Control Structure