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Applications of Fast Truncated Multiplication in Cryptography

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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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Keywords

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