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New Modular Multiplication Algorithms for Fast Modular Exponentiation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1070)

Abstract

A modular exponentiation is one of the most important oper- ations in public-key cryptography. However, it takes much time because the modular exponentiation deals with very large operands as 512-bit integers. The modular exponentiation is composed of repetition of mod- ular multiplications. Therefore, we can reduce the execution time of it by reducing the execution time of each modular multiplication. In this paper, we propose two fast modular multiplication algorithms. One is for modular multiplications between different integers, and the other is for modular squarings. These proposed algorithms require single-precision multiplications fewer than those of Montgomery modular multiplication algorithms by 1/2 and 1/3 times, respectively. Implementing on PC, pro- posed algorithms reduce execution times by 50% and 30% compared with Montgomery algorithms, respectively.

Keywords

Modular Multiplication Ular Multiplication Modular Reduction Modular Exponentiation Addition Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.Department of Computer Science and Center for AI ResearchKorea Advanced Institute of Science and Technology (KAIST)TaejeonKorea

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