DESIGNING A MULTI-PRECISION NUMBER THEORY LIBRARY

Authors

  • Catalin Hritcu
  • Iulian Goriac
  • Raluca Mihaela Gordan
  • Elena Erbiceanu

DOI:

https://doi.org/10.47839/ijc.2.3.228

Keywords:

Large numbers, multiple precision, high performance, unlimited precision, library, design principles, number theory algorithms, cryptography

Abstract

The aim of this paper is twofold. First, we present the basic principles and point out the main difficulties in writing a library supporting operations with arbitrarily large numbers. Aspects such as library structure, number representation, algorithm selection, memory management, etc., are discussed and exemplified on the most efficient libraries developed. Secondly, we present work in progress regarding the design of a new multi-precision library, MpNT. Comparisons between our library and the existing ones show that it achieves high performance.

References

A. Lenstra. LIP – Long Integer Package, Bellcore, http://usr/spool/ftp/pub/lenstra/LIP.

LiDIA Group. LiDIA: A C++ Library for Computational Number Theory, Darmstadt University of Technology, http://www.informatik.tu-darmstadt.de/TI/LiDIA/.

B. Haible, R. Kreckel. CLN – Class Library for Numbers, http://www.ginac.de/CLN/.

V. Schoup. NTL: A Library for Doing Number Theory, http://www.shoup.net/ntl/

PARI-GP Group. PARI-GP, http://www.parigp-home.de/.

GMP Group. GMP – The GNU Multiple Precision Arithmetic Library, www.swox.com/gmp/.

F.L. Tiplea, S. Iftene, C. Hritcu, I. Goriac, R.M. Gordan, E. Erbiceanu. MpNT: A Multi-precision Number Theory Package. Number-Theoretic Algorithms (I), Faculty of Computer Science, “Al. I. Cuza” University of Iasi, Technical Report TR03-02 (2003), http://thor.info.uaic.ro/~tr/tr.pl.cgi

Coq Site. The Coq Proof Assistant, http://pauillac.inria.fr/coq/

P. Zimmermann. A Proof of the GMP Square Root Using the Coq Assistant, Rapport de recherche 4475, INRIA, 2002.

P. Zimmermann. A Proof of the GMP Fast Division and Square Root Implementations, Rapport de recherche, INRIA, 2000.

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Published

2014-08-01

How to Cite

Hritcu, C., Goriac, I., Gordan, R. M., & Erbiceanu, E. (2014). DESIGNING A MULTI-PRECISION NUMBER THEORY LIBRARY. International Journal of Computing, 2(3), 44-48. https://doi.org/10.47839/ijc.2.3.228

Issue

2003, Volume 2, Issue 3

Section

Articles

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