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Arithmetic operations in the polynomial modular number system

Conference Paper


Abstract


  • We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The so-called Polynomial Modular Number System (PMNS) allows for fast polynomial arithmetic and easy parallelization. The most important contribution of this paper is the fundamental theorem of a Modular Number System, which provides a bound for the coefficients of the polynomials used to represent the set ℤp. However, we also propose a complete set of algorithms to perform the arithmetic operations over a PMNS, which make this system of practical interest for people concerned about efficient implementation of modular arithmetic. © 2005 IEEE.

Publication Date


  • 2005

Citation


  • Bajard, J. C., Imbert, L., & Plantard, T. (2005). Arithmetic operations in the polynomial modular number system. In Proceedings - Symposium on Computer Arithmetic (pp. 206-213).

Scopus Eid


  • 2-s2.0-27944467947

Start Page


  • 206

End Page


  • 213

Abstract


  • We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The so-called Polynomial Modular Number System (PMNS) allows for fast polynomial arithmetic and easy parallelization. The most important contribution of this paper is the fundamental theorem of a Modular Number System, which provides a bound for the coefficients of the polynomials used to represent the set ℤp. However, we also propose a complete set of algorithms to perform the arithmetic operations over a PMNS, which make this system of practical interest for people concerned about efficient implementation of modular arithmetic. © 2005 IEEE.

Publication Date


  • 2005

Citation


  • Bajard, J. C., Imbert, L., & Plantard, T. (2005). Arithmetic operations in the polynomial modular number system. In Proceedings - Symposium on Computer Arithmetic (pp. 206-213).

Scopus Eid


  • 2-s2.0-27944467947

Start Page


  • 206

End Page


  • 213