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MODULAR SQUARING IN BINARY FIELD ARITHMETIC

  • US 20090157788A1
  • Filed: 10/31/2008
  • Published: 06/18/2009
  • Est. Priority Date: 10/31/2007
  • Status: Abandoned Application
First Claim
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1. A method of obtaining a modular product of a n-bit polynomial and itself in a field defined by a field polynomial, said method comprising:

  • receiving, from a requester, said n-bit polynomial and a request for a square of said n-bit polynomial;

    representing a squaring result of said n-bit polynomial as a (2n−

    1)-bit polynomial having;

    a first portion that is the most significant g bits of said squaring result;

    a second portion that is the next most significant n bits of said squaring result after said most significant g bits; and

    a third portion that is the remaining bits of said squaring result after removal of said first portion and said second portion;

    reducing said first portion modulo said field polynomial, thereby producing a (g+d)-bit reduction, where d is a second highest degree of said field polynomial;

    forming a sum of said reduction and said second portion with least significant bits aligned;

    assigning, to said squaring result, a concatenation of said third portion to said sum;

    repeating said representing, said reducing, said forming and said assigning until said squaring result has a length of n bits; and

    returning said squaring result.

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