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Koblitz exponentiation with bucketing

  • US 7,139,396 B2
  • Filed: 06/27/2002
  • Issued: 11/21/2006
  • Est. Priority Date: 06/27/2002
  • Status: Expired due to Fees
First Claim
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1. A computer-readable medium having at least one physical media and having computer-executable instructions that, when executed by a computer, perform a method to improve the speed and security of eltiptic curve exponentiation for subfield curves used in cryptography, the method comprising:

  • forming, with a set of coefficients (ci), a Frobenius expansion of an exponent, the Frobenius expansion having a width (w);

    gathering elements of the Frobenius expansion into collections of elements having matching coefficients;

    merging the collections;

    selecting the set of coefficients (ci) from elements of Z[τ

    ] that are congruent to odd integers modulo 2w; and

    using the elliptic curve exponentiation during generation of at least part of a cryptographic key for securing data via encryption.

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