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Hashing byte streams into elements of the Shafarevich-Tate group of an abelian variety

  • US 7,707,426 B2
  • Filed: 10/28/2005
  • Issued: 04/27/2010
  • Est. Priority Date: 12/14/2004
  • Status: Expired due to Fees
First Claim
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1. A computer-implemented method comprising:

  • generating, via a computer, a Shafarevich-Tate group from an abelian variety;

    determining, via the computer, a Cassels-Tate pairing based on elements of the Shafarevich-Tate group;

    cryptographically processing, via the computer, data based on the Cassels-Tate pairing by hashing the data into an element of the Shafarevich-Tate group using Kolyvagin cohomology classes; and

    communicating, by the computer, the cryptographically processed data that includes signed data and a calculated signature that is used to verify the signed data based on a calculated Cassels-Tate pairing.

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