Cryptographically processing data based on a Cassels-Tate...

Details Cryptographically processing data based on a Cassels-Tate... Cryptographically processing data based on a Cassels-Tate...

2004-12-14

2009-12-29

Barron, Jr., Gilberto (Department: 2432)

Cryptography

Particular algorithmic function encoding

Public key

C713S176000

Reexamination Certificate

active

07639799

ABSTRACT:
Systems and methods for cryptographically processing data as a function of a Cassels-Tate pairing are described. In one aspect, a Shafarevich-Tate group is generated from a cohomology group. A Cassels-Tate pairing is determined as a function of elements of the Shafarevich-Tate group. Data is then cryptographically processed as a function of the Cassels-Tate pairing.

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McCallum, William. On the Shafarevich-Tate group of the jacobian of a quotient of the Fermat curve. Oct. 1988. Springer Berlin/Heidelberg. vol. 93, No. 3. http://www.springerlink.com/content/pn8357642r5p2152/.
Flach, “A generalisation of the Cassels-Tate pairing” Journal Fur Die Reine Und Angewandte Mathematik, vol. 412, 1990, pp. 113-127.
Maas, “Pairing-Based Cryptography”, Master's Thesis at Technische Universitat Eindhoven, Department of Mathematics and Computing Science, Jan. 2004, pp. 1-91.
Poonen et al., “The Cassels-Tate pairing on polarized abelian varieties” Annals of Mathematics, 150, 1999, pp. 1109-1149.
Stein, William A., “Shafarevich-Tate Groups of Nonsquare Order”, In Modular Curves and Abelian Varieties Barcelona Conference Proceedings, Brikhauser Progress in Mathematics 224, Jul. 2003, pp. 277-289.
EPO Communication with Search Report dated Feb. 21, 2005, from counterpart EP patent application, European Patent Application No. 05 110 688.8, 4 pages.

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