Jacobian group element adder

Details Jacobian group element adder Jacobian group element adder

2007-03-27

2007-03-27

Mai, Tan V. (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

C708S492000

Reexamination Certificate

active

10643972

ABSTRACT:
An objective is to obtain a Jacobian group element adder that can calculate addition in a Jacobian group of a Cabcurve at a high speed, and can enhance practicality of the Cabcurve.An algebraic curve parameter file A10, and Groebner bases I1and I2of ideals of a coordinate ring of an algebraic curve designated by this file A are input into an ideal composition section11to perform arithmetic of producing a Groebner basis J of an ideal product of the ideal generated by I1 and ideal generated by I2. In a first ideal reduction section12, arithmetic is performed of producing a Groebner basis J* of an ideal that is smallest in a monomial order designated by the file A among ideals equivalent to an inverse ideal of an ideal that J in the coordinate ring of the algebraic curve designated by the file A generates. In a second ideal reduction section13, arithmetic is performed of producing a Groebner basis J** of a ideal that is smallest in the monomial order designated by the file A among ideals equivalent to an inverse ideal of an ideal that this J* generates to output it.

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R. Harasawa et al., “A Fast Jacobian Group Arithmetic Scheme for Algebraic Curve Cryptography”, IEICE Trans. Fundamentals, vol. E84-A, No. 1, Jan. 2001, pp. 130-139.

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