Cryptography – Particular algorithmic function encoding
Reexamination Certificate
2006-04-04
2006-04-04
Vu, Kim (Department: 2135)
Cryptography
Particular algorithmic function encoding
C380S030000, C380S044000, C380S045000, C380S046000, C380S047000, C380S277000
Reexamination Certificate
active
07023990
ABSTRACT:
The Stickelberger element computing device computes a Stickelberger element ω in an ab cyclotomic; the Jacobian addition candidate value computing device computes the Jacobian addition candidate value j and a prime number p corresponding to the Jacobian addition candidate value j, based on the prime number a, the prime number b, the size n of an encryption key, and the Stickelberger elementω; the order candidate value computing device computes a class H consisting of a plurality of candidate values for the order of the Jacobian group of an algebraic curve, based on the prime number a, the prime number b, and the Jacobian addition candidate value j; the security judging device searches for a candidate value h meeting a security condition such as almost prime number characteristic from the class H; and the parameter deciding device computes a parameter of an algebraic curve whose order of the Jacobian group is in accord with the candidate value h, of the algebraic curves specified by the prime number a, the prime number b, and the prime number p.
REFERENCES:
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patent: 6-282226 (1994-10-01), None
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“Sitckelberger elements and modular parametrization of elliptic curves”, Stevens, Glenn, Inventiones mathematicae, Volumne 98; pp. 75-106, 1989.
An addition Algorith in Jacobian of C34 curve, Seigo Arita.
Addition in the Jacobian of a curve over a finite field, Emil J. Volcheck, Jun. 1995.
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Arita et al., “A Software Implementation of Discrete-log-based Cryptosystems with CabCurve”, Security Symposium on Cryptography and Information, (1999) pp. 573-578.
Dada Beemnet W
Foley & Lardner LLP
NEC Corporation
Vu Kim
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