Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2007-12-11
2007-12-11
Mai, Tan V. (Department: 2193)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
10172776
ABSTRACT:
Methods for determining whether an arbitrary elliptic curve over a binary field is secure, by using a novel non-converging Arithmetic-Geometric Mean iteration to determine the exact number of points on the curve. The methods provide rapid generation of secure curves for Elliptic-Curve Cryptography by selecting a secure curve from among candidate curves with the new method. The secure curve chosen is a curve whose number of points, is found to be divisible by a large prime number. The number of points on candidate curves is computed by a first phase, which lifts the curve to a certain related curve, followed by a second phase, which computes a certain norm that yields the result. The new Arithmetic-Geometric Mean iteration is used for the lifting phase or for the norm phase or for both.
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Mestre, Jean-Francois, Utilisation de I'AGM pour le calcul de E(F2n), published letter, 2 pages, www.math.jussieu.fr/'mestre, Paris, France, no publication date.
Harley Robert Joseph
Mestre Jean-Francois
Mai Tan V.
Townsend and Townsend / and Crew LLP
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