Koblitz exponentiation with bucketing

Details Koblitz exponentiation with bucketing Koblitz exponentiation with bucketing

2006-11-21

2006-11-21

Barron, Gilberto (Department: 2132)

Cryptography

Particular algorithmic function encoding

Public key

C380S028000

Reexamination Certificate

active

07139396

ABSTRACT:
An implementation of a technology, described herein, for facilitating cryptographic systems and techniques. At least one implementation, described herein, maximizes the speed and security of fast exponentiation while minimizing its expense. At least one implementation, described herein, employs elliptic curves with a fast exponentiation technique so that it maximizes speed and security while minimizing expense. At least one implementation, described herein, employs Koblitz exponentiation with “bucketing” techniques to maximize speed and security of cryptosystems while minimizing expense of such techniques. This abstract itself is not intended to limit the scope of this patent. The scope of the present invention is pointed out in the appending claims.

REFERENCES:
patent: 2002/0041681 (2002-04-01), Hoffstein et al.
patent: 2002/0044649 (2002-04-01), Gallant et al.
Solinas, Jerome A.; “Efficient Implementation of Koblitz Curves and Generalized Mersenne Arithmetic”; Nov. 3, 1999; ECC '99; Slies 1-25; http://cacr.math.uwaterloo.ca; retrieved Dec. 8, 2005.
Smart, Nigel P; “Elliptic Curves Over Small Fields of Odd Characteristics”; Oct. 1997; Hewlett-Packard Company; pp. 1-10.

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