Method and system for solving the word problem in braid...

Cryptography – Particular algorithmic function encoding

Reexamination Certificate

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C380S277000

Reexamination Certificate

active

07133523

ABSTRACT:
A method for exchange of information I over a communications link, a communications system including a data processor for carrying out the method, and computer readable media for providing program code to the data processor. The system receives a signal transmitted over the link, the signal being generated in accordance with a braid group based cryptosystem; transforming the signal to obtain a word expressive of a braid in Bn, braid encoding the information; and transforming the word into a word in novel standard form to recover the information. Word is represented by arrays a[m], a[m] in {0, 1, . . . , n−1}, and p[m], p[m] in {−1, 1}, and transforming the word to a standard form includes: inputting the arrays a[m], and p[m]; processing a[m] and p[m] to obtain array b[s], b[s] in {0, 1, . . . , n−1} and representing a positive braid word P, and variable r, Δr·P being a word in standard form representative of the braid; and outputting b[s] and r. In one embodiment of the invention the information I is an encryption key.

REFERENCES:
patent: 5241309 (1993-08-01), Cideciyan et al.
patent: 2004/0174278 (2004-09-01), Kadono et al.
patent: 2004/0240672 (2004-12-01), Girault et al.
“Entity Authentications Schemes Using Braid Word Reduction”, by Herve Sibert, Patrick Dehornoy, and Mark Girault.
“A New Algorithm for Solving the Word Problem in Braid Groups”, D. Garber, S. Kaplan, and M. Teicher-Department of Mathematics and Computer Science, Bar-Ilan University.
“An Overview of Braid Group Cryptography”, by Karl, Mahlburg.
“Brand-generator presentation for the 4-braid Group”, by Eun Sook Kang: Department of Mathematics, Korea University- Ki Hyoung Ko: Department of Mathematics, Korea Advanced Institute of Science and Technology- Sang Jin Lee, Department of Mathematics, Korea Advanced Institute of Science and Technology.

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