Cryptosystems using commuting pairs in a monoid

Details Cryptosystems using commuting pairs in a monoid Cryptosystems using commuting pairs in a monoid

2006-11-14

2006-11-14

Moazzami, Nasser (Department: 2136)

Cryptography

Particular algorithmic function encoding

C380S030000

Reexamination Certificate

active

07136484

ABSTRACT:
Apparati, methods, and computer readable media for enabling two parties (1,2) to exchange encrypted messages, exchange symmetric cryptographic keys, and perform functions of public key cryptography. First and second key exchange algorithms use commuting pairs of subsets of a monoid. The first key exchange algorithm has four principal embodiments. In three of the embodiments, a set of matrices over a hyperbolic ring is used as the monoid. In the fourth embodiment, a braid group is used as the monoid. The second key exchange algorithm has five principal embodiments. In four of the embodiments, a set of matrices over a hyperbolic ring is used as the monoid. In the fifth embodiment, a braid group is used as the monoid.

REFERENCES:
patent: 4078152 (1978-03-01), Tuckerman, III
patent: 4195200 (1980-03-01), Feistel
patent: 4200770 (1980-04-01), Hellman et al.
patent: 4218582 (1980-08-01), Hellman et al.
patent: 4405829 (1983-09-01), Rivest et al.
patent: 4723284 (1988-02-01), Munck et al.
patent: 5020105 (1991-05-01), Rosen et al.
patent: 5241599 (1993-08-01), Bellovin et al.
patent: 5289397 (1994-02-01), Clark et al.
patent: 5396558 (1995-03-01), Ishiguro et al.
patent: 5479513 (1995-12-01), Protopopescu et al.
patent: 5627893 (1997-05-01), Demytko
patent: 5633929 (1997-05-01), Kaliski, Jr.
patent: 5751811 (1998-05-01), Magnotti et al.
patent: 5787178 (1998-07-01), Schwenk
patent: 5812072 (1998-09-01), Masters
patent: 5889865 (1999-03-01), Vanstone et al.
patent: 5966444 (1999-10-01), Yuan et al.
patent: 6081597 (2000-06-01), Hoffstein et al.
patent: 6108783 (2000-08-01), Krawczyk et al.
patent: 6111952 (2000-08-01), Patarin
patent: 6243466 (2001-06-01), Young et al.
patent: 6286101 (2001-09-01), Suzuki
patent: 6298137 (2001-10-01), Hoffstein et al.
patent: 6385725 (2002-05-01), Baum-Waidner
patent: 6415032 (2002-07-01), Doland
patent: 6430588 (2002-08-01), Kobayashi et al.
patent: 6446205 (2002-09-01), Lenstra
patent: 6493449 (2002-12-01), Anshel et al.
patent: 6651167 (2003-11-01), Terao et al.
patent: 6666381 (2003-12-01), Kaminaga et al.
patent: 6782100 (2004-08-01), Vanstone et al.
patent: 6986054 (2006-01-01), Kaminaga et al.
patent: 2001/0010077 (2001-07-01), McGregor et al.
patent: 2001/0037457 (2001-11-01), Inada
patent: 2002/0027986 (2002-03-01), Brekne
patent: 2003/0223579 (2003-12-01), Kanter et al.
patent: 2005/0157871 (2005-07-01), Komano et al.
patent: 2005/0175173 (2005-08-01), Nakamura et al.
patent: 2005/0175174 (2005-08-01), Kahl
patent: WO 9944324 (1999-09-01), None
Ko et al., New Public-Key Cryptosystem Using Braid Groups, 2000, Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology, Lecture Notes In Computer Science; vol. 1880, pp. 166-183.
Anshel et al., An Algebraic Method for Public-Key Cryptography, 1999, Mathematical Research Letters.
Menezes et al., Handbook of Applied Cryptography, 1996, CRC Press, chaper 12.
Neal R Wagner, Searching for Public-Key Cryptosystems, 1984, IEEE Symposium on Security and Privacy.
Neal Wagner, A Public-Key Cryptosystem Based on the World Problem, 1985, Crypto 84, pp. 19-36.
Computer Letter, Oct. 15, 2001, pp. 1-4, vol. 17, No. 34, published by Technologic Partners, U.S.A.
Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman; “The NTRU Signature Scheme: Theory and Practice”;[online], [retrieved on Oct. 25, 2001]. Retrieved from the Internet <URL: http:/
tru.com/technology/tech.technical.htm.
Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman; “NTRU: A Ring Based Public Key Cryptosystem” [online], [retrieved on Oct. 25, 2001]. Retrieved from the Internet <URL: http:/
tru.com/technology/tech.technical.htm.
NTRU Technical center, [online], [retrieved on Oct. 25, 2001]. Retrieved from the Internet <URL: http:/
tru.com/technology/tech.technical.htm, 3 pages.

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