Closed galois field combination

Cryptography – Communication system using cryptography

Reexamination Certificate

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C380S268000, C708S250000

Reexamination Certificate

active

07995757

ABSTRACT:
A method is provided for combining two or more input sequences in a communications system to increase a repetition period of the input sequences in a resource-efficient manner. The method includes a receiving step, a mapping step, and a generating step. The receiving step involves receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[pk]. The mapping step involves mapping the first and second number sequences to a Galois extension field GF[pk+1]. The generating step involves generating an output sequence by combining the first number sequence with the second number sequence utilizing a Galois field multiplication operation in the Galois extension field GF[pk+1]. p is a prime number. k is an integer. pk+1defines a finite field size of the Galois extension field GF[pk+1].

REFERENCES:
patent: 3564223 (1971-02-01), Harris et al.
patent: 3780275 (1973-12-01), Nakamura
patent: 4646326 (1987-02-01), Backof, Jr. et al.
patent: 4703507 (1987-10-01), Holden
patent: 5007087 (1991-04-01), Bernstein et al.
patent: 5048086 (1991-09-01), Bianco et al.
patent: 5077793 (1991-12-01), Falk et al.
patent: 5276633 (1994-01-01), Fox et al.
patent: 5297153 (1994-03-01), Baggen et al.
patent: 5297206 (1994-03-01), Orton
patent: 5319735 (1994-06-01), Preuss et al.
patent: 5412687 (1995-05-01), Sutton et al.
patent: 5598476 (1997-01-01), LaBarre et al.
patent: 5757923 (1998-05-01), Koopman, Jr.
patent: 5811998 (1998-09-01), Lundberg et al.
patent: 5852630 (1998-12-01), Langberg et al.
patent: 5900835 (1999-05-01), Stein
patent: 5924980 (1999-07-01), Coetzee
patent: 5937000 (1999-08-01), Lee et al.
patent: 6014446 (2000-01-01), Finkelstein
patent: 6023612 (2000-02-01), Harris et al.
patent: 6038317 (2000-03-01), Magliveras et al.
patent: 6078611 (2000-06-01), La Rosa et al.
patent: 6304216 (2001-10-01), Gronemeyer
patent: 6331974 (2001-12-01), Yang et al.
patent: 6377782 (2002-04-01), Bishop et al.
patent: 6570909 (2003-05-01), Kansakoski et al.
patent: 6614914 (2003-09-01), Rhoads et al.
patent: 6744893 (2004-06-01), Fleming-Dahl
patent: 6754251 (2004-06-01), Sriram et al.
patent: 6766345 (2004-07-01), Stein et al.
patent: 6842479 (2005-01-01), Bottomley
patent: 6980656 (2005-12-01), Hinton, Sr. et al.
patent: 6986054 (2006-01-01), Kaminaga et al.
patent: 7023323 (2006-04-01), Nysen
patent: 7027598 (2006-04-01), Stojancic et al.
patent: 7069492 (2006-06-01), Piret et al.
patent: 7076065 (2006-07-01), Sherman et al.
patent: 7078981 (2006-07-01), Farag
patent: 7079651 (2006-07-01), Den Boer
patent: 7095778 (2006-08-01), Okubo et al.
patent: 7133522 (2006-11-01), Lambert
patent: 7170997 (2007-01-01), Petersen et al.
patent: 7190681 (2007-03-01), Wu
patent: 7200225 (2007-04-01), Schroeppel
patent: 7233969 (2007-06-01), Rawlins et al.
patent: 7233970 (2007-06-01), North et al.
patent: 7245723 (2007-07-01), Hinton, Sr. et al.
patent: 7269198 (2007-09-01), Elliott et al.
patent: 7269258 (2007-09-01), Ishihara et al.
patent: 7272168 (2007-09-01), Akopian
patent: 7277540 (2007-10-01), Shiba et al.
patent: 7529292 (2009-05-01), Bultan et al.
patent: 7643537 (2010-01-01), Giallorenzi et al.
patent: 7779060 (2010-08-01), Kocarev et al.
patent: 7830214 (2010-11-01), Han et al.
patent: 7853014 (2010-12-01), Blakley et al.
patent: 2002/0099746 (2002-07-01), Tie et al.
patent: 2003/0044004 (2003-03-01), Blakley et al.
patent: 2004/0001556 (2004-01-01), Harrison et al.
patent: 2004/0059767 (2004-03-01), Liardet
patent: 2004/0196212 (2004-10-01), Shimizu
patent: 2005/0031120 (2005-02-01), Samid
patent: 2005/0050121 (2005-03-01), Klein et al.
patent: 2005/0089169 (2005-04-01), Kim et al.
patent: 2005/0207574 (2005-09-01), Pitz et al.
patent: 2005/0274807 (2005-12-01), Barrus et al.
patent: 2006/0072754 (2006-04-01), Hinton et al.
patent: 2006/0123325 (2006-06-01), Wilson et al.
patent: 2006/0209932 (2006-09-01), Khandekar et al.
patent: 2006/0251250 (2006-11-01), Ruggiero et al.
patent: 2007/0121945 (2007-05-01), Han et al.
patent: 2007/0230701 (2007-10-01), Park et al.
patent: 2008/0008320 (2008-01-01), Hinton et al.
patent: 2008/0016431 (2008-01-01), Lablans
patent: 2008/0095215 (2008-04-01), McDermott et al.
patent: 2008/0198832 (2008-08-01), Chester
patent: 2008/0263119 (2008-10-01), Chester et al.
patent: 2008/0294710 (2008-11-01), Michaels
patent: 2008/0294956 (2008-11-01), Chester et al.
patent: 2008/0304553 (2008-12-01), Zhao et al.
patent: 2008/0304666 (2008-12-01), Chester et al.
patent: 2008/0307022 (2008-12-01), Michaels et al.
patent: 2008/0307024 (2008-12-01), Michaels et al.
patent: 2009/0034727 (2009-02-01), Chester et al.
patent: 2009/0044080 (2009-02-01), Michaels et al.
patent: 2009/0110197 (2009-04-01), Michaels
patent: 2009/0122926 (2009-05-01), Azenkot et al.
patent: 2009/0196420 (2009-08-01), Chester et al.
patent: 2009/0202067 (2009-08-01), Michaels et al.
patent: 2009/0245327 (2009-10-01), Michaels
patent: 2009/0279688 (2009-11-01), Michaels et al.
patent: 2009/0279690 (2009-11-01), Michaels et al.
patent: 2009/0296860 (2009-12-01), Chester et al.
patent: 2009/0300088 (2009-12-01), Michaels et al.
patent: 2009/0309984 (2009-12-01), Bourgain et al.
patent: 2009/0310650 (2009-12-01), Chester et al.
patent: 2009/0323766 (2009-12-01), Wang et al.
patent: 2009/0327387 (2009-12-01), Michaels et al.
patent: 2010/0111296 (2010-05-01), Brown et al.
patent: 0 849 664 (1998-06-01), None
patent: 0 949 563 (1999-10-01), None
patent: 2 000 900 (2008-12-01), None
patent: 2 000 902 (2008-12-01), None
patent: 1167272 (1969-10-01), None
patent: WO-0135572 (2001-05-01), None
patent: WO-2006 110954 (2006-10-01), None
patent: WO 2008 65191 (2008-06-01), None
patent: WO-2008099367 (2008-08-01), None
patent: WO-2008130973 (2008-10-01), None
patent: WO 2009 146283 (2009-12-01), None
Deckert, T., et al: “Throughput of WLAN with TDMA and Superimposed Transmission with Resource and Traffic Constraints” Personal, Indoor and Mobile Radio Communications, 2006 IEEE 17th Inter National Symposium on, IEEE, PI, Sep. 1, 2006, pp. 1-5, XP031023581, ISBN: 978-1-4244-0329-5.
Deckert, T., et al: 1-10 “Superposed Signaling Option for Bandwidth Efficient Wireless LANs” Proceedings of the 7th International Symposium on Wireless Personal Multimedia Communications, [Online] Sep. 15, 2004,XPOO2558039.
Manikandan, et al, “A Novel Pulse Based Ultrawide Band System Using Chaotic Spreading Sequences” Communication Systems Software and Middleware, 2007. COMSWARE 2007. 2nd International Conference on, IEEE, PI, Jan. 1, 2007, pp. 1-5, XP031113946 ISBN: 978-1-4244-0613-5; p. 1, page 5.
Nakamura, et al, “Chaotic synchronization-based communications using constant envelope pulse” Electrical Engineering in Japan, [Online] vol. 163, No. 3, Feb. 12, 2008, pp. 47-56, XP002539977 Japan. Retrieved from the Internet: URL:http://www3.interscience.wiley.com/cgi-bin/fulltext/117910986/PDFSTART>; [retrieved on Aug. 4, 2009] p. 47-p. 48; p. 50-p. 51.
Salberg, et al, “Stochastic multipulse-PAM: A subspace modulation technique with diversity” Signal Processing, Elsevier Science Publishers B.V. Amsterdam, NL, vol. 83, No. 12, Dec. 1, 2003, pp. 2559-2577, XP004467986; ISSN: 0165-1684.
Barile, Margherita. “Bijective.” From MathWorld—A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Bijective.html.
Weisstein, Eric W. “Injection.” From Mathworld—A Wolfram Web Resource. http://mathworld.wolfram.com/Injection.html.
Weisstein, Eric W. “Surjection.” From Mathworld—A Wolfram Web Resource. http://mathworld.wolfram.com/Surjection.html.
Abel, et al., “Chaos Communications-Principles, Schemes, and System Analysis” Proceedings for the IEEE, IEEE. New York, NY. vol. 90, No. 5, May 1, 2002, XP011064997, ISSN: 0018-9219.
Chren, W A: “PN Code Generator with Low Delay-power Product for Spread-Spectrum Communication Systems” IEEE Transactions on Circuits and Systems II: Express Briefs, IEEE Service Center, New York, NY US, vol. 46, No. 12, Dec

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