Cryptography – Key management – Having particular key generator
Reexamination Certificate
2006-07-11
2006-07-11
Zand, Kambiz (Department: 2132)
Cryptography
Key management
Having particular key generator
C380S028000
Reexamination Certificate
active
07076061
ABSTRACT:
Improvements are obtained in key generation and cryptographic applications in public key cryptography, by reducing the bit-length of public keys, thereby reducing the bandwidth requirements of telecommunications devices, such as wireless telephone sets.
REFERENCES:
patent: 4405829 (1983-09-01), Rivest et al.
patent: 4587627 (1986-05-01), Omura
patent: 4745568 (1988-05-01), Onyszchuk et al.
patent: 4870681 (1989-09-01), Sedlak
patent: 4995082 (1991-02-01), Schnorr
patent: 5231668 (1993-07-01), Kravitz
patent: 5351297 (1994-09-01), Miyaji et al.
patent: 5406628 (1995-04-01), Beller et al.
patent: 5442707 (1995-08-01), Miyaji et al.
patent: 5481613 (1996-01-01), Ford et al.
patent: 5787028 (1998-07-01), Mullin
patent: 6252960 (2001-06-01), Serroussi
patent: WO 85/01625 (1985-04-01), None
Neal Koblitz, “A Course in Number Theory and Cryptography,” Springer, pp. 87-89, 99-106, 178-182.
Bruce Schneier, “Applied Cryptography”, 2e, John Wiley & Sons, Inc., pp. 496-499.
P. Duhamel et al., “A Decomposition of the Arithmetic for NTT's with 2 as a Root of Unity,” ICASSP '84.
R.L. Rivest et al., “A Method for Obtaining Digital Structures and Public-Key Cryptosystems”,Communications of the ACM,vol. 21, No. 2, pp. 120-126, 1978.
A.K. Lenstra and H. W. Lenstra Jr., “Algorithms in Number Theory”,Handbook of Theoretical Computer Science,pp. 675-715, 1990.
D. Coppersmith, “Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known”,EUROCRYPT'96,Proceedings,LNCS 1070, pp. 178-189, 1996.
S. Garfinkel, “PBP: Pretty Good Privacy,” 1995, pp. 42-43.
Guillou, Davio and Quisquater, “Public Key Techniques: Randomness and Redundancy”, Cryptologia, 1989, pp. 167-182.
S. Gao and H. Lenstra, “Optimal Normal Bases, Codes and Cryptography,” 2, pp. 315-323.
Elwyn R. Berlekamp, “Algebraic Coding Theory” revised 1984 edition, Aegean Park Press, Chapter 10.
U.M. Maurer, “Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters”,Journal of Cryptology,vol. 8, p. 123-155, 1995.
P.L. Montgomery, “Modular Multiplication Without Trial Division”,Mathematics of Computation,vol. 44, No. 170, pp. 519-521, 1985.
Vanstone et al., “Short RSA Keys and Their Generation”, Journal of Cryptology, Spring 1995, vol. 8, No. 2, pp. 101-114.
Young, A. et al., “The dark side of “black-box” cryptography or: Should we trust Capstone”, Advances on Cryptology, CRYPTO '96, Aug. 18-22, 1996; pp. 89-103.
Vanstone et al., “Using Four-Prime RSA in which some of the Bits are Specified,” Electronics Letters, GV, IEE Stevenage, vol. 30, No. 25, Aug. 12, 1994, pp. 2118-2119.
Coppersmith and Andrew Odlyzko, “Discrete Logarithms in GF(p)”, Algorithmica, vol. 1, No. 1, 1986; pp. 1-15.
Guillou and Quisquater, “Precautions Taken against Various Potential Attacks”, Europcrypt '90, Springer 1990, pp. 465-473.
“Information Technology—Open System Interconnection—The Directory: Authentication Framework”, ITU-T Recommendation X-509, ISO/IEC 9594-8: 1995(E), pp. 1-35. 1995.
Agnew, G.B. et al., “An Implementation for a Fast Public-Key Cryptosystem”, Journal of Cryptology, 1991, vol. 3, pp. 63-79.
Robert D. Silverman, “Fast Generation of Random, Strong RSA Primes”,RSA Laboratories' CryptoBytes,vol. 3, No. 1, pp. 9-13 Spring 1997.
Ohta et al., (Eds), “Advances in Cryptology”, CRYPTO '98, pp. 1-10.
Arjen K. Lenstra, “Generating RSA Moduli with a Predetermined Portion,” Advances in Cryptology, ASIACRYPT '98, Beijing, China, Oct. 18-22, 1998; pp. 1-10.
R.C. Mullin et al., Optimal Normal Bases in GF(pn)*.,Discrete Applied Mathematics,22 (1988/89), pp. 149-161.
Lenstra et al. “Fast Irreducibility and Subgroup Membership Testing in XTR”, Public Key Cryptography, Kim (ed) Springer-Verlag, 2001.
Lentra et al. “The XTR Public Key System”, (extended version of Crypto 2000 Presentation), pp. 73-86.
“Chapter 12. A New Public-Key Cryptosystem”:pp. 1-11.
“The XTR Cryptosystem”, Internet, Sept. 2001, pp. 1-5.
More “Letter to DDJ”, Doctor Dobb's Journal on CD-Rom, May 1993, pp. 2-3.
Smith “Cryptography Without Exponentiation”, Dr. Dobb's Journal on CD-Rom, Apr. 1994, pp. 1-3.
Smith “LUC Public-Key Encryption”, Dr. Dobb's Journal on CD-Rom, Jan. 1993, pp. 1-12.
Mc Eliece “Finiate Fields for Computer Scientists and Engineers”, Kluwer Academic Publishers, 1987, pp. 96-119.
Gong et al. “Public-Key Cryptosystems Based on Cubic Finite Field Extensions”, IEEE Transactions on Information Theory, vol. 45, No. 7, Nov. 1999, pp. 2601-2605.
Menezes et al. “Handbook of Applied Cryptography”, CRC Press, 1997.
Lenstra et al. “Key Improvements to XTR”, Asiacrypt, 2000.
Brouwer et al.; “Doing More with Fewer Bits”; Advances in Cryptology—Asiacrypt' 99, 1999, pp. 321-332.
Elgamal, “A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms”, IEEE Transations on Information Theory, vol. 31, No. 4, pp. 469-472, Jul. 1985.
Lidl et al., “Introduction to Finite Fields and Applications”, pp. 50-55, 1986.
“Choosing Good Elliptic Curves”, Author Unknown, Date Unknown.
Lenstra Arjen K.
Verheul Eric R.
Citibank N.A.
Lanier Benjamin E.
Morgan & Finnegan , LLP
Zand Kambiz
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