Cryptography – Particular algorithmic function encoding – Public key
Reexamination Certificate
2006-06-13
2006-06-13
Revak, Christopher (Department: 2131)
Cryptography
Particular algorithmic function encoding
Public key
C380S044000, C708S490000
Reexamination Certificate
active
07062043
ABSTRACT:
A method of generating and verifying a cryptographic digital signature using coefficient splitting. The digital signature is formed by first selecting a finite field, an elliptic curve of a first type or a second type, a point P, an integer w1, and an integer k1. Next, generating, via coefficient splitting, a point W=w1P and a point K=k1P. Next, transforming, K to a bit string K*. Next, combining K*, W, and a message M in a first manner to produce h1, and in a second manner to produce c. Next, generating s be either s=h1w1+ck1(mod q), s=(h1w1+c)/k1(mod q), or s=(h1k1+c)/w1(mod q). Next, forming the cryptographic digital signature as (K*,s). The digital signature is verified by acquiring the finite field, the elliptic curve, the point P, the point W, the message M, and the cryptographic digital signature (K*,s). Next, computing h1and c. Next, selecting (n0, n1) from (sc−1(mod q), −h1c−1(mod q)), (cs−1(mod q), h1s−1(mod q)) or (−ch1−1(mod q), sh1−1(mod q)). Next, generating the point n0P via coefficient splitting. Next, generating the point n1W via coefficient splitting. Next, summing the points computed in the last two steps and designating the sum Q. Next, transforming Q to Q*. Lastly, verifying the digital signature (K*,s) if Q*=K*. Otherwise rejecting the cryptographic digital signature (K*,s) as unverified.
REFERENCES:
patent: 4200770 (1980-04-01), Hellman et al.
patent: 4405829 (1983-09-01), Rivest et al.
patent: 4995082 (1991-02-01), Schnorr
patent: 5231668 (1993-07-01), Kravitz
patent: 5497423 (1996-03-01), Miyaji
patent: 5581616 (1996-12-01), Crandall
patent: 5600725 (1997-02-01), Rueppel et al.
patent: 5604805 (1997-02-01), Brands
patent: 5606617 (1997-02-01), Brands
patent: 5761305 (1998-06-01), Vanstone et al.
patent: 6212279 (2001-04-01), Reiter et al.
patent: 6490352 (2002-12-01), Schroeppel
patent: 6618483 (2003-09-01), Vanstone et al.
patent: 6778666 (2004-08-01), Kuzmich et al.
patent: 6782100 (2004-08-01), Vanstone et al.
patent: 6898284 (2005-05-01), Solinas
patent: 6993136 (2006-01-01), Solinas
Karpynskyy et al, “Elliptic Curve Parameters Generation”, Feb. 2004, TCSET '2004, p. 294-295.
Menezes et al, “Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field”, 1991, ACM, p. 80-89.
Menezes, “Elliptic Curve Public Key Cryptosystems”, 1993, Kluwer Academic Publishers, p. 13-34.
Enge, “Elliptic Curves and Their Applications to Cryptography, An Introduction”, 1999, Kluwer Academic Publishers, p. 125-152.
Rosing, “Implementing Elliptic Curve Cryptography”, 1999, Manning Publications Co., p. 129-163.
Francois Morain, Jorge Olivos, “Speeding Up The Computations on An Elliptic Curve Using Addition-Subtraction Chains,” Theoretical Informatics & Appls. vol. 24 No. 6 1990, pp. 531-544.
Chae Hoon Lim, Pil Joong Lee, More Flexible Exponentiation with Precomputation; Crypto '94, Springer-Verlag, 1994, pp. 95-107.
R. Gallant, R. Lambert, S. Vanstone, “Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms,” Centre For Applied Cryptographic Research, Corr-20000-53, 2000.
Laurie Law, Alfred Menezes, Minghua Qu, Jerry Solinas, Scott Vanstone, “An Efficient Protocol for Authenticated Key Agreement” Copp-98-05, Dept. of C & O Univ. of Waterloo Canada 1998.
Morelli Robert D.
Revak Christopher
The United States of America as represented by the National Secu
LandOfFree
Method of elliptic curve digital signature using coefficient... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Method of elliptic curve digital signature using coefficient..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method of elliptic curve digital signature using coefficient... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3650981