Cryptography – Particular algorithmic function encoding
Reexamination Certificate
2006-09-19
2006-09-19
Barron, Jr., Gilberto (Department: 2132)
Cryptography
Particular algorithmic function encoding
Reexamination Certificate
active
07110538
ABSTRACT:
This invention provides a method for accelerating multiplication of an elliptic curve point Q(x,y) by a scalar k, the method comprising the steps of selecting an elliptic curve over a finite field Fq where q is a prime power such that there exists an endomorphism Ψ, where Ψ(Q)=λ.Q for all points Q(x,y) on the elliptic curve: and using smaller representations kiof the scalar k in combination with the mapping Ψ to compute the scalar multiple of the elliptic curve point Q.
REFERENCES:
patent: 5999626 (1999-12-01), Mullin et al.
patent: 6243467 (2001-06-01), Reiter et al.
Lercier, Finding Good Random Elliptic Curves for Cryptosystems Defined over Finite Fields, 1997, Springer, Advances in Cryptography—Eurocrypt '97, vol. 1233, pp. 379-392.
Alfed J. Menezes, Handbook of Applied Cryptography, CRC Press, 1997, pp. 613, 614, 618.
Volker Mueller, Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two, URL: ftp://ftp.informatik.tu-damstadt.de/pub/TI/reports/vmueller.jc.ps.gz, Jun. 30, 1997, pp. 1-19, Darmstadt, Germany.
Jung Hee Cheon, Sungmo Park, Sangwoo Park, and Daeho Kim, Two Efficient Algorithms for Arithmetic of Elliptic Curves Using Frobenius Map, Public Key Cryptography First International Workshop on Practice and Theory in Public Key Cryptography PKC 98, 1998, pp. 195-202, Springer-Verlag, New York.
Jerome A. Solinas, An Improved Algorithm for Arithmetic on a Family of Elliptic Curves, Advances in Cryptology Crypto 97, 1997, pp. 357-271, Springer-Verlag, New York.
Neal Koblitz, CM-Curves With Good Cryptographic Properties, Advances in Cryptography Crypto 91, 1991, pp. 279-287, Springer-Verlag, New York.
Gallant Robert
Lambert Robert
Vanstone Scott A.
Barron Jr. Gilberto
Certicom Corp.
Chari Santosh K.
Lanier Benjamin E.
Orange John R. S.
LandOfFree
Method for accelerating cryptographic operations on elliptic... 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 for accelerating cryptographic operations on elliptic..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Method for accelerating cryptographic operations on elliptic... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3593284