Method for accelerating cryptographic operations on elliptic...

Cryptography – Particular algorithmic function encoding

Reexamination Certificate

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Reexamination Certificate

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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.

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