Non supersingular elliptic curves for public key cryptosystems

Authors:
T. Beth;F. Schaefer
Affiliations:
Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, Karlruhe;Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, Karlruhe
Venue:
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Year:
1991

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Abstract

For public key cryptosystems multiplication on elliptic curves can be used instead of exponentiation in finite fields. One attack to such a system is embedding the elliptic curve group into the multiplicative group of a finite field via weilpairing; calculating the discrete logarithm on the curve by solving the discrete logarithm in the finite field. This attack can be avoided by constructing curves so that every embedding in a multiplicative group of a finite field requires a field of very large size.