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.
CITATION STYLE
Beth, T., & Schaefer, F. (1991). Non supersingular elliptic curves for public key cryptosystems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 547 LNCS, pp. 316–327). Springer Verlag. https://doi.org/10.1007/3-540-46416-6_27
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