Non supersingular elliptic curves for public key cryptosystems

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.