Monday March 24, 2003

Speaker: Eric Bone

Title: The Elliptic Curve Discrete Logarithm Problem in Cryptography

Abstract: In a multiplicative group G, we can state the Discrete Logarithm Problem (DLP) as follows: If b is in G, and y is in the subgroup generated by b, find any x in Z such that y = bx. Until 1985, cryptographic uses of the DLP were limited to the multiplicative groups of finite fields. Then V. Miller and N. Koblitz independently suggested that a finite subgroup of the points on an elliptic curve E over a finite field could also be used. From these suggestions, cryptosystems have been constructed using the integer multiplication maps on E. In collaboration with F. Diamond, I investigate the construction of generalized cryptosystems using the entire endomorphism ring when End(E) =Z[f], where f is the p-th power Frobenius map.