In this talk I will review the definition and applications of certain multilinear maps in cryptography.   Miller showed that a useful bilinear map arises from the Weil pairing on elliptic curves over the algebraic closure of a finite field.  I will then describe some work of Bleher and Chinburg on a candidate for a trilinear map. This candidate arises from cup products in the cohomology of elliptic curves over a finite field.  I will discuss the complexity of computing such cup products and give some examples of their computation.