Mathematics Of Computation

ottlenecks. Whoever wants to deal with algorithmal aspects of elliptic curves will find here an excellent and, in most cases, su#cient starting point. The book is therefore not intended either as primary didactical material (proofs are scarcely given) nor as a compendium of the various short or long lived cryprographical mechanisms related to elliptic curves. For the first, books such as [7] for the practical and [3] for the mathematical aspects, are recommendable. For the latter, the technical IEEE standard P1363, which has been meanwhile released, is the relevant source for those mechanisms which are likely to be spread in practice. The first two chapters o#er a succinct introduction to general ideas of public key cryptography and the underlying arithmetic in finite fields. The important third chapter introduces the arithmetic of elliptic curves together with the various connections to division polynomials, Weil pairing, and modular functions, which have found explicit use in appli