This book contains the proceedings of EUROCRYPT 85, held in Paris in 1984, April 9-11, at the University of Paris, Sorbonne. EIJROCRYPT is now an annual international European meeting in cryptology, intended primarily for the international of researchers in this area. EUROCRYPT 84 was community following previous meetings held at Burg Feuerstein in 1982 and at IJdine in 1983. In fact EUROCRYPT 84 was thc first such meeting being organized under IXCR (International Association of Cryptology Research). Other sponsors were the well-known French association on cybernetics research AFCET, the LITP (Laborstoire d’ Informntique thcorique called et de Programmation), which is a laboratory of computer science associated with CNRS, and the department of mathematics and computer science at the Ilniversity RenE Descartcs, Sorbonne. EUROCRYPT 83 was very successfull, with about 180 participants from a great variety of foreign countries and 50 papers addressing all aspects of cryptology, close to applied as well as theoretical. It also had a special feature, i.e. a special session on smart cards particularly welcome at the time, since France was then carrying on an ambitious program on smart cards. EUROCRYPT 84 was a great experience. We like to thank all the sponsors and all the authors for their submission of papers. Pakin, Decemben 74ti4. CONTENTS SECTION I: GENERAL THEORY, CLASSICAL METHODS 3 Cryptology and Complexity Theories …G. RLiGGTU 1 0 On Cryptosystems based on Folynomials md I'inite Fields…R. irvi 16 Algehraical Structures of Cryptographic lransformations…