Applications of Finite Geometry to Cryptography
In this paper we survey several applications of classical geometric structures to cryptology. Particularly we shall deal with authentication schemes, threshold schemes, network problems and WOM-codes. As geometric counterparts we shall nearly exclusively
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GEOMETRIES, CODESANDCRYPTOGRAPHY
EDITEDBY G.LONGO UNIVERSITY OF TRIESTE M.MARcm
UNIVERSITY OF UDINE
A.SGARRO UNIVERSITY OF UDINE
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da contributi deI Consiglio Nazionale delle Ricerche.
This volume contains 36 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 1990 by Springer-Verlag Wien Originally pnblished by Springer Verlag Wien-New York in 1990
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-82205-0 DOI 10.1007/978-3-7091-2838-1
ISBN 978-3-7091-2838-1 (eBook)
PREFACE
Geometry is the an not to make calculations. The InternationalCentrefor Mechanical Sciences has a long-standing tradition of advanced schools in coding theory and information theory, started as early as 1970 (cf the list ofvolumes in this series at the end ofthis book).1n 1983 a rather exciting event took place, namelyan advanced school on the new subject of cryptology (queer indeed, that the the century-long art of secret writing should be called new!). The 1983 meeting (cf volume n. 279 in this series) has by now entered the history of contemporary European cryptologic research, preceded as it is only by one similar event in Burg Feuerstein, Germany, in 1982, andfollowed by the 1984 workshop at the Sorbonne of Paris, which was the first of this sort to bear the by now well-established name of Eurocrypt. So, in a way, the Udine meeting was Eurocrypt number zero, second in a list whose origin is curiously set at n= -1. After this, CISM kept secretive for several years on the subject of coding, be it source coding, channel coding or ciphering./n 1989 the second editor, M. Marchi, who is a "pure" geometer, having heard about the spectacular success that finite (pure!) geometries were experiencing in the domain of authentication schemes (a very matter-oJfact subject nowadays, as it has so much to do with the proper handling of our credit cards), decided to appease his curiosity and contacted the third editor, A. Sgarro, an information theorist active in Shannon-theoretic cryptology. From their conversations the idea ofthis school originated; thefirst editor, G. Longo, himself an information theorist but also a writer, added his experience to their enthusiasm. The result was a delightjul week during which students and researchers alike were given the opponunity to meet, to exchange ideas, to get along in their field, and, why not!, to make friends. About fifty people participated, coming from fifteen different countries. Geometers and coding
theorists (not necessarily distinct per
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