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On the cardinality of systematic authentication codes via error-correcting codes

Författare:
Publiceringsår: 1996
Språk: Engelska
Sidor: 566-578
Publikation/Tidskrift/Serie: IEEE Transactions on Information Theory
Volym: 42
Nummer: 2
Dokumenttyp: Artikel

Sammanfattning

In both open and private communication the participants face potential threats from a malicious enemy who has access to the communication channel and can insert messages (impersonation attack) or alter already transmitted messages (substitution attack). Authentication codes (A-codes) have been developed to provide protection against these threats. In this paper we introduce a new distance, called the authentication distance (A-distance), and show that an A-code can be described as a code for the A-distance. The A-distance is directly related to the probability PS of success in a substitution attack. We show how to transform an error-correcting code into an A-code and vice versa. We further use these transformations to provide both upper and lower bounds on the size of the information to be authenticated, and study their asymptotic behavior. As examples of obtained results, we prove that the cardinality of the source state space grows exponentially with the number of keys provided PS>PI, we generalize the square-root bound given by Gilbert, MacWilliams, and Sloane in 1979, and we provide very efficient constructions using concatenated Reed-Solomon codes.

Disputation

Nyckelord

  • Technology and Engineering

Övriga

Published
Yes
"©1996 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."
  • ISSN: 0018-9448

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