New Combinatorial Bounds for Authentication Codes and KeyPredistribution Schemes

Authors:
Kaoru Kurosawa;Koji Okada;Hajime Saido;Douglas R. Stinson
Affiliations:
Department of Electrical and Electronic Engineering, Faculty of Engineering, Tokyo Institute of Technology, 2–12–1 O-okayama, Meguro-ku, Tokyo 152, Japan;Department of Electrical and Electronic Engineering, Faculty of Engineering, Tokyo Institute of Technology, 2–12–1 O-okayama, Meguro-ku, Tokyo 152, Japan;Department of Electrical and Electronic Engineering, Faculty of Engineering, Tokyo Institute of Technology, 2–12–1 O-okayama, Meguro-ku, Tokyo 152, Japan;Computer Science and Engineering Department, University of Nebraska, Lincoln NE 68588, U.S.A.
Venue:
Designs, Codes and Cryptography
Year:
1998

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Abstract

This paper provides new combinatorial bounds and characterizationsof authentication codes (A-codes) and key predistributionschemes (KPS). We first prove a new lower bound on the numberof keys in an A-code without secrecy, which canbe thought of as a generalization of the classical Rao boundfor orthogonal arrays. We also prove a new lower bound on thenumber of keys in a general A-code, which is basedon the Petrenjuk, Ray-Chaudhuri and Wilson bound for t-designs.We also present new lower bounds on the size of keys and theamount of users‘ secret information in KPS, the latter of whichis accomplished by showing that a certain A-codeis ’’hiding‘‘ inside any KPS.