GOB designs for authentication codes with arbitration

Combinatorial characterization of optimal authentication codes with arbitration was previously given by several groups of researchers in terms of affine α-resolvable  +  BIBDs and α-resolvable designs with some special properties, respectively. In this paper, we revisit this known characterization and restate it using a new idea of GOB designs. This newly introduced combinatorial structure simplifies the characterization, and enables us to extend Johansson’s well-known family of optimal authentication codes with arbitration to any finite projective spaces with dimension greater than or equal to 3.

[1]  C. R. Rao,et al.  Factorial Experiments Derivable from Combinatorial Arrangements of Arrays , 1947 .

[2]  Satoshi Obana,et al.  Combinatorial Bounds on Authentication Codes with Arbitration , 2001 .

[3]  Satoshi Obana,et al.  Combinatorial Bounds on Authentication Codes with Arbitration , 1995, Des. Codes Cryptogr..

[4]  Gustavus J. Simmons,et al.  A cartesian product construction for unconditionally secure authentication codes that permit arbitration , 1990, Journal of Cryptology.

[5]  Masakazu Jimbo,et al.  Optimal authentication systems and combinatorial designs , 1990, IEEE Trans. Inf. Theory.

[6]  Satoshi Obana,et al.  Combinatorial Classification of Optimal Authentication Codes with Arbitration , 2000, Des. Codes Cryptogr..

[7]  J. L. Massey,et al.  Cryptography ― a selective survey , 1986 .

[8]  Reihaneh Safavi-Naini,et al.  Characterization of Optimal Authentication Codes with Arbitration , 1999, ACISP.

[9]  Gustavus J. Simmons,et al.  Authentication Theory/Coding Theory , 1985, CRYPTO.

[10]  F. MacWilliams,et al.  Codes which detect deception , 1974 .

[11]  Thomas Johansson.  Lower bounds on the probability of deception in authentication with arbitration , 1994, IEEE Trans. Inf. Theory.

[12]  Jennifer Seberry,et al.  Error-correcting codes for authentication and subliminal channels , 1991, IEEE Trans. Inf. Theory.

[13]  Gustavus J. Simmons,et al.  Message Authentication with Arbitration of Transmitter/Receiver Disputes , 1987, EUROCRYPT.

[14]  Satoshi OBANA,et al.  A2-code = Affine resolvable = BIBD , 1997, ICICS.

[15]  Douglas R. Stinson,et al.  The combinatorics of authentication and secrecy codes , 2005, Journal of Cryptology.