A cartesian product construction for unconditionally secure authentication codes that permit arbitration

An authentication code consists of a collection of encoding rules associating states of an information source with messages that are to be used to communicate the state to a designated receiver. In order for a collection of encoding rules to be useful as an authentication code there must also exist one or more probability distributions on the rules which, if used by the receiver and transmitter (the insiders) to choose secretly the encoding rule they use, will result in the receiver being able to (probably) detect fraudulent messages sent by an outsider or modifications by him of legitimate messages.Authentication codes that permit arbitration are codes that in addition to protecting the insiders from deception by outsiders, also protect against some forms of insider deception. This is accomplished by making it possible for an arbiter to resolve (again in probability) certain disputes between the transmitter and receiver: the transmitter disavowing a message that he actually sent or the receiver claiming to have received a message that the transmitter did not send.An infinite class of authentication codes that permit arbitration is constructed and some bounds on the probability of a deception going undetected are proven. These codes are shown to be unconditionally secure, i.e., it is shown that the probability of a deception either going undetected or else of being unjustly attributed to an innocent party is independent of the computing capability or investment that a would-be cheater is willing to make.

[1]  Douglas R. Stinson.  Some Constructions and Bounds for authentication Codes , 1986, CRYPTO.

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

[3]  Marijke De Soete,et al.  Some Constructions for Authentication-Secrecy Codes , 1988, EUROCRYPT.

[4]  F. C. Piper.  COMBINATORIAL THEORY (second edition) (Wiley‐Interscience Series in Discrete Mathematics) , 1987 .

[5]  Paul Schöbi,et al.  Perfect Authentication Systems for Data Sources with Arbitrary Statistics , 1986, EUROCRYPT.

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

[7]  Jean-Jacques Quisquater,et al.  How Easy is Collision Search? Application to DES (Extended Summary) , 1990, EUROCRYPT.

[8]  Gustavus J. Simmons,et al.  A Natural Taxonomy for Digital Information Authentication Schemes , 1987, CRYPTO.

[9]  Gustavus J. Simmons.  A protocol to provide verifiable proof of identity and unforgeable transaction receipts , 1989, IEEE J. Sel. Areas Commun..

[10]  J. Levine,et al.  The Hill cryptographic system with unknown cipher alphabet but known plaintext , 1984 .

[11]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[12]  Douglas R. Stinson,et al.  A construction for authentication/secrecy codes from certain combinatorial designs , 1987, Journal of Cryptology.

[13]  R. H. Bruck.  Finite Nets, I. Numerical Invariants , 1951, Canadian Journal of Mathematics.

[14]  Hugh C. Williams,et al.  A modification of the RSA public-key encryption procedure (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[15]  M. D. Soete.  Some Constructions for Authentication-Secrecy Codes , 1988, EUROCRYPT.

[16]  P. D. Merillat.  Secure stand alone positive personnel identity verification system (SSA-PPIV) , 1979 .

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

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

[19]  Ernest F. Brickell,et al.  Authentication Codes with Multiple Arbiters (Extended Abstract) , 1988, EUROCRYPT.

[20]  R. H. Bruck.  Finite nets. II. Uniqueness and imbedding. , 1963 .

[21]  Silvio Micali,et al.  A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks , 1988, SIAM J. Comput..

[22]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[23]  Hanfried Lenz,et al.  Design theory , 1985 .

[24]  M. Rabin.  DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION , 1979 .

[25]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[26]  Gustavus J. Simmons,et al.  A System for Verifying User Identity and Authorization at the Point-of Sale or Access , 1984, Cryptologia.