Abstract
Authentication codes with secrecy and with splitting are investigated. An information-theoretic lower bound for the probability of successful deception for a spoofing attack of order r is obtained. The condition necessary on authentication codes to achieve the lower bound is determined as a single simple requirement. Based on the simplicity of the result a construction, by use of so-called partially balanced t-designs, for authentication codes that can achieve the lower bound is suggested.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. F. Brickell, A few results in message authentication. Congr. Numer., 43 (1984), 141–154.
M. De Soete, Some constructions for authentication-secrecy does. In Advances in Cryptology-Eurocrypt '88. Lecture Notes in Computer Science, Vol. 330, Springer-Verlag, Berlin, 1988, pp. 57–75.
R. Johannesson and A. Sgarro, Strengthening Simmons' bound on impersonation. IEEE Trans. Inform. Theory, 37(4) (1991), 1182–1185.
J. L. Massey, Cryptography—a selective survey. Alta Frequenza, LV(1) (1986), 4–11.
J. L. Massey, Contemporary cryptology: an introduction. In Contemporary Cryplology (edited by G. J. Simmons). IEEE Press, New York, 1991, pp. 1–39.
D. K. Ray-Chaudhuri, Application of the geometry of quadrics for constructing PBIB design. Ann. of Math. Statist., 33 (1962), 1175–1186.
U. Rosenbaum, A lower bound on authentication after having observed a sequence of messages. J. Cryptology, 6 (1993), 135–156.
R. Safavi-Naini and L. Tombak, Optimal authentication systems. In Advances in Cryptology—Eurocrypt '93. Lecture Notes in Computer Science, Vol. 765, Springer-Verlag, Berlin, 1994, pp. 12–27.
P. Schöbi, Perfect authentication systems for data sources with arbitrary statistics. Presented at Eurocrypt '86.
A. Sgarro, Informational divergence bounds for authentication codes. In Advances in Cryptology—Eurocrypt '89, Lecture Notes in Computer Science, Vol. 434, Springer-Verlag, Berlin, 1990, pp. 93–101.
A. Sgarro, Information-theoretic bounds for authentication frauds. J. Comput. Security, 2 (1993), 53–63.
G. J. Simmons, Authentication theory/coding theory. In Advances in Cryptology—Crypto '84, Lecture Notes in Computer Science, Vol. 196, Springer-Verlag, Berlin 1985, pp. 411–431.
B. Smeets, A short proof of a lower bound on the probability of deception in multiple authentication, to appear.
D. R. Stinson, The combinatorics of authentication and secrecy codes. J. Cryptology, 2 (1990), 23–49.
M. Walker, Information-theoretic bounds for authentication schemes. J. Cryptology, 2 (1990), 131–143.
Z. Wan, Z. Dai, X. Feng, and B. Yang, Studies in Finite Geometries and Incomplete Block Designs (in Chinese). Science Press, Beijing, 1966.
Author information
Authors and Affiliations
Additional information
Communicated by James L. Massey
This research was partially supported by a K. C. Wong Fellowship.
Rights and permissions
About this article
Cite this article
Pei, D. Information-theoretic bounds for authentication codes and block designs. J. Cryptology 8, 177–188 (1995). https://doi.org/10.1007/BF00191354
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00191354