Gao, You; Yu, Huafeng Some new constructions of authentication codes with arbitration and multi-receiver from singular symplectic geometry. (English) Zbl 1235.94071 J. Appl. Math. 2011, Article ID 675484, 18 p. (2011). Summary: A new construction of authentication codes with arbitration and multireceiver from singular symplectic geometry over finite fields is given. The parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of deception are also computed. MSC: 94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory PDF BibTeX XML Cite \textit{Y. Gao} and \textit{H. Yu}, J. Appl. Math. 2011, Article ID 675484, 18 p. (2011; Zbl 1235.94071) Full Text: DOI References: [1] G. J. Simmons, “Message authentication with arbitration of transmitter/receiver disputes,” in Proceedings of the Workshop on the Theory and Application of of Cryptographic Techniques (EUROCRYPT ’87), vol. 304 of Lecture Notes in Computer Science, pp. 151-165, 1987. [2] Z. X. Wan, “Construction of Cartesian authentication codes from unitary geometry,” Designs, Codes and Cryptography, vol. 2, no. 4, pp. 333-356, 1992. · Zbl 0764.94022 [3] H. You and Y. Gao, “Some new constructions of Cartesian authentication codes from symplectic geometry,” Systems Science and Mathematical Sciences, vol. 7, no. 4, pp. 317-327, 1994. · Zbl 0819.94024 [4] T. Yayuan, “Construction of cartesian authentication codes from symplectic geometry,” Journal of Hebei Polytechnic University (Natual Science Edition), vol. 30, no. 1, pp. 49-53, 2008 (Chinese). [5] G. You, S. Xinhua, and W. Hongli, “Constructions of authentication codes with arbitration from singular sympleetic geometry over finite fields,” Acta Scientiarum Naturalium Universitatis Nankaiensis, vol. 41, no. 6, pp. 72-77, 2008. · Zbl 1199.94092 [6] R. Li and L. Guo, “Construction of authentication codes with arbitration from unitary geometry,” Applied Mathematics Series B, vol. 14, no. 4, pp. 475-480, 1999. · Zbl 1158.94386 [7] G. You and W. Hong-Li, “Construction of authentication codes with arbitration from singular pseudo-symplectic geometry,” in Proceedings of the 7th International Conference on Machine Learning and Cybernetics (ICMLC ’08), vol. 2, pp. 1183-1188, Kunming, China, 2008. [8] W. Zhexian, Geometry of Classical Groups over Finite Fields, Science Press, Beijing, China, 2nd edition, 2002. · Zbl 1029.05157 [9] R. Safavi-Naini and H. Wang, “Multireceiver authentication codes: models, bounds, constructions, and extensions,” Information and Computation, vol. 151, no. 1-2, pp. 148-172, 1999. · Zbl 1011.94018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.