Authentication code with secrecy based on projective geometry

A. U. Zubov

Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 39-49.

Résumé

An authentication code with the secrecy based on the projective geometry is proposed. It ensures the secure authentication and confidentiality for the equiprobable source of information.

Détail

Keywords: authentication code with secrecy, perfect cipher, projective geometry.

Bibliographie

[1] Zubov A. Yu., “K teoretiko-igrovomu podkhodu issledovaniya kodov autentifikatsii”, Diskretnaya matematika, 21:3 (2009), 45–72 | DOI | MR | Zbl

[2] Zubov A. Yu., “O vybore optimalnoi strategii dlya koda autentifikatsii s dvumya sostoyaniyami istochnika”, Diskretnaya matematika, 21:4 (2009), 135–147 | DOI | MR | Zbl

[3] Zubov A. Yu., Matematika kodov autentifikatsii, Gelios ARV, M., 2007

[4] Zubov A. Yu., “Pochti sovershennye shifry i kody autentifikatsii”, Prikladnaya diskretnaya matematika, 2011, no. 4(14), 28–33

[5] Casse L. R. A., Martin K. M., Wild P. R., “Bound and characterizations of authentication/ secrecy schemes”, Designs, Codes and Cryptography, 13 (1998), 107–129 | DOI | MR | Zbl

[6] Ding C., Tian X., “Three constructions of authentication codes with perfect secrecy”, Designs, Codes and Cryptography, 33 (2004), 227–239 | DOI | MR | Zbl

[7] Huber M., Authentication and secrecy codes for equiprobable source probability distributions, 2009, arXiv: 0904.0109

[8] Huber M., “Constructing optimal authentication codes with perfect multi-fold secrecy”, Proc. IEEE Int. Zurich Seminar on Communications, IZS (March 3–5, 2010), Zurich, 2010, 86–89

[9] Mitchell C. J., Piper C., Walker M., Wild P., “Authentication schemes, perfect local randomizers, perfect secrecy and secret sharing schemes”, Designs, Codes and Cryptography, 7 (1996), 101–110 | MR | Zbl

[10] Rees R., Stinson D. R., “Combinatorial characterizations of authentication codes. II”, Designs, Codes and Cryptography, 7 (1996), 239–259 | MR | Zbl

[11] Sgarro A., “An introduction to the theory of unconditional secrecy and authentication”, Geometries, Codes and Cryptography, CISM Courses and Lectures, 313, Springer Verlag, 1990, 131–160 | MR

[12] Saygi Z., Constructions of authentication codes, A thesis submitted to the Graduate School of Applied Mathematics of the METU, Ankara, 2007, 74 pp.

[13] Smeets B., Vanrose P., Wan C.-X., “On the constraction of authentication codes with secrecy and codes withstanding spoofing attack of order $L$”, Eurocrypt' 90, LNCS, 473, 1990, 307–312

[14] De Soete M., “Some constructions for authentication – secrecy codes”, Eurocrypt' 88, LNCS, 330, 1988, 57–75 | MR | Zbl

[15] De Soete M., “Authentication/secrecy codes”, Geometries, Codes and Cryptography, CISM Courses and Lectures, 313, Springer Verlag, 1990, 187–199 | MR

[16] Stinson D. R., “A construction for authentication secrecy codes from certain combinatorial designs”, Crypto' 87, LNCS, 293, 1988, 355–366 | MR | Zbl

[17] Stinson D. R., “The combinatorics of authentication and secrecy codes”, J. Cryptology, 2:1 (1990), 23–49 | DOI | MR | Zbl

[18] Van Tran T., “On the construction of authentication and secrecy codes”, Designs, Codes and Cryptography, 5 (1995), 269–280 | DOI | MR | Zbl

[19] Kholl M., Kombinatorika, IL, M., 1970

[20] Zubov A. Yu., Kriptograficheskie metody zaschity informatsii. Sovershennye shifry, Gelios ARV, M., 2005

[21] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, M., 2004

[22] Gilbert E., MacWilliams F. J., Sloane J. A., “Codes which detect deception”, Bell System Tech. J., 53 (1974), 405–424 | MR | Zbl