On the equivalence of authentication codes and robust (2, 2)-threshold schemes. (English) Zbl 1466.94047
Summary: In this paper, we show a “direct” equivalence between certain authentication codes and robust threshold schemes. It was previously known that authentication codes and robust threshold schemes are closely related to similar types of designs, but direct equivalences had not been considered in the literature. Our new equivalences motivate the consideration of a certain “key-substitution attack.” We study this attack and analyze it in the setting of “dual authentication codes.” We also show how this viewpoint provides a nice way to prove properties and generalizations of some known constructions.
MSC:
| 94A62 | Authentication, digital signatures and secret sharing |
| 94A60 | Cryptography |
| 05B05 | Combinatorial aspects of block designs |
| 05B10 | Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) |
References:
| [1] | W. Ogata, K. Kurowawa and D.R. Stinson, Optimum secret sharing scheme secure against cheating, SIAM J. Discrete Math. 20 (2006), 79-95. · Zbl 1119.94011 |
| [2] | W. Ogata, K. Kurowawa, D.R. Stinson and H. Saido, New combinatorial designs and their applications to authentication codes and secret sharing schemes, Discrete Math. 279 (2004), 383-405. · Zbl 1044.94013 |
| [3] | R. Cramer, Y. Dodis, S. Fehr, C. Padró and D. Wichs, Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors, Lecture Notes in Computer Science 4965 (2008), 471-488 (Eurocrypt 2008). · Zbl 1149.94333 |
| [4] | M.B. Paterson and D.R. Stinson, Combinatorial characterizations of algebraic manipulation detection codes involving generalized difference families, Discrete Math. 339 (2016), 2891-2906. · Zbl 1401.94168 |
| [5] | M. Tompa and H. Woll, How to share a secret with cheaters, Journal of Cryptology 1 (1988), 133-138. · Zbl 0659.94008 |
| [6] | M. Carpentieri, A. De Santis and U. Vaccaro, Size of shares and probability of cheating in threshold schemes, Lecture Notes in Computer Science 765 (1994), 118-125 (Eurocrypt ’93). · Zbl 0951.94538 |
| [7] | K. Kurowawa, S. Obana andW. Ogata, t-cheater identifiable k, n threshold secret sharing schemes, Lecture Notes in Computer Science 963 (1995), 410-423. (CRYPTO ’95 Proceedings.) · Zbl 0876.94032 |
| [8] | C. Blundo and A. De Santis, Lower bounds for robust secret sharing schemes, Information Processing Letters 63 (1997) 317-321. · Zbl 1336.94077 |
| [9] | L. Cianciullo and H. Ghodosi, Improvements to almost optimum secret sharing with cheating detection, Lecture Notes in Computer Science 11049 (2018), 193-205 (IWSEC 2018). · Zbl 1398.94195 |
| [10] | Y. Liu, Linear k, n secret sharing scheme with cheating detection, Security Comm. Networks 9 (2016), 2115-2121. |
| [11] | D. Becerra and G. Vega, Secret sharing scheme with efficient cheating detection, In “NISS19: Proceedings of the 2nd International Conference on Networking, Information Systems & Security”, 2019, Article No. 5. |
| [12] | G.J. Simmons, Authentication theory / coding theory, Lecture Notes in Computer Science 196 (1985), 411-431. (CRYPTO ’84 Proceedings.) · Zbl 0575.94011 |
| [13] | J.L. Massey, Cryptography—a selective survey, In “Digital Communications,” 1986, pp. 3-21. |
| [14] | D.R. Stinson, The combinatorics of authentication and secrecy codes, Journal of Cryptology 2 (1990), 23-49. · Zbl 0701.94006 |
| [15] | R.S. Rees and D.R. Stinson, Combinatorial characterizations of authentication codes II, Designs, Codes and Cryptography 7 (1996), 239-259. · Zbl 0853.94019 |
| [16] | G. Ge, Y. Miao and L. Wang, Combinatorial constructions for optimal splitting authentication codes, SIAM J. Discrete Math. 18 (2005), 663-678. · Zbl 1076.94024 |
| [17] | M. De Soete, New bounds and constructions for authentication/secrecy codes with splitting, Journal of Cryptology 3 (1991), 173-186. · Zbl 0739.94010 |
| [18] | C. Blundo, A. De Santis, K. Kurosawa and W. Ogata, On a fallacious bound for authentication codes, Journal of Cryptology 12 (1999), 155-159. · Zbl 0936.94012 |
| [19] | M. Liang, L. Ji and J. Zhang, Some new classes of 2-fold optimal or perfect splitting authentication codes, Cryptogr. Commun. 9 (2017) 407-430. · Zbl 1355.05057 |
| [20] | M. Li, M. Liang, B. Du and J. Chen, A construction for optimal c-splitting authentication and secrecy codes, Designs, Codes and Cryptography 86 (2018), 1739-1755. · Zbl 1401.94186 |
| [21] | C.J. Colbourn and J.H. Dinitz, eds. Handbook of Combinatorial Designs, Second Edition. Chapman & Hall/CRC, 2007. · Zbl 1101.05001 |
| [22] | M.B. Paterson and D.R. Stinson. Algebraic manipulation detection codes and authentication codes with perfect secrecy. Preprint. |
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