{"title":"A Cheating Model for Cellular Automata-Based Secret Sharing Schemes","authors":"Borna Jafarpour, Azadeh Nematzadeh, Vahid Kazempour, Babak Sadeghian","volume":7,"journal":"International Journal of Computer and Information Engineering","pagesStart":1984,"pagesEnd":1989,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12471","abstract":"
Cellular automata have been used for design of cryptosystems. Recently some secret sharing schemes based on linear memory cellular automata have been introduced which are used for both text and image. In this paper, we illustrate that these secret sharing schemes are vulnerable to dishonest participants- collusion. We propose a cheating model for the secret sharing schemes based on linear memory cellular automata. For this purpose we present a novel uniform model for representation of all secret sharing schemes based on cellular automata. Participants can cheat by means of sending bogus shares or bogus transition rules. Cheaters can cooperate to corrupt a shared secret and compute a cheating value added to it. Honest participants are not aware of cheating and suppose the incorrect secret as the valid one. We prove that cheaters can recover valid secret by removing the cheating value form the corrupted secret. We provide methods of calculating the cheating value.<\/p>\r\n","references":"[1] J. Pieprzyk, T. Hardjono, J. Seberry, \"Fundamentals of Computer\r\nSecurity,\" Springer, 2003.\r\n[2] G. R. Blakley, \"Safeguarding cryptographic keys,\" in Proc. of 1979\r\nAFIPS National Computer Conference, 1979, pp. 313-317.\r\n[3] A. Shamir, \"How to Share a Secret,\" Communications of the ACM, Vol.\r\n22. No. 11., 1979, pp. 612 - 613.\r\n[4] M. Tompa, H. Woll, \"How to share a secret with cheaters,\" Journal of\r\nCryptology, Vol. 1. No. 2. , 1988, pp. 133-138.\r\n[5] H. Ghodosi, J. Pieprzyk, \"Cheating prevention in secret sharing,\"\r\nAustralasian Conference on Information Security and Privacy, 2000, pp.\r\n328-341.\r\n[6] J. Pieprzyk, X. Zhang, \"Cheating Prevention in Linear Secret Sharing,\"\r\nInformation Security and Privacy. Lecture Notes in Computer Science,\r\nVol. 2384, 2002, pp. 121-131.\r\n[7] A. Rey , J. P. Mateus, G. R. Sanchez, \"A secret sharing scheme based on\r\ncellular automata,\" Applied Mathematics and Computation, Vol. 170,\r\n2005, pp. 1356-1364.\r\n[8] G. A. Maranon, L.H. Encinas, A. M. Rey, \"Sharing secret color images\r\nusing cellular automata with memory,\" CoRR 0312034, 2003.\r\n[9] G. Alvarez, A.H. Encinas, L.H. Encinas, A. M. Rey, \"A secure scheme\r\nto share secret color images,\" Computer and Physics communication,\r\nVol. 173. No. 1-2., 2005, pp. 9-16.\r\n[10] G. A. Maranon, L.H. Encinas, A. M. Rey, \"A new secret sharing\r\nschemes for images based on additive 2-dimensional cellular automata,\"\r\nPattern Recognition and Image Analysis. Lecture note in computer\r\nscience, Vol. 3522, 2005, pp. 411-418.\r\n[11] S. Wolfram, \"Cellular Automata, Los Alamos Science,\" Vol. 9, 1983,\r\npp. 2-21.\r\n[12] R. Alonso-Sanz, M. Mart\u2500\u2592n, \"Elementary cellular automata with\r\nmemory,\" Complex Systems, Vol. 14, 2003, pp. 99-126.\r\n[13] R. Alonso-Sanz, M. Mart\u2500\u2592n, \"One-dimensional cellular automata with\r\nmemory: patterns from a single site seed,\" Int. J. Bifur. Chaos\r\nApplication Science Engineering, Vol. 12, 2002, pp. 205-226.\r\n[14] C. Meadows, \"A formal framework and evaluation method for network\r\ndenial of service,\" in Proc. Of 1999 IEEE Computer Security\r\nFoundations Workshop, 1998, pp. 4-13.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 7, 2007"}