A multisecret sharing scheme for color images based on cellular automata. (English) Zbl 1231.94058

Summary: A new multisecret sharing scheme for secret color images among a set of users is proposed. The protocol allows that each participant in the scheme to share a secret color image with the rest of participants in such a way that all of them can recover all the secret color images only if the whole set of participants pools their shadows. The proposed scheme is based on the use of bidimensional reversible cellular automata with memory. The security of the scheme is studied and it is proved that the protocol is ideal and perfect and that it resists the most important statistical attacks.


94A62 Authentication, digital signatures and secret sharing
68Q80 Cellular automata (computational aspects)
Full Text: DOI Link


[1] Alonso-Sanz, R., Reversible cellular automata with memory: two-dimensional patterns from a single seed, Physica D, 175, 1-30, (2003) · Zbl 1008.37008
[2] Álvarez Marañón, G.; Hernández Encinas, L.; Martín del Rey, A., A new secret sharing scheme for images based on additive 2-dimensional cellular automata, Lecture notes in comput. sci., pattern recognition and image analysis, 3522, 411-418, (2005)
[3] Bao, F., Cryptanalysis of a partially known cellular automata cryptosystem, IEEE trans. comput., 53, 1493-1497, (2004)
[4] Blakley, G.R., Safeguarding cryptographic keys, AFIPS conf. proc., 48, 313-317, (1979)
[5] Chang, C.C.; Chuang, J.C., An image intellectual property protection scheme for gray-level images using visual secret sharing strategy, Pattern recogn. lett., 23, 931-941, (2002) · Zbl 1015.68159
[6] Chaudhuri, P.; Chowdhury, D.; Nandi, S.; Chattopadhyay, S., Additive cellular automata. theory and applications, vol. 1, (1997), IEEE Computer Society Press Los Alamitos
[7] Chen, Y.F.; Chan, Y.K.; Huang, C.C.; Tsai, M.H.; Chu, Y.P., A multiple-level visual secret-sharing scheme without image size expansion, Inform. sci., 177, 21, 4696-4710, (2007) · Zbl 1142.94368
[8] Chien, H.Y.; Jan, J.K.; Tseng, Y.M., A practical \((t, n)\) multi-secret sharing scheme, IEICE trans. fundam., E83-A, 2762-2765, (2000)
[9] Chu, C.K.; Tzeng, W.G., Optimal resilient threshold GQ signatures, Inform. sci., 177, 8, 1834-1851, (2007) · Zbl 1110.94027
[10] Díaz Len, R.; Hernández Encinas, A.; Hernández Encinas, L.; Hoya White, S.; Martín del Rey, A.; Rodríguez Sánchez, G.; Visus Ruíz, I., Wolfram cellular automata and their cryptographic use as pseudorandom bit generators, Int. J. pure appl. math., 4, 87-103, (2003) · Zbl 1036.94007
[11] FIPS 140-2, Security requirements for cryptographic modules, Federal Information Processing Standards Publication 140-2, US Department of Commerce/National Institute of Standards and Technology, Springfield, VA, Issued May 25, 2001.
[12] Fraile Rubio, C.; Hernández Encinas, L.; Hoya White, S.; Martín del Rey, A.; Rodríguez Sánchez, G., The use of linear hybrid cellular automata as pseudorandom bit generators in cryptography, Neural parallel sci. comput., 12, 175-192, (2004) · Zbl 1161.68439
[13] Fredkin, E., Digital mechanics. an informal process based on reversible universal cellular automata, Physica D, 45, 254-270, (1990) · Zbl 0719.68044
[14] Guan, P., Cellular automaton public-key cryptosystem, Complex syst., 1, 51-57, (1987) · Zbl 0652.94014
[15] Harn, L., Comment: multistage secret sharing based on one-way function, Electron. lett., 31, 262, (1995)
[16] Harn, L., Efficient sharing (broadcasting) of multiple secret, IEE proc., comput. digital techn., 142, 237-240, (1995)
[17] He, J.; Dawson, E., Multisecret-sharing scheme based on one-way function, Electron. lett., 30, 1591-1592, (1994)
[18] He, J.; Dawson, E., Multisecret-sharing scheme based on one-way function, Electron. lett., 31, 93-95, (1995)
[19] Hwang, R.J.; Chang, C.C., An on-line secret sharing scheme for multi-secrets, Comput. commun., 21, 1170-1176, (1998)
[20] Kaya, K.; Selçuk, A.A., Threshold cryptography based on asmuthbloom secret sharing, Inform. sci., 177, 19, 4148-4160, (2007) · Zbl 1142.94372
[21] Koga, H.; Ueda, E., Basic properties of the \((t, n)\)-threshold visual secret sharing scheme with perfect reconstruction of black pixels, Des. codes cryptogr., 40, 1, 81-102, (2006) · Zbl 1261.94026
[22] Meier, W.; Staffelbach, O., Analysis of pseudorandom sequences generated by cellular automata, Advances in cryptology - EUROCRYPT’91, Lecture notes in comput. sci., 547, 186-189, (1991) · Zbl 0791.68121
[23] Menezes, A.; van Oorschot, P.; Vanstone, S., Handbook of applied cryptography, (1997), CRC Press Boca Raton, FL · Zbl 0868.94001
[24] Nandi, S.; Kar, B.K.; P Chaudhuri, P., Theory and applications of cellular automata in cryptography, IEEE trans. comput., 43, 1346-1357, (1994)
[25] Naor, M.; Shamir, A., Visual cryptography, Advances in cryptology - EUROCRYPT’94, Lect. notes comput. sci., 950, 1-12, (1995) · Zbl 0878.94048
[26] Shamir, A., How to share a secret, Commun. ACM, 22, 612-613, (1979) · Zbl 0414.94021
[27] Stinson, D.R., An explication of secret sharing schemes, Des. codes cryptogr., 2, 357-390, (1992) · Zbl 0793.68111
[28] Stinson, D.R., Cryptography theory and practice, (2002), CRC Press Boca Raton, FL · Zbl 0997.94001
[29] Thien, C.; Lin, J., Secret image sharing, Comput. graphics, 26, 765-770, (2002)
[30] Toffoli, T.; Margolus, N., Invertible cellular automata: a review, Physica D, 45, 229-253, (1990) · Zbl 0729.68066
[31] Tsai, C.S.; Chang, C.C.; Chen, T.S., Sharing multiple secrets in digital images, J. syst. software, 64, 163-170, (2002)
[32] Wang, L.; Cao, Z.; Li, X.; Qian, H., Simulatability and security of certificateless threshold signatures, Inform. sci., 177, 6, 1382-1394, (2007) · Zbl 1125.94039
[33] Wang, F.H.; Yen, K.K.; Jain, L.C.; Pan, J.S., Multiuser-based shadow watermark extraction system, Inform. sci., 177, 12, 2522-2532, (2007)
[34] Wolfram, S., Random sequence generation by cellular automata, Adv. appl. math., 7, 123-169, (1986) · Zbl 0603.68053
[35] Wolfram, S., Cryptography with cellular automata, Advances in cryptology - CRYPTO’85, Lecture notes in comput. sci., 218, 429-432, (1986)
[36] Yang, C.C.; Chang, T.Y.; Hwang, M.S., A\((t, n)\) multi-secret sharing scheme, Appl. math. comput., 151, 483-490, (2004) · Zbl 1045.94018
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.