zbMATH — the first resource for mathematics

On ASGS framework: general requirements and an example of implementation. (English) Zbl 1129.68439
Summary: In the paper we propose a general, abstract framework for Automatic Secret Generation and Sharing (ASGS) that should be independent of underlying secret sharing scheme. ASGS allows to prevent the Dealer from knowing the secret. The basic property conjecture forms the base of the framework. Due to the level of abstraction, results are portable into the realm of quantum computing. Two situations are discussed. First concerns simultaneous generation and sharing of the random, prior nonexistent secret. Such a secret remains unknown until it is reconstructed. Next, we propose the framework for automatic sharing of a known secret. In this case the Dealer does not know the secret and the secret Owner does not know the shares. We present opportunities for joining ASGS with other extended capabilities, with special emphasis on PVSS and pre-positioned secret sharing. Finally, we illustrate framework with practical implementation.
68P25 Data encryption (aspects in computer science)
94A60 Cryptography
Full Text: DOI arXiv
[1] Anderson, R., 2001. Security Engineering—A Guide to Building Dependable Distributed Systems. John Wiley & Sons, New York.
[2] Asmuth, C.; Bloom, J., A modular approach to key safeguarding, IEEE Trans. Inf. Theory, 29, 208-211, (1983)
[3] Blakley, G.R., 1979. Safeguarding Cryptographic Keys. Proceedings AFIPS 1979 National Computer Conference, p.313-317.
[4] Blundo, C.; Stinson, D. R., Anonymous secret sharing schemes, Discrete Applied Mathematics, 77, 13-28, (1997) · Zbl 0943.94009
[5] Blundo, C.; Giorgio Gaggia, A.; Stinson, D. R., On the dealer’s randomness required in secret sharing schemes, Designs, Codes and Cryptography, 11, 107-122, (1997) · Zbl 0884.94019
[6] Brickell, E. F., Some ideal secret sharing schemes, J. Combin. Math. Combin. Comput., 6, 105-113, (1989) · Zbl 0685.94003
[7] Budd, T., 1997. The Introduction to Object-Oriented Programming. Addison-Wesley, Reading.
[8] Desmedt, Y.; Frankel, Y., Threshold cryptosystems. crypto’89, LNCS, 435, 307-315, (1989)
[9] Gennaro, R.; Jarecki, S.; Krawczyk, H.; Rabin, T., Secure distributed key generation for discrete-log based cryptosystems. eurocrypt’99, LNCS, 1592, 295-310, (1999) · Zbl 0931.94021
[10] Gruska, J., 1999. Quantum Computing. McGraw Hill, New York. · Zbl 0985.81022
[11] Herstein, I.N., 1964. Topics in Algebra. Blaisdell Publishing, Waltham, Massachusetts. · Zbl 0122.01301
[12] Ito, M., Saito, A., Nishizeki, T., 1987. Secret Sharing Scheme Realizing General Access Structure. Proc. IEEE Globecom’87, p.99-102.
[13] Karnin, E. D.; Greene, J. W.; Hellman, M. E., On secret sharing systems, IEEE Trans. Inf. Theory, 29, 35-41, (1983) · Zbl 0503.94018
[14] Knuth, D.E., 1997. The Art of Computer Programming—Seminumerical Algorithms. Vol. 2, 3rd Ed., Addison-Wesley, Reading. · Zbl 0191.18001
[15] Koblitz, N., 1993. Introduction to Elliptic Curves and Modular Forms. Springer-Verlag, New York. · Zbl 0804.11039
[16] Kulesza, K.; Kotulski, Z., No article title, On Secret Sharing Schemes with Extended Capabilities. RCMIS’02, 1, 79-88, (2002)
[17] Kulesza, K., Kotulski, Z., Pieprzyk, J., 2002. On Alternative Approach for Verifiable Secret Sharing. Esorics’02. Available from IACR’s Cryptology ePrint Archive (http://eprint.iacr.org/).
[18] Kulesza, K.; Kotulski, Z.; Soldek, J. (ed.); Drobiazgiewicz, L. (ed.), On automatic secret generation and sharing for karin-Greene-hellman scheme, 281-292, (2003), Boston
[19] Li, C.; Hwang, T.; Lee, N., (t,n) threshold signature schemes based on discrete logarithm. eurocrypt’94, LNCS, 950, 191-200, (1994)
[20] Menezes, A.J., van Oorschot, P., Vanstone, S.C., 1997. Handbook of Applied Cryptography. CRC Press, Boca Raton. · Zbl 0868.94001
[21] Pedersen, T., A threshold cryptosystem without a trusted third party. eurocrypt’99, LNCS, 547, 522-526, (1991) · Zbl 0766.94014
[22] Pieprzyk, J., Hardjono, T., Seberry, J., 2003. Fundamentals of Computer Security. Springer-Verlag, Berlin. · Zbl 1011.68034
[23] Shamir, A., How to share a secret, Commun. ACM, 22, 612-613, (1979) · Zbl 0414.94021
[24] Shoup, V.; Gennaro, R., Securing threshold cryptosystems against chosen ciphertext attack. crypto’98, LNCS, 1403, 1-16, (1998) · Zbl 0919.94031
[25] Stadler, M., Publicly verifiable secret sharing. eurocrypt’96, LNCS, 1070, 190-199, (1996) · Zbl 1304.94109
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.