Abstract：To address the problem that participant can not be added or deleted dynamically in rational secret sharing scheme so far, this paper proposed a dynamic rational secret sharing scheme which combined game theory with cryptography. The scheme based on Chinese remainder theorem, can add or delete the participant dynamically in the secret reconstruction phase. And it is verifiable by using the verifiable random function, and the cheat of participants cannot work. The participants did not know whether the current round was a testing round. And the gain of following the protocol was more than the gain of deviating, so rational player had an incentive to abide the protocol. Finally, every player could obtain the secret fairly. In addition, the scheme satisfied resilient equilibrium and could withstand the conspiracy attack.
SHAMIR A. How to share a secret［J］. Communications of the ACM, 1979，22（11）： 612-613。
［2］
BLAKELEY G R. Safeguarding cryptographic keys［C］// Proceedings of the National Computer Conference。New York:AFIPS Press, 1979：313-317。
［3］
CHOR B, GOLDWASSER S, MICALI S. Verifiable secret sharing and achieving simultaneity in the presence of faults［C］// 26th Annual Symposium on Foundations of Computer Science. Washington, DC: IEEE Computer Society，1985：383-395.
［4］
FELDMAN P. A practical scheme for non-interactive verifiable secret sharing［C］// FOCS’ 87:28th IEEE Symposium on Foundations of Comp, Science。 Washington, DC: IEEE Computer Society, 1987: 427-437.
［5］
PEDERSEN T P. Distributed provers with applications to undeniable signatures［C］// Proceedings of Eurocrypt’91,LNCS 547。 Berlin: Springer, 1991: 221-238。
［6］
LIN H Y, HARN L. Fair reconstruction of a secret［J］。 Information Processing Letters, 1995, 55(1): 45-47.
［7］
HALPERN J, TEAGUE V. Rational secret sharing and multiparty computation［C］// Proceedings of the 36th Annual ACM Symposium on Theory of Computing。 New York : ACM, 2004: 623-632.
［8］
KOL G, NAOR M. Cryptography and game theory: Designing protocols for exchanging information［C］// Proceedings of the 5th Theory of Cryptography Conference。 Berlin: Springer, 2008: 317-336.
［9］
MALEKA S, AMJED S, RANGAN C P. Rational secret sharing with repeated games［C］// 4th Information Security Practice and Experience Conference, LNCS 4991。 Berlin: Springer, 2008: 334-346.
［10］
MALEKA S, AMJED S, RANGAN C P. The deterministic protocol for rational secret sharing［C］// the 22 th IEEE International Parallel and Distributed Processing Symposium。 Washington, DC: IEEE Computer Society, 2008: 3651-3657.
［11］
IZMALKOV S, LEPINSKI M, MICALI S. Veriably secure devices［C］// TCC 2008:5th Theory of Cryptography Conference, LNCS 4948。 Berlin: Springer, 2008: 273-301.
［12］
MICALI S, SHELAT A. Purely rational secret sharing［C］// TCC 2009:6th Theory of Cryptography Conference, LNCS 5444。 Berlin: Springer, 2009：54-71.
［13］
TOSHIYHKI I, KOICHIRO W, KEISUKE T. A rational secret-sharing scheme based on RSA-OAEP ［J］. IEICE Transactions on Fundamentals of Electronics Communications and Computer Science, 2010, E93-A(1): 42-49.
〖HJ1.7mm〗
［14］
KATZ J. Bridging game theory and cryptography: Recent results and future directions［C］// TCC 2008：5th Theory of Cryptography Conference， LNCS 4984. Berlin: Springer, 2008: 251-272.
［15］
ABRAHAM I, DOLEV D, GONEN R, et al。 Distributed computing meets game theory: Robust mechanisms for rational secret sharing and multiparty computation［C］// 25th ACM Symposium Annual on Principles of Distributed Computing. New York: ACM, 2006: 53-62.
［16］
MICALI S, RABIN M, VADHAN S. Verifiable random functions［C］// Proceedings of the 40th IEEE Symposium on Foundations of Computer Science。Washington, DC: IEEE Computer Society, 1999: 120-130.
［17］
DODIS Y, YAMPOLSKIY A. A verifiable random function with short proof and keys［C］//
8t
h International Workshop on Theory and Practice in Public Key Cryptography,LNCS 3386. Berlin: Springer, 2005: 416-431.
2012, Vol. 32 
