基于马尔可夫决策的理性秘密共享方案

doi:10.11959/j.issn.1000-436x.2015249

通信学报 ›› 2015, Vol. 36 ›› Issue (9): 222-229.doi: 10.11959/j.issn.1000-436x.2015249

基于马尔可夫决策的理性秘密共享方案

田有亮¹,王雪梅²(),刘琳芳¹

¹ 贵州大学理学院，贵州贵阳 550025
² 贵阳职业技术学院，贵州贵阳 550023

出版日期:2015-09-25 发布日期:2017-09-15
基金资助:
国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;中国博士后基金资助项目;贵州省自然科学基金资助项目;贵州大学博士基金资助项目;贵州大学青年基金资助项目

Rational secret sharing scheme based on Markov decision

You-liang TIAN¹,Xue-mei WANG²(),Lin-fang LIU¹

¹ College of Science,Guizhou University,Guiyang 550025,China
² Guiyang Vocational and Technical College,Guiyang 550023,China

Online:2015-09-25 Published:2017-09-15
Supported by:
The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;China Postdoctoral Sci-ence Foundation;The Natural Science Foundation of Guizhou Province;The Doctors Science Founda-tion of Guizhou University;The Youth Foundation of Guizhou University

摘要/Abstract

摘要：

基于马尔可夫决策理论研究理性密码共享系统模型和秘密重构方法。首先利用马尔可夫决策方法，提出适合于理性秘密共享的系统模型，该模型包括参与者集合、状态集合、风险偏好函数、状态转移函数、回报函数等。在模型中，引入秘密重构中的参与者的风险偏好函数刻画秘密共享模型的状态集合和状态转移函数。其次，基于所提出的系统模型构造相应的理性秘密共享方案，基于马尔可夫策略解决各理性参与者在秘密共享方案中的秘密重构问题。最后对方案进行理论分析证明，给出理性秘密重构方案中折扣因子、回报函数、参与者风险偏好函数间的函数关系，其结果表明所提系统模型方法的合理性和有效性。

关键词: 理性秘密共享, 马尔可夫决策, 博弈论, 折扣因子, 风险偏好函数

Abstract:

The reconstruction methods of a rational secret sharing based on the Markov decision was studied.Firstly,a rational secret sharing system model was proposed using the Markov decision process,which included the players set,the states set,the risk preference function,the state transfer function,the return function,etc.The risk preference function was introduced in order to depict the state set and the state transfer function in this model.Secondly,a rational secret sharing scheme was constructed based on the proposed system model,which was able to solve the secret reconstruction problems according to the Markov strategy.Finally,the functional relations of among the discount factor,the return func-tion and the risk preference function was proposed in this scheme.The analysis results show that the proposed model and scheme are rationality and validity.

Key words: rational secret sharing, Markov decision, game theory, discount factor, risk preference function

田有亮,王雪梅,刘琳芳. 基于马尔可夫决策的理性秘密共享方案[J]. 通信学报, 2015, 36(9): 222-229.

You-liang TIAN,Xue-mei WANG,Lin-fang LIU. Rational secret sharing scheme based on Markov decision[J]. Journal on Communications, 2015, 36(9): 222-229.

图/表 7

图1

图2

图3

图4

图5

图6

表1

参考文献 18

[1]	HALPEN J , TEAGUE V . Rational secret sharing and multiparty com-putation:extended abstract[A]. Proc of the 36th annual ACM Sympo-sium on Theory of Computing[C]. New York, 2004.623-632.
[2]	FISCHERR M , WRIGHT R . An application of game-theoretic tech-niques to cryptography[EB/OL]. . 2011.
[3]	DODIS Y , HALEVI S , RABIN T . A cryptographic solution to a game theoretic problem[A]. Proc of CRYPTO2000[C]. Heidelberg,Springer, 2000.112-131.
[4]	GORDON S D , KATZ J . Rational secret sharing,revisited[A]. Proc of SCN 2006[C]. Heidelberg,Springer, 2006.229-241.
[5]	ABRAHAM I , DOLEV D , GONEN R , et al. Distributed computing meets game theory:robust mechanisms for rational secret sharing and multiparty computation[A]. Proc of the 25th Annual ACM Symp on Principles of Distributed Computing[C]. New York, 2006.53-62.
[6]	LYSYANSKAYA A , TRIANDOPOULOS N . Rationality and adver-sarial behaviour in multi-party computation(extended abstract)[A]. Proc of CRYPTO2006[C]. Heidelberg,Springer, 2006.180-197.
[7]	MALEKA S , AMJED S , PANDU R C. . The deterministic protocol for rational secret sharing[A]. Proc of IEEE Int Parallel and Distributed Processing Symp[C]. Piscataway,NJ, 2008.1-7.
[8]	MALEKA S , AMJED S , PANDU R C. . Rational secret sharing with repeated games[A]. Proc of Information Security Practice and Experi-ence[C]. Berlin,Springer, 2008.334-346.
[9]	ASHAROY G , LINDELL Y . Utility dependence in correct and fair rational secret sharing[A]. Proc of CRYPTO2009[C]. Heidelberg,Springer, 2009.559-576.
[10]	ZHANG Z F , LIU M L . Rational secret sharing as extensive games[J]. Science China Information Sciences, 2013,56(3): 1-13.
[11]	田有亮，马建峰，彭长根，等. 秘密共享体制的博弈论分析[J]. 电子学报 2011,39(12): 2790-2795. TIAN Y L , MA J F , PENG C G , et al. Game-theoretic analysis for the secret sharing scheme[J]. Acta Electronica Sinica, 2011,39(12): 2790-2795.
[12]	TIAN Y L , MA J F , PENG C G , et al. One-time rational secret sharing scheme based on Bayesian game[J]. Wuhan University Journal of Nature Science, 2011,16(5): 430-434.
[13]	TIAN Y L , MA J F , PENG C G , et al. A rational framework for secure communication[J]. Information Sciences, 2013,250:215-226.
[14]	TIAN Y L , PENG C G , LIN D D , et al. Bayesian mechanism for ra-tional secret sharing scheme[J]. Science China Information Sciences, 2015,58(5): 1-13.
[15]	田有亮，彭长根，马建峰，等. 通用可组合公平安全多方计算协议[J]. 通信学报 2014,35(2): 54-62. TIAN Y L , PENG C G , MA J F , et al. Universally composable secure multiparty computation protocol with fairness[J]. Journal on Commu-nications, 2014,35(2): 54-62.
[16]	张恩，蔡永泉 . 理性的安全两方计算协议[J]. 计算机研究与发展 2013,50(7): 1409-1417. ZHANG E , CAI Y Q . Rational secure two-party computation proto-col[J]. Journal of Computer Research and Development, 2013,50(7): 1409-1417.
[15]	彭长根，刘海，田有亮，等. 混合偏好模型下的分布式理性秘密共享方案[J]. 计算机研究与发展 2014,51(7): 1476-1485. PENG C G , LIU H , TIAN Y L , et al. A distributed rational secret sharing scheme with hybrid preference model[J]. Journal of Computer Research and Development, 2014,51(7): 1476-1485.
[18]	王伊蕾，郑志华，王皓，等. 满足可计算序贯均衡的理性公平计算[J]. 计算机研究与发展 2014,51(7): 1527-1537. WANG Y L , ZHENG Z H , WANG H , et al. Rational fair computation with computational sequential equilibrium[J]. Journal of Computer Research and Development, 2014,51(7): 1527-1537.

方案	安全基础	通信轮数	规则	均衡结果
文献[10]	消息认证码	L足够大	惩罚策略	序贯均衡
文献[11]	单向函数	n+1	惩罚策略	纳什均衡
文献[13]	签密算法	常数轮	效用最大	纳什均衡
文献[14]	签密算法	Poly(k)	贝叶斯规则	贝叶斯均衡
本文	消息认证码	Poly(k)	状态转移函数	马尔可夫均衡

基于马尔可夫决策的理性秘密共享方案

Rational secret sharing scheme based on Markov decision

在线阅读

PDF下载

可视化

被引次数

摘要/Abstract

引用本文

使用本文

图/表 7

参考文献 18

相关文章 15

Metrics

推荐阅读 0

[1]	冯智斌, 徐煜华, 杜智勇, 刘鑫, 李文, 韩昊, 张晓博. 对抗智能干扰的主动防御技术[J]. 通信学报, 2022, 43(10): 42-54.
[2]	张红斌, 尹彦, 赵冬梅, 刘滨. 基于威胁情报的网络安全态势感知模型[J]. 通信学报, 2021, 42(6): 182-194.
[3]	王桐, 高山, 龚慧雯, 孙博. 基于分时MDP的出租车载客预测推荐技术研究[J]. 通信学报, 2021, 42(2): 37-51.
[4]	赵临东,庄文芹,陈建新,周亮. 异构蜂窝网络中分层任务卸载：建模与优化[J]. 通信学报, 2020, 41(4): 34-44.
[5]	李沓,田有亮,向康,高鸿峰. 委托计算下基于区块链的公平支付方案[J]. 通信学报, 2020, 41(3): 80-90.
[6]	曾锋,王润华,彭佳,陈志刚. 口碑参与模式下移动众包网络的用户博弈研究[J]. 通信学报, 2019, 40(3): 125-138.
[7]	朱江,王婷婷,宋永辉,刘亚利. 无线网络中基于深度Q学习的传输调度方案[J]. 通信学报, 2018, 39(4): 35-44.
[8]	单芳芳,李晖,朱辉. 基于博弈论的社交网络转发控制机制[J]. 通信学报, 2018, 39(3): 172-180.
[9]	曹傧,梁裕丞,罗雷,唐述. ad hoc云环境中分布式博弈卸载策略[J]. 通信学报, 2017, 38(11): 24-34.
[10]	耿少峰,王永恒,李仁发,张佳. 主动式复杂事件处理方法的研究[J]. 通信学报, 2016, 37(9): 111-120.
[11]	贾亚男,岳殿武. 认知小蜂窝网络中基于能效的下行资源分配算法[J]. 通信学报, 2016, 37(4): 116-127.
[12]	曹傧,郎文强,陈卓,李云. 无线网络虚拟化中资源共享的功率分配算法[J]. 通信学报, 2016, 37(2): 64-72.
[13]	胡松华,张建军,陆阳,刘斌,韩江洪. 基于博弈论功率控制的串行干扰消除算法[J]. 通信学报, 2015, 36(9): 215-221.
[14]	王洁,蔡永泉,田有亮. 基于博弈论的门限签名体制分析与构造[J]. 通信学报, 2015, 36(5): 148-155.
[15]	郭晶晶，马建峰，李琦，万涛，高聪，张亮. 基于博弈论的移动自组织网络的信任管理方法[J]. 通信学报, 2014, 35(11): 6-49.