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arXiv 1301.4289cs.CRcs.ITmath.IT
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一种卡片密码学的几何协议

A geometric protocol for cryptography with cards

Andrés Cordón-Franco, Hans van Ditmarsch, David Fernández-Duque, Fernando Soler-Toscano

摘要:

在广义的俄罗斯纸牌问题中,三个玩家Alice、Bob和Cath分别从一副a+b+c牌中抽出a、b和c牌。玩家只知道自己的牌和这副牌是什么。然后,爱丽丝和鲍勃需要通过公共消息的方式将他们手中的牌相互通信。如果Cath不知道任何特定卡的所有权,则该通信被认为是安全的;在本文中,我们考虑了Swanson和Stinson引入的加强的安全概念,我们称之为K-安全。阿特金森提出了一个优雅的解决方案,将纸牌视为有限投影平面上的点。我们提出了一个普遍的解决方案的精神阿特金森的,虽然基于有限的向量空间,而不是投影平面,并称之为“几何协议”。给定任意的c,k>0,该协议给出了无限多个(a,b,c)值且b=O(ac)的广义Russian cards问题的信息量和k-安全的解决方案。这改进了已知解的参数的收集。特别是,它是第一个在Cath有多个卡时保证$k$安全性的解决方案。

英文摘要:

In the generalized Russian cards problem, the three players Alice, Bob and Cath draw a,b and c cards, respectively, from a deck of a+b+c cards. Players only know their own cards and what the deck of cards is. Alice and Bob are then required to communicate their hand of cards to each other by way of public messages. The communication is said to be safe if Cath does not learn the ownership of any specific card; in this paper we consider a strengthened notion of safety introduced by Swanson and Stinson which we call k-safety. An elegant solution by Atkinson views the cards as points in a finite projective plane. We propose a general solution in the spirit of Atkinson's, although based on finite vector spaces rather than projective planes, and call it the `geometric protocol'. Given arbitrary c,k>0, this protocol gives an informative and k-safe solution to the generalized Russian cards problem for infinitely many values of (a,b,c) with b=O(ac). This improves on the collection of parameters for which solutions are known. In particular, it is the first solution which guarantees $k$-safety when Cath has more than one card.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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