Secure and practical constant round mental poker
Secure and practical constant round mental poker
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安全实用的恒轮智力扑克
DOI：
10.1016/j.ins.2014.02.151
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Tzer
中科院分区：
文献类型：
--
作者：
Tzer
我们提出了一个新的心理扑克协议，它实现了在恒定轮作弊的概率可以忽略不计。以往的安全心理扑克协议都采用L轮零知识协议来保证主动作弊成功的概率为O（2-L）。我们的协议使用不同的方式来验证洗牌的完整性。我们的协议的密码系统和基本结构是基于Castellà-Roca的心理协议，这是非常有效和安全的。L轮零知识混洗验证被类似校验和的框架所取代。在我们的shuffle中使用了两种校验和：线性校验和和和双幂运算。“线性校验和”用于确保牌组中的每张牌都是不同的。“双幂校验和”用于确保每张卡都具有合法的面值。在DDH假设下证明了该方案的安全性。成功作弊的概率是可以忽略不计的，即使对手可以主动腐蚀大多数玩家。它也非常快。对于一个9人游戏，我们洗牌的计算成本与L= 4的L轮验证相当。我们的洗牌的时间复杂度是Θ（MN+ N 2）E（与L轮洗牌的Θ（MN 2 L）E相比），其中N是玩家的数量，M是卡片的数量，E是一次模幂运算的计算成本。通信成本也降低了。与L轮协议相比，该协议的消息数从Θ（N3 L）减少到Θ（N2），消息总长度从Θ（N2 L（M+ N））η减少到Θ（MN 2）η，其中η为密钥长度。对于9人游戏，我们的洗牌只需要53%的消息，消息的总长度只有7%（与L= 30的情况相比，所有L轮洗牌验证都允许并行运行）。这是第一个常数轮心理扑克协议，是可证明的安全和有效的，足以满足实际需要。作弊成功的概率微乎其微，
We present a new mental poker protocol, which achieves negligible probability of cheating in constant round. All of previous secure mental poker protocol use L-round zero-knowledge protocols to ensure the probability of successful active cheating to be O (2-L). Our protocol uses a different way to verify the integrity of the shuffle. The cryptosystem and the basic structure of our protocol is based on Castellà-Roca’s mental protocol, which is very efficient and secure. The L-round zero-knowledge shuffle verification is replaced by a checksum-like framework. There are two kinds of checksums used in our shuffle: linear checksum and double exponentiation. The “linear checksum” is used to make sure that every card in the deck is distinct. The “double exponentiation checksum” is used to make sure that every card has a legitimate face value. The security can be proved under DDH assumption. The probability of successful cheating is negligible, even if the adversary can actively corrupt the majority of players. It is also very fast. For a 9 player game, the computation cost of our shuffle is comparable to the L-round verification with L= 4. The time complexity of our shuffle is Θ (MN+ N 2) E (compares to Θ (MN 2 L) E for a L-round shuffle), where N is the number of players, M is the number of cards, and E is the computation cost of one modular exponentiation. The communication cost is also reduced. Compares to the L-round protocol we based on, number of messages is reduced from Θ (N 3 L) to Θ (N 2), and the total length of messages is reduced from Θ (N 2 L (M+ N)) η to Θ (MN 2) η, where η is the length of an encryption key. For a 9-player game, our shuffle requires only 53% messages, and total length of messages is only 7%(compares to the case L= 30 and all L rounds of shuffle verification are allowed to run in parallel). It is the first constant round mental poker protocol that is provably secure and efficient enough to satisfy the practical needs. The probability of successful cheating is negligible,