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Computer Technology and Development

Fair Coin Toss Protocol Based on Composite Degree Residue Classes

LI Ji-lian

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In real life,tend to encounter many difficult choices. At this time,tend to solve the coin toss. It becomes difficult to play the game that needs face-to-face mechanism to ensure the fairness on Internet at the network information age,so playing coin toss game on Internet has valuable significance. Bit commitment can solve this problem. In this paper,using public-key cryptosystem based on composite degree residue classes,propose a new bit commitment scheme and prove the feasibility and security of the protocol. In the design of the protocol,introduce algorithmic game theory to guarantee that all players will loyally follow the prescribed game protocols.

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Secure coin-tossing is typically modeled as an input-less functionality, where parties with no private inputs jointly generate a fair coin. In the dishonest majority setting, however, a strongly fair coin-tossing protocol is impossible. To circumvent this barrier, recent work has adopted the weaker notion of game-theoretic fairness, where adversaries are rational parties with preferences for specific outcomes, seeking to bias the coin in their favor. Yet these preferences may encode secret information, making prior protocols that assume preferences are public, fundamentally incompatible with privacy. We initiate a comprehensive study of privacy-preserving game-theoretically fair coin-tossing, where the preferences of honest parties remain private. We propose a simulation-based security framework and a new ideal functionality that reconciles both preference-privacy and game-theoretic fairness. A key ingredient is a certifying authority that authenticates each party’s preference and publishes only aggregate statistics, preventing misreporting while hiding parties' preferences. The functionality guarantees that every honest party receives an output: either a uniform coin; or, if an adversary deviates, a coin that does not increase the adversarial coalition's expected utility. Within this framework, we construct a protocol realizing our ideal functionality under standard cryptographic assumptions that works for both binary and general m -sided coin-tossing. Our binary scheme matches the corruption threshold of Wu-Asharov-Shi (EUROCRYPT '22); our multi-sided scheme builds on Thyagarajan-Wu-Soni (CRYPTO '24) with a corruption guarantee depending on the coalition's preference counts. Technically, our protocols combine authenticated preferences with an anonymous communication layer that decouples identities from preference-dependent actions, together with a deviation-penalty mechanism that enforces game-theoretic fairness. Our work is the first to reconcile game-theoretic fairness with preference privacy, offering new definitional tools and efficient protocols for rational multi-party computation in dishonest majority settings.

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In real life,tend to encounter many difficult choices. At this time,tend to solve the coin toss. It becomes difficult to play the game that needs face-to-face mechanism to ensure the fairness on Internet at the network information age,so playing coin toss game on Internet has valuable significance. Bit commitment can solve this problem. In this paper,using public-key cryptosystem based on composite degree residue classes,propose a new bit commitment scheme and prove the feasibility and security of the protocol. In the design of the protocol,introduce algorithmic game theory to guarantee that all players will loyally follow the prescribed game protocols.
Quantum coin tossing is a simple cryptographic primitive with many applications in more complicated tasks and plays a crucial role in complex quantum cryptography protocol design. Coin tossing protocols in classical environment are often based on bit commitment protocol. It has been proved that unconditionally secure quantum bit commitment schemes are insecure. Therefore, quantum coin tossing based on quantum bit commitment protocol isn't unconditionally secure. In general, quantum coin tossing is strictly weaker than bit commitment. In this paper, we have proposed a quantum coin tossing protocol based on quantum public-key cryptosystems. According to quantum CSS codes, we constructed a class of quantum quasi-cyclic low-density parity-check codes, and then proposed a novel quantum coin tossing protocol. Security analysis show that the proposed protocols are more secure.
In real life,tend to encounter many difficult choices,by this time,tend to solve by coin toss.Such as the football match,before the match,the captain of two sides of the football team chooses one side to decide their half-court,then judge the toss of a coin,if a coin is positive,then party a from left to right attack;conversely,party b from left to right attack.This experiment is a kind of simple coin drop agreement,however,for two people not in the same place,how to fairly toss a coin,which is a research remains to be the problem.Based on operational properties and the difficulty of factorization for Jacobi symbols,give the solution to the problem of a safe and effective and fair coin tossing.Compared with the existing program,the program is simple,and to overcome the problem of a one-way hash function is difficult to construct.
Along with the Internet universal,the safe problem of network also increasingly important,we need a kind of legal means urgently to guarantee the communications' safety,protocol appear under this kind of background.Start from self-enforcing protocol that in the code protocol,intelligence poker game based on a fair coin toss protocol hare studied,it was RSA key system that employed in the agreement.The fairness of random number generator communication employed has got the further assurance in the procedure.
Secure coin-tossing is typically modeled as an input-less functionality, where parties with no private inputs jointly generate a fair coin. In the dishonest majority setting, however, a strongly fair coin-tossing protocol is impossible. To circumvent this barrier, recent work has adopted the weaker notion of game-theoretic fairness, where adversaries are rational parties with preferences for specific outcomes, seeking to bias the coin in their favor. Yet these preferences may encode secret information, making prior protocols that assume preferences are public, fundamentally incompatible with privacy. We initiate a comprehensive study of privacy-preserving game-theoretically fair coin-tossing, where the preferences of honest parties remain private. We propose a simulation-based security framework and a new ideal functionality that reconciles both preference-privacy and game-theoretic fairness. A key ingredient is a certifying authority that authenticates each party’s preference and publishes only aggregate statistics, preventing misreporting while hiding parties' preferences. The functionality guarantees that every honest party receives an output: either a uniform coin; or, if an adversary deviates, a coin that does not increase the adversarial coalition's expected utility. Within this framework, we construct a protocol realizing our ideal functionality under standard cryptographic assumptions that works for both binary and general m -sided coin-tossing. Our binary scheme matches the corruption threshold of Wu-Asharov-Shi (EUROCRYPT '22); our multi-sided scheme builds on Thyagarajan-Wu-Soni (CRYPTO '24) with a corruption guarantee depending on the coalition's preference counts. Technically, our protocols combine authenticated preferences with an anonymous communication layer that decouples identities from preference-dependent actions, together with a deviation-penalty mechanism that enforces game-theoretic fairness. Our work is the first to reconcile game-theoretic fairness with preference privacy, offering new definitional tools and efficient protocols for rational multi-party computation in dishonest majority settings.
Coin-flipping protocols allow mutually distrustful parties to generate a random bit with uniform distribution. Minimizing bias and keeping fairness are two key requirements in designing such protocols. However, the best previously known fair coin-flipping protocol only guarantees with bias O (1/ r ). In the paper, we introduce a new approach for fair coin-flipping protocol construction by using Garay et al ’s “resource fairness” technique and propose a resource-fair two-party coin-flipping protocol according to the standard real/ideal simulation paradigm. Compared with the other coin-flipping protocols, our protocol enjoys an important advantage that its bias is 0.