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Computer Technology and Development

Fair Coin Tossing Scheme Based on Jacobi Symbol

Hongyuan Wang

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

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.

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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.
We study various classical secure computation problems in the context of fairness, and relate them with each other. We also systematically study fair sampling problems (i.e., inputless functionalities) and discover three levels of complexity for them. Our results include the following: • Fair exchange cannot be securely reduced to the problem of fair coin-tossing by an r-round protocol, except with an error that is Ω ( 1 r). • Finite fair sampling problems with rational probabilities can all be reduced to fair cointossing and unfair 2-party computation (or equivalently, under computational assumptions). Thus, for this class of functionalities, fair coin-tossing is complete. • Only sampling problems which have fair protocols without any fair setup are the trivial ones in which the two parties can sample their outputs independently. Others all have an) error, roughly matching an upper bound for fair sampling from [22]. Ω ( 1 r
It is well known that it is impossible for two parties to toss a coin fairly (Cleve, STOC 1986). This result implies that it is impossible to securely compute with fairness any function that can be used to toss a coin fairly. In this paper, we focus on the class of deterministic Boolean functions with finite domain, and we ask for which functions in this class is it possible to information-theoretically toss an unbiased coin, given a protocol for securely computing the function with fairness. We provide a complete characterization of the functions in this class that imply and do not imply fair coin tossing. This characterization extends our knowledge of which functions cannot be securely computed with fairness. In addition, it provides a focus as to which functions may potentially be securely computed with fairness, since a function that cannot be used to fairly toss a coin is not ruled out by the impossibility result of Cleve (which is the only known impossibility result for fairness). In addition to the above, we draw corollaries to the feasibility of achieving fairness in two possible fail-stop models. Keywords: Fairness, coin tossing, secure computation, malicious and fail-stop adversaries
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.
An ideal coin tossing resource for two parties outputs the same random bit to both parties. We introduce the notion of an unfair coin tossing resource by relaxing both the fairness and the non-influenceability guarantees that an ideal coin toss would provide. The presence of this non-ideal behavior is necessary in order to understand what coin tossing protocols really achieve in the setting of two distrustful parties, since it is known that such an ideal coin tossing resource cannot be constructed whenever a majority of players is dishonest.
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.
The coin-tossing protocol is an important research area in cryptography. It generates a random bit with uniform distribution even if some participants might fraud. However, traditional coin-tossing protocol could not solve the situation of multiparty. It only divides participants into two parts. In this paper, a new kind of multiparty strict coin-tossing protocol based on the eigenvalue of matrix was proposed. First, matrix tampering attacks can be resisted. On the other hand, collusion attack which was caused by the addition of the Lagrange interpolation formula could be overcome. The analysis shows that the correctness and security of both protocols was guaranteed. Based on the above statements, comparing with the classic coin-tossing protocols, the proposed scheme has the advantage of resisting parties aborting, low complexity, and practicability.