A Threshold Scheme under Peer-to-Peer Network

Resource sharing among peers is one of important application in Peer-to-Peer（P2P） network. Inexistenee of server makes P2P network to be a less trustable tool for property owners to distribute their resource. In order to protect intelligent property, reputation management strategy is adopted in many P2P network. As long as a P2P network reputation strategy is confirmed, application designer can employ a special detailed distribution scheme to fulfill content distribution within the net. Shmir （k, n） threshold scheme, for example, is an encryption scheme to enhance the distribution se curity of this kind of design. （k＊, n） threshold scheme is a new tool similar to Shmir scheme is proposed in this paper. The new scheme based on polynomial expansion and its security is decided by the one way function used in the secret distribution procedure. The scheme efficiency and its features as well as comparison between new and Shmir scheme are also discussed in this paper.

Verifiable quantum secret sharing scheme based on orthogonal product states

In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques.This protocol is initiated by the dealer Alice,who initially prepares a quantum product state,selected from a predefined set of orthogonal product states within the C~d■C~d framework.Subsequently,the participants execute unitary operations on this product state to recover the underlying secret.Furthermore,we subject the protocol to a rigorous security analysis,considering both eavesdropping attacks and potential dishonesty from the participants.Finally,we conduct a comparative analysis of our protocol against existing schemes.Our scheme exhibits economies of scale by exclusively employing quantum product states,thereby realizing significant cost-efficiency advantages.In terms of access structure,we adopt a(t, n)-threshold architecture,a strategic choice that augments the protocol's practicality and suitability for diverse applications.Furthermore,our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol.

THRESHOLD SCHEMES WITH WEIGHTS

In this paper, we present the model of threshold schemes with weights as a natural generalization of Shamir's threshold scheme and show how to apply the model to construct secret sharing schemes by two examples.

Efficient Dynamic Threshold Group Signature Scheme Based on Elliptic Curve Cryptosystem

The short secret key characteristic of elliptic curve cryptosystem （ECC） are integrated with the （ t, n ） threshold method to create a practical threshold group signature scheme characterized by simultaneous signing. The scheme not only meets the requirements of anonymity and traceability of group signature but also can withstand Tseng and Wang＇s conspiracy attack. It allows the group manager to add new members and delete old members according to actual application, while the system parameters have a little change. Cryptanalysis result shows that the scheme is efficient and secure.

AN EFFICIENT AND SECURE (t, n) THRESHOLD SECRET SHARING SCHEME

Based on Shamir’s threshold secret sharing scheme and the discrete logarithm problem, a new (t, n) threshold secret sharing scheme is proposed in this paper. In this scheme, each participant’s secret shadow is selected by the participant himself, and even the secret dealer cannot gain anything about his secret shadow. All the shadows are as short as the shared secret. Each participant can share many secrets with other partici- pants by holding only one shadow. Without extra equations and information designed for verification, each participant is able to check whether another participant provides the true information or not in the recovery phase. Unlike most of the existing schemes, it is unnecessary to maintain a secure channel between each par- ticipant and the dealer. Therefore, this scheme is very attractive, especially under the circumstances that there is no secure channel between the dealer and each participant at all. The security of this scheme is based on that of Shamir’s threshold scheme and the difficulty in solving the discrete logarithm problem. Analyses show that this scheme is a computationally secure and efficient scheme.

Threshold Decryption Scheme withMultiple Policies

Based on the difficulty in computing discrete logarilhm and square 1001 onsome special conditions, we propose a basic threshold seeret sharing scheme for multiple secretswith multiple policies, which allows a group of users to share multiple secrttkeys and only onesecret shadow to be ktpt by each user. An efficient threshold decryption scheme with multiplepolicies is designed on the basis of the basic threshold scheme. This decryption scheme allowsmultiple secret keys to he shared among a groupof users, and each user to ketp only one secretshadow. Different public keys can be used to encrypt documents. If and only if the number ofcooperated users who koop the secret shadows is greater than or c-qual to the threshold value of thecorresponding secret key, they can cooperate to decrypt the documents. It is proved that theproposed scheme has very strong security, unless the attackers can solve the discrete logarithmproblem and the square root problem.

Threshold Signature Scheme Based on Discrete Logarithm and Quadratic Residue

Digital signature scheme is a very important research field in computer security and modern cryptography. A (k, n) threshold digital signature scheme is proposed by integrating digital signature scheme with Shamir secret sharing scheme. It can realize group-oriented digital signature, and its security is based on the difficulty in computing discrete logarithm and quadratic residue on some special conditions. In this scheme, effective digital signature can not be generated by anyk?1 or fewer legal users, or only by signature executive. In addition, this scheme can identify any legal user who presents incorrect partial digital signature to disrupt correct signature, or any illegal user who forges digital signature. A method of extending this scheme to an Abelian group such as elliptical curve group is also discussed. The extended scheme can provide rapider computing speed and stronger security in the case of using shorter key. Key words threshold scheme - digital signature - discrete logarithm - quadratic residuc - threshold digital signature CLC number TP 309. 7 Foundation item: Supported the National Nature Science Foundation of China, Hubei Province (90104005, 2002 AB0039)Biography: FEI Ru-chun (1964-), male, Ph. D candidate, Associated professor, research direction: information security and cryptography.

Robust Threshold Guillou-Quisquater Signature Scheme

The deficiencies of the first threshold Guilbu-Quisquater signature schemepresented by Li-San Liu, Cheng-Kang Chu and Wen-Guey Tzeng arc analysiscd at first, and then a newthreshold Guillou-Quisquater signature scheme is presented. The new scheme isunforgeable and robustagainst any adaptive adversary if the base Guillou-Quisquater signature scheme is unforgeable underthe chosen message attack and computing the discrete logarithm modulo a prime is hard This schemecan also achieve optimal resilience. However, the new scheme does not need the assumption that N isthe product of two safe primes. The basie signature scheme underlying the new scheme is exactlyGuillou-Quisqualtr signature scheme, and the additional strong computation assumption introduced bythe first threshold Guillou-Quisquater scheme is weaken.

A Secure and Efficient (t, n) Multi-Secret Sharing Scheme

Based on Shamir's secret sharing, a (t, n) multi-secret sharing scheme isproposed in this paper p secrets can be shared among n participants, and t or more participants canco-operate to reconstruct these secrets at the same time, but t— 1 or fewerparticipants can derivenothing about these secrets. Each participant's secret shadow is as short as each secret. Comparedwith the existing schemes, the proposed scheme is characterized by the lower complexity of thesecret reconstruction and less public information. The security of this scheme is the same as thatof Shamir' a threshold scheme. Analyses show that this scheme is an efficient, computationallysecure scheme.

基于门限签名的时间轮换公证人组模型研究

随着各类区块链系统的不断涌现,跨链交互需求不断增加,跨链桥验证环节的安全性显得愈发重要。公证人机制原理简单、效率较高,常用于跨链交易验证、跨链交易确认等环节。但公证人机制存在去中心化程度低、低签名比例可验证交易、验证节点信息公开等问题。为提高跨链桥验证环节的安全性,提出了一种基于门限签名的时间轮换公证人组模型。该模型中的公证人组由同时拥有源区块链和目标区块链账户的高信用值节点组成。公证人组中的验证节点有任期要求且需质押保证金,公证人组采用门限签名技术对跨链交易进行签名,一半以上的验证节点签名后,跨链交易才能实施;候选公证人组为时间轮换公证人组提供新验证节点。分析结果表明,所提模型去中心化程度高,验证节点恶意攻击率低,验证签名环节安全性高,验证节点私密性高,跨链消息验证效率高。

Optimization of threshold for local spectrum sensing with energy detector

Spectrum sensing is the first step of cognitive radio （CR）. In this area, previous researches mostly consider distributed local nodes which are under identical channel conditions, hence uniform and fixed detection threshold is set with energy detector. However, the distributions of nodes in real environments are not quite the same. In this paper, the optimal threshold to minimize the total detection error over add＇itive white Gaussion noise （AWGN） channel is derived firstly. Then the dynamic threshold scheme is proposed to reduce the average total detection error. Simulations have shown that, with this scheme, sensing performance is improved.

Verifiable Secret Sharing Scheme Based on the Plane Parametric Curve

Verifiable secret sharing is a special kind of secret sharing. In this paper, A secure and efficient threshold secret sharing scheme is proposed by using the plane parametric curve on the basis of the principle of secret sharing. And the performance of this threshold scheme is analyzed. The results reveal that the threshold scheme has its own advantage of one-parameter representation for a master key, and it is a perfect ideal secret sharing scheme. It can easily detect cheaters by single operation in the participants so that the probability of valid cheating is less than 1/p (where p is a large prime).

A THRESHOLD BLIND SIGNATURE FROM WEIL PAIRING ON ELLIPTIC CURVES

The idea behind a (t, n) threshold blind signature is that a user can ask at least t out of n players of a group to cooperate to generate a signature for a message without revealing its content. This paper first presents a new blind signature scheme from Weil pairing on elliptic curves. Based on this scheme, a threshold blind signature scheme is proposed. It is efficient and has the security properties of robustness and unforgeability. In the proposed scheme, the group manger is introduced to take the role of distributing the group secret key to each player. However, he cannot forge the players to generate partial blind signatures (Each partial blind signature depends on not only the secret key of the player, but also a random number the player picks). Compared with a threshold signature with a trusted third party, its advantage is obvious; Compared with a threshold signature without a trusted third party, it is more simple and efficient.

Special secret sharing scheme with the function of assignment

A concept of secret sharing scheme with the function of assignment is proposed. It provides great capabilities for many practical applications. In this scheme, the dealer can randomly assign one or more than one participant to get the secret at any time, but these participants can get nothing about the secret before that moment. At the same time, the other participants cannot get anything about the secret by stealing the secret value when it is transferred. However, if the dealer is lost, a certain number or more partidtmnts of them can reoonstruct the secret by ccoperating. In order to clear this concept, an illustrating scheme with geometry method and a practical scheme with algebra method is given.

On Accelerated Singular Value Thresholding Algorithm for Matrix Completion

An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.

Threshold Parameter for the Control of Unemployment in the Society: Mathematical Model and Analysis

Unemployment is one of the major vices in our contemporal society, which weigh greatly on the economy of such nation. It is also, a fact that knowing ones enemy before battle gives 50 per cent chance of victory;thus, this research aimed at providing understanding about dynamics of unemployment with consideration for retirement and possible control criterion. And the objectives are;formulation of mathematical model using the concept of deterministic model and mathematical epidemiology;then, model analysis. The model analysis includes, a numerical semi-analytical scheme for investigating validity of analytical solutions. The result of the analysis were that: 1) the model was mathematically well-pose and biologically meaningful 2) two equilibria points exist, and 3) a threshold for recruitment from the pool of unemployment, assuring victory in the fight against unemployment was also, obtained. The threshold is required to be well managed in order to win the battle against the socio-vice (unemployment) in the contemporary society. In addition, variational iterative method (VIM) is the numerical semi-analytic scheme employed to solve the model;thus, the approximate solution gave a practical meaningful interpretation supporting the analytical results and proof of verdict of assumptions of the model. The article concluded with three points;everyone has roles to play to curtail the socio-menace, beseech government and policy makers to look kindly, and create policy(ies) to sustain population growth, and the retiree should also, plan live after service, because over dependence on pension scheme could be died before death because of corruption in the scheme.

Asynchronous Secret Reconstruction and Its Application to the Threshold Cryptography

In Shamir’s(t,n) threshold of the secret sharing scheme, a secret is divided into n shares by a dealer and is shared among n shareholders in such a way that (a) the secret can be reconstructed when there are t or more than t shares;and (b) the secret cannot be obtained when there are fewer than t shares. In the secret reconstruction, participating users can be either legitimate shareholders or attackers. Shamir’s scheme only considers the situation when all participating users are legitimate shareholders. In this paper, we show that when there are more than t users participating and shares are released asynchronously in the secret reconstruction, an attacker can always release his share last. In such a way, after knowing t valid shares of legitimate shareholders, the attacker can obtain the secret and therefore, can successfully impersonate to be a legitimate shareholder without being detected. We propose a simple modification of Shamir’s scheme to fix this security problem. Threshold cryptography is a research of group-oriented applications based on the secret sharing scheme. We show that a similar security problem also exists in threshold cryptographic applications. We propose a modified scheme to fix this security problem as well.

Some Secret Sharing Schemes Based on the Finite Fields

A （t, n）--secret sharing scheme is a method of distribution of information among n participants such that t 〉 1 can reconstruct the secret but （t - 1） cannot. We explore some （k, n）--secret sharing schemes based on the finite fields.

An Efficient Threshold Blind Signature from Weil Pairing

Threshold blind signature is playing an important role in cryptography as well as in practical applications such as e-cash and e-voting systems, etc. In this paper, we present an efficient and practical threshold bind signature from Weil pairing on super-singular elliptic curves or hyper-elliptic curves over finite field and prove that our scheme is provably secure in the random oracle model.

Influence of multi-photon excitation on the atomic above-threshold ionization

Using the time-dependent pseudo-spectral scheme, we solve the time-dependent Schrodinger equation of a hydrogen- like atom in a strong laser field in momentum space. The intensity-resolved photoelectron energy spectrum in abovethreshold ionization is obtained and further analyzed. We find that with the increase of the laser intensity, the abovethreshold ionization emission spectrum exhibits periodic resonance structure. By analyzing the population of atomic bound states, we find that it is the multi-photon excitation of bound state that leads to the occurrence of this phenomenon, which is in fairly good agreement with the experimental results.