A (t, n) Threshold Secret Sharing System with Efficient Identification of Cheaters

In this paper, we propose a new (t, n) threshold scheme. The scheme allows a user to divide portions of a secret among the designated group. Any t or more participants from a designated group of n members can cooperate to reconstruct the secret while (t-1) or less participants can not. Furthermore, the scheme provides an efficient mechanism to detect and identify cheaters. From the security analysis, we conclude that any participant does not have the ability to deceive other participants to obtain their portion of the secret. Therefore, this scheme is very practical for a broad spectrum of applications

An Epitome of Multi Secret Sharing Schemes for General Access Structure

Secret sharing schemes are widely used now a days in various applications, which need more security, trust and reliability. In secret sharing scheme, the secret is divided among the participants and only authorized set of participants can recover the secret by combining their shares. The authorized set of participants are called access structure of the scheme. In Multi-Secret Sharing Scheme (MSSS), k different secrets are distributed among the participants, each one according to an access structure. Multi-secret sharing schemes have been studied extensively by the cryptographic community. Number of schemes are proposed for the threshold multi-secret sharing and multi-secret sharing according to generalized access structure with various features. In this survey we explore the important constructions of multi-secret sharing for the generalized access structure with their merits and demerits. The features like whether shares can be reused, participants can be enrolled or dis-enrolled efficiently, whether shares have to modified in the renewal phase etc., are considered for the evaluation

A granular approach to source trustworthiness for negative trust assessment

The problem of determining what information to trust is crucial in many contexts that admit uncertainty and polarization. In this paper, we propose a method to systematically reason on the trustworthiness of sources. While not aiming at establishing their veracity, the metho

Application of Recursive Algorithm on Shamir's Scheme Reconstruction for Cheating Detection and Identification

Information data protection is necessary to ward off and overcome various fraud attacks that may be encountered. A secret sharing scheme that implements cryptographic methods intends to maintain the security of confidential data by a group of trusted parties is the answer. In this paper, we choose the application of recursive algorithm on Shamir-based linear scheme as the primary method. In the secret reconstruction stage and since the beginning of the share distribution stage, these algorithms have been integrated by relying on a detection parameter to ensure that the secret value sought is valid. Although the obtained scheme will be much simpler because it utilizes the Vandermonde matrix structure, the security aspect of this scheme is not reduced. Indeed, it is supported by two detection parameters formulated from a recursive algorithm to detect cheating and identify the cheater(s). Therefore, this scheme is guaranteed to be unconditionally secure and has a high time efficiency (polynomial running time)

Efficient Threshold Secret Sharing Schemes Secure against Rushing Cheaters

In this paper, we consider three very important issues namely detection, identification and robustness of $k$-out-of-$n$ secret sharing schemes against rushing cheaters who are allowed to submit (possibly forged) shares {\em after} observing shares of the honest users in the reconstruction phase. Towards this we present five different schemes. Among these, first we present two $k$-out-of-$n$ secret sharing schemes, the first one being capable of detecting $(k-1)/3$ cheaters such that $|V_i|=|S|/\epsilon^3$ and the second one being capable of detecting $n-1$ cheaters such that $|V_i|=|S|/\epsilon^{k+1}$, where $S$ denotes the set of all possible secrets, $\epsilon$ denotes the successful cheating probability of cheaters and $V_i$ denotes set all possible shares. Next we present two $k$-out-of-$n$ secret sharing schemes, the first one being capable of identifying $(k-1)/3$ rushing cheaters with share size $|V_i|$ that satisfies $|V_i|=|S|/\epsilon^k$. This is the first scheme whose size of shares does not grow linearly with $n$ but only with $k$, where $n$ is the number of participants. For the second one, in the setting of public cheater identification, we present an efficient optimal cheater resilient $k$-out-of-$n$ secret sharing scheme against rushing cheaters having the share size $|V_i|= (n-t)^{n+2t}|S|/\epsilon^{n+2t}$. The proposed scheme achieves {\em flexibility} in the sense that the security level (i.e. the cheater(s) success probability) is independent of the secret size. Finally, we design an efficient $(k, \delta)$ robust secret sharing secure against rushing adversary with optimal cheater resiliency. Each of the five proposed schemes has the smallest share size having the mentioned properties among the existing schemes in the respective fields

An Efficient tt-Cheater Identifiable Secret Sharing Scheme with Optimal Cheater Resiliency

In this paper, we present an efficient $k$-out-of-$n$ secret sharing scheme, which can identify up to $t$ rushing cheaters, with probability at least $1 - \epsilon$, where $0<\epsilon<1/2$, provided $t < k/2$. This is the optimal number of cheaters that can be tolerated in the setting of public cheater identification, on which we focus in this work. In our scheme, the set of all possible shares $V_i$ satisfies the condition that $|V_i|= \frac{(t+1)^{2n+k-3}|S|}{\epsilon^{2n+k-3}}$, where $S$ denotes the set of all possible secrets. In PODC-2012, Ashish Choudhury came up with an efficient $t$-cheater identifiable $k$-out-of-$n$ secret sharing scheme, which was a solution of an open problem proposed by Satoshi Obana in EUROCRYPT-2011. The share size, with respect to a secret consisting of one field element, of Choudhury\u27s proposal in PODC-2012 is $|V_i|=\frac{(t+1)^{3n}|S|}{\epsilon^{3n}}$. Therefore, our scheme presents an improvement in share size over the above construction. Hence, to the best of our knowledge, our proposal currently has the minimal share size among existing efficient schemes with optimal cheater resilience, in the case of a single secret