Secret Sharing Based on a Hard-on-Average Problem

The main goal of this work is to propose the design of secret sharing schemes based on hard-on-average problems. It includes the description of a new multiparty protocol whose main application is key management in networks. Its unconditionally perfect security relies on a discrete mathematics problem classiffied as DistNP-Complete under the average-case analysis, the so-called Distributional Matrix Representability Problem. Thanks to the use of the search version of the mentioned decision problem, the security of the proposed scheme is guaranteed. Although several secret sharing schemes connected with combinatorial structures may be found in the bibliography, the main contribution of this work is the proposal of a new secret sharing scheme based on a hard-on-average problem, which allows to enlarge the set of tools for designing more secure cryptographic 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

Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes

It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies to codes which recover the message exactly. Naively, one might expect that correcting errors to very high fidelity would only allow small violations of this bound. This intuition is incorrect: in this paper we describe quantum error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors with fidelity exponentially close to 1, at the price of increasing the size of the registers (i.e., the coding alphabet). This demonstrates a sharp distinction between exact and approximate quantum error correction. The codes have the property that any $t$ components reveal no information about the message, and so they can also be viewed as error-tolerant secret sharing schemes. The construction has several interesting implications for cryptography and quantum information theory. First, it suggests that secret sharing is a better classical analogue to quantum error correction than is classical error correction. Second, it highlights an error in a purported proof that verifiable quantum secret sharing (VQSS) is impossible when the number of cheaters t is n/4. More generally, the construction illustrates a difference between exact and approximate requirements in quantum cryptography and (yet again) the delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure

Nearly optimal robust secret sharing

Abstract: We prove that a known approach to improve Shamir's celebrated secret sharing scheme; i.e., adding an information-theoretic authentication tag to the secret, can make it robust for n parties against any collusion of size δn, for any constant δ ∈ (0; 1/2). This result holds in the so-called “nonrushing” model in which the n shares are submitted simultaneously for reconstruction. We thus finally obtain a simple, fully explicit, and robust secret sharing scheme in this model that is essentially optimal in all parameters including the share size which is k(1+o(1))+O(κ), where k is the secret length and κ is the security parameter. Like Shamir's scheme, in this modified scheme any set of more than δn honest parties can efficiently recover the secret. Using algebraic geometry codes instead of Reed-Solomon codes, the share length can be decreased to a constant (only depending on δ) while the number of shares n can grow independently. In this case, when n is large enough, the scheme satisfies the “threshold” requirement in an approximate sense; i.e., any set of δn(1 + ρ) honest parties, for arbitrarily small ρ > 0, can efficiently reconstruct the secret

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)

Cheating Detection and Cheater Identification in CRT-based Secret Sharing Schemes

In this paper we analyze the cheating detection and cheater identification problems for the secret sharing schemes based on the Chinese remainder theorem (CRT), more exactly for Mignotte [1] and Asmuth-Bloom [2] schemes. We prove that the majority of the solutions for Shamir’s scheme [3] can be translated to these schemes and, moreover, there are some interesting specific solutions