Related papers: Secret Sharing with Binary Shares
This note analyses one of the existing space efficient secret sharing schemes and suggests vulnerabilities in its design. We observe that the said algorithm fails for certain choices of the set of secrets and there is no reason for…
Shamir's (n, k) threshold secret sharing is an important component of several cryptographic protocols, such as those for secure multiparty-computation and key management. These protocols typically assume the presence of direct communication…
In this paper, we present an unconditionally secure $N$-party comparison scheme based on Shamir secret sharing, utilizing the binary representation of private inputs to determine the $\max$ without disclosing any private inputs or…
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of…
Secret sharing schemes with optimal and universal communication overheads have been obtained independently by Bitar et al. and Huang et al. However, their constructions require a finite field of size q > n, where n is the number of shares,…
We consider a secret-sharing model where a dealer distributes the shares of a secret among a set of participants with the constraint that only predetermined subsets of participants must be able to reconstruct the secret by pooling their…
An ideal secret sharing scheme is a method of sharing a secret key in some key space among a finite set of participants in such a way that only the authorized subsets of participants can reconstruct the secret key from their shares which…
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…
We consider a private distributed multiplication problem involving N computation nodes and T colluding nodes. Shamir's secret sharing algorithm provides perfect information-theoretic privacy, while requiring an honest majority, i.e., N \ge…
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…
We propose an adaptive threshold multi secret sharing scheme based solely on cryptographically secure hash functions. We show that the proposed scheme is also: perfect, ideal, verifiable, and proactive. Moreover the proposed scheme has a…
We study the arithmetic circuit complexity of threshold secret sharing schemes by characterizing the graph-theoretic properties of arithmetic circuits that compute the shares. Using information inequalities, we prove that any unrestricted…
We consider the problem of private distributed multi-party multiplication. It is well-established that Shamir secret-sharing coding strategies can enable perfect information-theoretic privacy in distributed computation via the celebrated…
In an on-line secret sharing scheme the dealer assigns shares in the order the participants show up, knowing only those qualified subsets whose all members she has seen. We assume that the overall access structure is known and only the…
In Chen-Cramer Crypto 2006 paper \cite{cc} algebraic geometric secret sharing schemes were proposed such that the "Fundamental Theorem in Information-Theoretically Secure Multiparty Computation" by Ben-Or, Goldwasser and Wigderson…
In Shamir's secret sharing scheme, all participants possess equal privileges. However, in many practical scenarios, it is often necessary to assign different levels of authority to different participants. To address this requirement,…
The first construction of strongly secure quantum ramp secret sharing by Zhang and Matsumoto had an undesirable feature that the dimension of quantum shares must be larger than the number of shares. By using algebraic curves over finite…
For a secret sharing scheme, two parameters $d_{min}$ and $d_{cheat}$ are defined in [12] and [13]. These two parameters measure the error-correcting capability and the secret-recovering capability of the secret sharing scheme against…
We show a construction of a quantum ramp secret sharing scheme from a nested pair of linear codes. Necessary and sufficient conditions for qualified sets and forbidden sets are given in terms of combinatorial properties of nested linear…
Bipartite secret sharing schemes have a bipartite access structure in which the set of participants is divided into two parts and all participants in the same part play an equivalent role. Such a bipartite scheme can be described by a…