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Beijing Youdian Xueyuan xuebao

Construction of Cheating Immune Secret Sharing

Jie Zhang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Cheating immune secret sharing in the unconditionally secure case was investigated. Secret sharing is a k-cheating immune if any k cheaters are not better off than a participant which follows the protocol honestly. k-cheating immune secret sharing scheme under the unconditionally secure would be given. The obtained function of the secret sharing scheme is k-resilient and satisfies k-strengthened propagation criterion. Furthermore, its degree is high. So it has better cryptographic properties than that of the known results.

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International Symposium on Information Theory and its Applications•Oct 24, 2020•1 citation
Cheating immune secret sharing in the unconditionally secure case was investigated. Secret sharing is a k-cheating immune if any k cheaters are not better off than a participant which follows the protocol honestly. k-cheating immune secret sharing scheme under the unconditionally secure would be given. The obtained function of the secret sharing scheme is k-resilient and satisfies k-strengthened propagation criterion. Furthermore, its degree is high. So it has better cryptographic properties than that of the known results.
The paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all original vectors, i.e., 1/n 2^n ∑ _c=1...n ∑ _α ∈V n ρ _c,α , denoted by øverlineρ , satisfies øverlineρ ≥ \frac12 , and the equality holds if and only if ρ _c,α satisfies ρ _c,α = \frac12 for every cheating vector δ _c and every original vector α . In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions.This enables us to construct cheating-immune secret sharing.
Recently, Yang et al. proposed a kind of quantum cryptographic schemes based on secret sharing. The main idea is drawn from the case, where any n participants who share a secret K can co-operate as K does. This process can be applied to encryption, authentication, signature and so on. Unfortunately, since there is no identity authentication of the share’s holder, these schemes inherit the limitation of secret sharing in practice. If some participants do not follow the protocol, the protocol would be a failure at last. Moreover, these schemes encounter another serious attack. Any two participants can co-operate to defeat the schemes by sending different shares to the parties unknown to the distributor of the secret K, such that these parties can execute the protocol as well. The attack proves that it is not enough for quantum cryptographic schemes that only the secret key is secure.
Abstract. An n -player -secure robust secret sharing scheme is a ( t , n )-threshold secret sharing scheme with the additional property that the secret can be recovered, with probability at least , from the set of all shares even if up to t players provide incorrect shares. The existing constructions of robust secret sharing schemes for the range have the share size larger than the secret size. An important goal in this area is to minimize the share size. In the paper, we propose a new unconditionally-secure robust secret sharing scheme for the case with share size equal to the secret size. This is the minimum possible size as dictated by the perfect secrecy of the scheme. We further extend our scheme to realize a class of multilevel access structures that satisfy a special condition. The property that the share size is equal to secret size is preserved in the extended scheme. The proposed scheme is the first known robust secret sharing scheme realizing multilevel access structure.
Abstract. Rational secret sharing protocols in both the two-party and multi-party settings are proposed. These protocols are built in standard communication networks and with unconditional security. Namely, the protocols run over standard point-to-point networks without requiring physical assumptions or simultaneous channels, and even a computationally unbounded player cannot gain more than ɛ by deviating from the protocol. More precisely, for the 2-out-of-2 protocol the ɛ is a negligible function in the size of the secret, which is caused by the informationtheoretic MACs used for authentication. The t-out-of-n protocol is (t−1)resilient and the ɛ is exponentially small in the number of participants. Although secret recovery cannot be guaranteed in this setting, a participant can at least reduce the Shannon entropy of the secret to less than 1 after the protocol. When the secret-domain is large, every rational player has great incentive to participate in the protocol.
Function secret sharing is a cryptographic protocol for secure distribution of a secret function. While the notion of function secret sharing is a conceptual extension of secret sharing schemes, it faces difficulties in its constructions. We demonstrate that if we consider function secret sharing schemes for Fourier basis functions then we can enjoy the linear properties of linear secret sharing schemes to construct function secret sharing schemes. In this paper, we construct a verifiable function secret sharing by using Fourier basis functions, where players can verify if the dealer is cheating.