Verifiable secret sharing

About: Verifiable secret sharing is a research topic. Over the lifetime, 4241 publications have been published within this topic receiving 99569 citations.

Weighted decomposition construction for perfect secret sharing schemes

Abstract: The purpose of this paper is to present a new decomposition technique, called the weighted decomposition construction, for perfect secret sharing schemes with general access structures. This construction is more general than previous constructions. Based on the weighted decomposition construction, we improve the information rates in four cases out of the 18 cases of secret sharing schemes left unsolved for connected graphs on six vertices.

Manicoding for communication verification

Abstract: Verifiable, secure communications between a sender and a receiver on at least one shared communication channel is provided. A manicoded key encoder produces an argument of knowledge for a secret key to the at least one shared communication channel, and a manicoded message encoder provides an implication argument indicating that knowledge of the secret key enables access to message content of the manicoded message. The argument of knowledge is included in a key manifest for the secret key within a manicoded key, and the implication argument is included in a message manifest of a manicoded message. In this way, the sender may provide message content within the manicoded message, and the receiver may operate a decoder to access the message content. A verifier may use the manicoded key and the manicoded message to verify that the receiver has access to the message content.

Boosting Verifiable Computation on Encrypted Data

Abstract: We consider the setting in which an untrusted server stores a collection of data and is asked to compute a function over it. In this scenario, we aim for solutions where the untrusted server does not learn information about the data and is prevented from cheating. This problem is addressed by verifiable and private delegation of computation, proposed by Gennaro, Gentry and Parno (CRYPTO’10), a notion that is close to both the active areas of homomorphic encryption and verifiable computation (VC). However, in spite of the efficiency advances in the respective areas, VC protocols that guarantee privacy of the inputs are still expensive. The only exception is a protocol by Fiore, Gennaro and Pastro (CCS’14) that supports arithmetic circuits of degree at most 2. In this paper we propose new efficient protocols for VC on encrypted data that improve over the state of the art solution of Fiore et al. in multiple aspects. First, we can support computations of degree higher than 2. Second, we achieve public delegatability and public verifiability whereas Fiore et al. need the same secret key to encode inputs and verify outputs. Third, we achieve a new property that guarantees that verifiers can be convinced about the correctness of the outputs without learning information on the inputs. The key tool to obtain our new protocols is a new SNARK that can efficiently handle computations over a quotient polynomial ring, such as the one used by Ring-LWE somewhat homomorphic encryption schemes. This SNARK in turn relies on a new commit-and-prove SNARK for proving evaluations on the same point of several committed polynomials. We propose a construction of this scheme under an extractability assumption over bilinear groups in the random oracle model.

Raziel: Private and Verifiable Smart Contracts on Blockchains.

Abstract: Raziel combines secure multi-party computation and proof-carrying code to provide privacy, correctness and verifiability guarantees for smart contracts on blockchains. Effectively solving DAO and Gyges attacks, this paper describes an implementation and presents examples to demonstrate its practical viability (e.g., private and verifiable crowdfundings and investment funds). Additionally, we show how to use Zero-Knowledge Proofs of Proofs (i.e., Proof-Carrying Code certificates) to prove the validity of smart contracts to third parties before their execution without revealing anything else. Finally, we show how miners could get rewarded for generating pre-processing data for secure multi-party computation.

On the information ratio of non-perfect secret sharing schemes

Abstract: A secret sharing scheme is non-perfect if some subsets of players that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes and the construction of efficient linear non-perfect secret sharing schemes. To this end, we extend the known connections between matroids, polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information on the secret value that is obtained by each subset of players. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, access functions whose values depend only on the number of players, generalize the threshold access structures. The optimal information ratio of the uniform access functions with rational values has been determined by Yoshida, Fujiwara and Fossorier. By using the tools that are described in our work, we provide a much simpler proof of that result and we extend it to access functions with real values.