A secret sharing scheme is said to be d-multiplicative if the scheme allows the players to multiply shared d secrets by locally converting their shares into an additive sharing of the product. In the previous work, the following negative result for perfect secret sharing has been shown: The d-multiplicative secret sharing for d players is impossible. This paper extends the impossibility result to non-perfect secret sharing. Our main result is a proof that d-multiplicative secret sharing for d players is impossible even if every player has partial information on the secret (e.g., all but one bit). This result means that there is no need to relax the privacy requirement with leakage of partial information only for the purpose of d-multiplication.
A secure Multi-Party Computation (MPC) is one of the distributed computational methods, where it computes a function over the inputs given by more than one party jointly and keeps those inputs private from the parties involved in the process. Randomization in secret sharing leading to MPC is a requirement for privacy enhancements; however, most of the available MPC models use the trust assumptions of sharing and combining values. Thus, randomization in secret sharing and MPC modules is neglected. As a result, the available MPC models are prone to information leakage problems, where the models can reveal the partial values of the sharing secrets. In this paper, we propose the first model of utilizing a random function generator as an MPC primitive. More specifically, we analyze our previous development of the Symmetric Random Function Generator (SRFG) for information-theoretic security, where the system is considered to have unconditional security if it is secure against adversaries with unlimited computing resources and time. Further, we apply SRFG to eradicate the problem of information leakage in the general MPC model. Through a set of experiments, we show that SRFG is a function generator that can generate the combined functions (combination of logic GATEs) with
n/2-private to
n-private norms. As the main goal of MPC is privacy preservation of the inputs, we analyze the applicability of SRFG properties in secret sharing and MPC and observe that SRFG is eligible to be a cryptographic primitive in MPC developments. We also measure the performance of our proposed SRFG-based MPC framework with the other randomness generation-based MPC frameworks and analyze the comparative attributes with the state-of-the-art models. We observe that our posed SRFG-based MPC is$\approx$30% better in terms of throughput and also shows 100% privacy attainment.
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy' game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.