Compilation of Function Representations for Secure Computing Paradigms

This paper introduces M-Circuits, a program representation which generalizes arithmetic and binary circuits. This new representation is motivated by the way modern multi-party computation (MPC) systems based on linear secret sharing schemes actually operate. We then show how this representation also allows one to construct zero knowledge proof (ZKP) systems based on the MPC-in-the-head paradigm. The use of the M-Circuit program abstraction then allows for a number of program-specific optimizations to be applied generically. It also allows to separate complexity and security optimizations for program compilation from those for application protocols (MPC or ZKP)

On secret sharing with nonlinear product reconstruction

Multiplicative linear secret sharing is a fundamental notion in the area of secure multi-party computation (MPC) and, since recently, in the area of two-party cryptography as well. In a nutshell, this notion guarantees that ``the product of two secrets is obtained as a linear function of the vector consisting of the coordinate-wise product of two respective share-vectors\u27\u27. This paper focuses on the following foundational question, which is novel to the best of our knowledge. Suppose we {\em abandon the latter linearity condition} and instead require that this product is obtained by {\em some}, not-necessarily-linear ``product reconstruction function\u27\u27. {\em Is the resulting notion equivalent to multiplicative linear secret sharing?} We show the (perhaps somewhat counter-intuitive) result that this relaxed notion is strictly {\em more general}. Concretely, fix a finite field \FF_q as the base field over which linear secret sharing is considered. Then we show there exists an (exotic) linear secret sharing scheme with an unbounded number of players $n$ such that it has $t$-privacy with $t = \Omega(n)$ and such that it does admit a product reconstruction function, yet this function is {\em necessarily} nonlinear. In addition, we determine the minimum number of players for which those exotic schemes exist. Our proof is based on combinatorial arguments involving quadratic forms. It extends to similar separation results for important variations, such as strongly multiplicative secret sharing

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

Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries

We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and other tasks, where the computing nodes is expected to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA) 200

An Effective Private Data storage and Retrieval System using Secret sharing scheme based on Secure Multi-party Computation

Privacy of the outsourced data is one of the major challenge.Insecurity of the network environment and untrustworthiness of the service providers are obstacles of making the database as a service.Collection and storage of personally identifiable information is a major privacy concern.On-line public databases and resources pose a significant risk to user privacy, since a malicious database owner may monitor user queries and infer useful information about the customer.The challenge in data privacy is to share data with third-party and at the same time securing the valuable information from unauthorized access and use by third party.A Private Information Retrieval(PIR) scheme allows a user to query database while hiding the identity of the data retrieved.The naive solution for confidentiality is to encrypt data before outsourcing.Query execution,key management and statistical inference are major challenges in this case.The proposed system suggests a mechanism for secure storage and retrieval of private data using the secret sharing technique.The idea is to develop a mechanism to store private information with a highly available storage provider which could be accessed from anywhere using queries while hiding the actual data values from the storage provider.The private information retrieval system is implemented using Secure Multi-party Computation(SMC) technique which is based on secret sharing. Multi-party Computation enable parties to compute some joint function over their private inputs.The query results are obtained by performing a secure computation on the shares owned by the different servers.Comment: Data Science & Engineering (ICDSE), 2014 International Conference, CUSA

Computer-aided proofs for multiparty computation with active security

Secure multi-party computation (MPC) is a general cryptographic technique that allows distrusting parties to compute a function of their individual inputs, while only revealing the output of the function. It has found applications in areas such as auctioning, email filtering, and secure teleconference. Given its importance, it is crucial that the protocols are specified and implemented correctly. In the programming language community it has become good practice to use computer proof assistants to verify correctness proofs. In the field of cryptography, EasyCrypt is the state of the art proof assistant. It provides an embedded language for probabilistic programming, together with a specialized logic, embedded into an ambient general purpose higher-order logic. It allows us to conveniently express cryptographic properties. EasyCrypt has been used successfully on many applications, including public-key encryption, signatures, garbled circuits and differential privacy. Here we show for the first time that it can also be used to prove security of MPC against a malicious adversary. We formalize additive and replicated secret sharing schemes and apply them to Maurer's MPC protocol for secure addition and multiplication. Our method extends to general polynomial functions. We follow the insights from EasyCrypt that security proofs can be often be reduced to proofs about program equivalence, a topic that is well understood in the verification of programming languages. In particular, we show that in the passive case the non-interference-based definition is equivalent to a standard game-based security definition. For the active case we provide a new NI definition, which we call input independence