Brief Announcement: Zero-Knowledge Protocols for Search Problems

We consider natural ways to extend the notion of Zero-Knowledge (ZK) Proofs beyond decision problems. Specifically, we consider search problems, and define zero-knowledge proofs in this context as interactive protocols in which the prover can establish the correctness of a solution to a given instance without the verifier learning anything beyond the intended solution, even if it deviates from the protocol. The goal of this work is to initiate a study of Search Zero-Knowledge (search-ZK), the class of search problems for which such systems exist. This class trivially contains search problems where the validity of a solution can be efficiently verified (using a single message proof containing only the solution). A slightly less obvious, but still straightforward, way to obtain zero-knowledge proofs for search problems is to let the prover send a solution and prove in zero-knowledge that the instance-solution pair is valid. However, there may be other ways to obtain such zero-knowledge proofs, and they may be more advantageous. In fact, we prove that there are search problems for which the aforementioned approach fails, but still search zero-knowledge protocols exist. On the other hand, we show sufficient conditions for search problems under which some form of zero-knowledge can be obtained using the straightforward way

Secret Sharing Schemes with a large number of players from Toric Varieties

A general theory for constructing linear secret sharing schemes over a finite field \Fq from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$. We present general methods for obtaining the reconstruction and privacy thresholds as well as conditions for multiplication on the associated secret sharing schemes. In particular we apply the method on certain toric surfaces. The main results are ideal linear secret sharing schemes where the number of players can be as large as $(q-1)^2-1$. We determine bounds for the reconstruction and privacy thresholds and conditions for strong multiplication using the cohomology and the intersection theory on toric surfaces.Comment: 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1203.454

Parallel Vectorized Algebraic AES in MATLAB for Rapid Prototyping of Encrypted Sensor Processing Algorithms and Database Analytics

The increasing use of networked sensor systems and networked databases has led to an increased interest in incorporating encryption directly into sensor algorithms and database analytics. MATLAB is the dominant tool for rapid prototyping of sensor algorithms and has extensive database analytics capabilities. The advent of high level and high performance Galois Field mathematical environments allows encryption algorithms to be expressed succinctly and efficiently. This work leverages the Galois Field primitives found the MATLAB Communication Toolbox to implement a mode of the Advanced Encrypted Standard (AES) based on first principals mathematics. The resulting implementation requires 100x less code than standard AES implementations and delivers speed that is effective for many design purposes. The parallel version achieves speed comparable to native OpenSSL on a single node and is sufficient for real-time prototyping of many sensor processing algorithms and database analytics.Comment: 6 pages; accepted to IEEE High Performance Extreme Computing Conference (HPEC) 201

Secure Computation for Cloud data Storage

One of the main goals of securing data transmission is focused on the security of cloud data storage. In this paper, we describe several cryptographic techniques which can be used to address the relevant threats and security goals for analyzing cloud computing security. Private semi-trusted clouds, allow researchers to design private clouds by using cryptographic techniques, to protect the semi-trusted ones. Finally, we elaborate on semi-trusted clouds which are related to real-world deployments of cloud resources, and how optimizing cryptographic protocols, would indeed lead to the usage of this certain cloud and therefore practical ways of securing this type of data

On the Round Complexity of Randomized Byzantine Agreement

We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that: 1) BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1/2+ o(1)]. 2) BA protocols resilient against n/4 corruptions terminate at the end of the second round with probability at most 1-Theta(1). 3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against n/3 [resp., n/4] corruptions terminate at the end of the second round with probability at most o(1) [resp., 1/2 + o(1)]. The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI). The third bound essentially matches the recent protocol of Micali (ITCS\u2717) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability

An implementation of the Paillier crypto system with threshold decryption without a trusted dealer

We consider the problem of securely generating the keys of the Paillier crypto system [11] with (t, n) threshold decryption, without a trusted dealer. Nishide and Sakurai [10] describe a solution, secure in the malicious model. We use their ideas to make a simpler solution for the semi-honest model, and further introduce a few optimisations. We implement the secure key generation protocol on a single computer, and consider its performance