We study the problem of commitment over channels under cost constraints. Commitment is a widely studied cryptographic primitive, where two mutually distrustful parties, say Alice and Bob, interact over two phases of a protocol, viz., commit phase followed by reveal phase, to achieve commitment on a bit string available to Alice. Commitment (over the string) is said to occur if (i) Alice commits to the string which remains securely hidden from Bob at the end of the commit phase involving Alice's transmission to Bob, and (ii) Alice reveals a string to Bob and Bob is able to successfully detect whether the string is the committed one or not. When Alice and Bob are computationally unbounded, i.e., under the information-theoretic setting, it is well known that even a single bit commitment is impossible when the channel available to Alice and Bob is noiseless. Noisy channels, however, offer the potential of non-zero commitment rate, and thus, are a valuable resource. We study information-theoretically secure commitment over noisy discrete memoryless channels (DMCs). The largest commitment throughput over noisy channels is called the commitment capacity or simply capacity. In this work, we completely characterize via a single-letter expression, the commitment capacity of DMCs under general cost constraints; this generalizes the previously known result in the absence of such cost constraints. We show that cost constrained commitment capacity of any given DMC can significantly differ from its unconstrained value. We also present a dual capacity characterization in terms of output distributions. Interestingly, we show that every input distribution achieving the capacity results in the same output distribution; the latter is the unique optimizer of our dual capacity expression.

We study private two-terminal hypothesis testing with simple hypotheses where the privacy goal is to ensure that participating in the testing protocol reveals little additional information about the other user's observation when a user is told what the correct hypothesis is. We show that, in general, meaningful correctness and privacy cannot be achieved if the users do not have access to correlated (but, not common) randomness. We characterize the optimal correctness and privacy error exponents when the users have access to non-trivial correlated randomness (those that permit secure multiparty computation).

In this paper, we study the problem of obtaining 1-of-2 string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users' inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice-Bob and Alice-Eve), we derive the 1-of-2 string OT capacity for both 2-privacy (when Eve can collude with either Alice or Bob) and 1-privacy (when no such collusion is allowed). We generalize these capacity results to 1-of-N string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice-Bob and Alice-Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice-Bob and Bob-Eve) and 1-of-2 string OT is desired between Alice and Bob with 1-privacy. For this setup, we derive an upper and lower bound on the 1-of-2 string OT capacity which match in one of two possible parameter regimes.

We study oblivious transfer (OT) between Alice and Bob in the presence of an eavesdropper Eve over a degraded wiretapped binary erasure channel from Alice to Bob and Eve. In addition to the privacy goals of oblivious transfer between Alice and Bob, we require privacy of Alice and Bob's private data from Eve. In previous work we derived the OT capacity (in the honest-but-curious model) of the wiretapped binary independent erasure channel where the erasure processes of Bob and Eve are independent. Here we derive a lower bound on the OT capacity in the same secrecy model when the wiretapped binary erasure channel is degraded in favour of Bob.

We study the following private data transfer problem: Alice has a database of files. Bob and Cathy want to access a file each from this database (which may or may not be the same file), but each of them wants to ensure that their choices of file do not get revealed even if Alice colludes with the other user. Alice, on the other hand, wants to make sure that each of Bob and Cathy does not learn any more information from the database than the files they demand (the identities of which will be unknown to her). Moreover, they should not learn any information about the other files even if they collude. It turns out that it is impossible to accomplish this if Alice, Bob, and Cathy have access only to private randomness and noiseless communication links. We consider this problem when a binary erasure broadcast channel with independent erasures is available from Alice to Bob and Cathy in addition to a noiseless public discussion channel. We study the file-length-per-broadcast-channel-use rate in the honest-but-curious model. We focus on the case when the database consists of two files, and obtain the optimal rate. We then extend to the case of larger databases, and give upper and lower bounds on the optimal rate.

We consider oblivious transfer between Alice and Bob in the presence of an eavesdropper Eve when there is a broadcast channel from Alice to Bob and Eve. In addition to the secrecy constraints of Alice and Bob, Eve should not learn the private data of Alice and Bob. When the broadcast channel consists of two independent binary erasure channels, we derive the oblivious transfer capacity for both 2-privacy (where the eavesdropper may collude with either party) and 1-privacy (where there are no collusions).

In secure multiparty computation, mutually distrusting users in a network want to collaborate to compute functions of data which is distributed among the users. The users should not learn any additional information about the data of others than what they may infer from their own data and the functions they are computing. Previous works have mostly considered the worst case context (i.e., without assuming any distribution for the data); Lee and Abbe (2014) is a notable exception. Here, we study the average case (i.e., we work with a distribution on the data) where correctness and privacy is only desired asymptotically. For concreteness and simplicity, we consider a secure version of the function computation problem of Körner and Marton (1979) where two users observe a doubly symmetric binary source with parameter p and the third user wants to compute the XOR. We show that the amount of communication and randomness resources required depends on the level of correctness desired. When zero-error and perfect privacy are required, the results of Data et al. (2014) show that it can be achieved if and only if a total rate of 1 bit is communicated between every pair of users and private randomness at the rate of 1 is used up. In contrast, we show here that, if we only want the probability of error to vanish asymptotically in blocklength, it can be achieved by a lower rate (binary entropy of p) for all the links and for private randomness; this also guarantees perfect privacy. We also show that no smaller rates are possible even if privacy is only required asymptotically.

We study oblivious transfer (OT) using a binary erasure broadcast channel from Alice to Bob and Charlie. Alice wants to establish independent OTs with Bob and Charlie with 2-privacy, i.e., where secrecy needs to be maintained even against pairs of parties in addition to against parties working on their own. We give an achievable rate-region in the honest-but-curious setting and show its optimality for a range of erasure probabilities.

GPUs have brought supercomputing-at-desk by offering hundreds of processing cores at a very cheap cost. This has motivated researchers to implement and test parallel solutions to compute-intensive problems on GPU. Most real-world optimization problems are NP-hard and therefore compute intensive. Meta-heuristics are frequently used to solve these optimization problems. Multi-Objective particle swarm optimization (MOPSO) is one of the Meta-heuristic that has attracted many researchers due to its accuracy and simplicity. In last couple of years, many parallel implementations of MOPSO have been proposed in literature. However none of the researchers have implemented and tested performance of MOPSO on GPU. In this paper, we describe our implementation of MOPSO on GPU using CUDA and OpenCL, two of the most popular GPU frameworks for writing parallel applications. The performance of both implementations has been compared with sequential implementation of MOPSO through simulations. Results show that performance can be improved by 90 percent using these parallel implementations. We then present a parallel archiving technique and implement MOPSO in GPU with the proposed archiving technique using CUDA. Simulation results show that the parallel archiving technique further improves the speedup.