Oblivious channels

Let C = {x_1,...,x_N} \subset {0,1}^n be an [n,N] binary error correcting code (not necessarily linear). Let e \in {0,1}^n be an error vector. A codeword x in C is said to be "disturbed" by the error e if the closest codeword to x + e is no longer x. Let A_e be the subset of codewords in C that are disturbed by e. In this work we study the size of A_e in random codes C (i.e. codes in which each codeword x_i is chosen uniformly and independently at random from {0,1}^n). Using recent results of Vu [Random Structures and Algorithms 20(3)] on the concentration of non-Lipschitz functions, we show that |A_e| is strongly concentrated for a wide range of values of N and ||e||. We apply this result in the study of communication channels we refer to as "oblivious". Roughly speaking, a channel W(y|x) is said to be oblivious if the error distribution imposed by the channel is independent of the transmitted codeword x. For example, the well studied Binary Symmetric Channel is an oblivious channel. In this work, we define oblivious and partially oblivious channels and present lower bounds on their capacity. The oblivious channels we define have connections to Arbitrarily Varying Channels with state constraints.Comment: Submitted to the IEEE International Symposium on Information Theory (ISIT) 200

Oblivious transfer and quantum channels

We show that oblivious transfer can be seen as the classical analogue to a quantum channel in the same sense as non-local boxes are for maximally entangled qubits.Comment: Invited Paper at the 2006 IEEE Information Theory Workshop (ITW 2006

The Oblivious Transfer Capacity of the Wiretapped Binary Erasure Channel

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).Comment: This is an extended version of the paper "The Oblivious Transfer Capacity of the Wiretapped Binary Erasure Channel" to be presented at ISIT 201

On the Commitment Capacity of Unfair Noisy Channels

Noisy channels are a valuable resource from a cryptographic point of view. They can be used for exchanging secret-keys as well as realizing other cryptographic primitives such as commitment and oblivious transfer. To be really useful, noisy channels have to be consider in the scenario where a cheating party has some degree of control over the channel characteristics. Damg\r{a}rd et al. (EUROCRYPT 1999) proposed a more realistic model where such level of control is permitted to an adversary, the so called unfair noisy channels, and proved that they can be used to obtain commitment and oblivious transfer protocols. Given that noisy channels are a precious resource for cryptographic purposes, one important question is determining the optimal rate in which they can be used. The commitment capacity has already been determined for the cases of discrete memoryless channels and Gaussian channels. In this work we address the problem of determining the commitment capacity of unfair noisy channels. We compute a single-letter characterization of the commitment capacity of unfair noisy channels. In the case where an adversary has no control over the channel (the fair case) our capacity reduces to the well-known capacity of a discrete memoryless binary symmetric channel

Static virtual channel allocation in oblivious routing

Most virtual channel routers have multiple virtual channels to mitigate the effects of head-of-line blocking. When there are more flows than virtual channels at a link, packets or flows must compete for channels, either in a dynamic way at each link or by static assignment computed before transmission starts. In this paper, we present methods that statically allocate channels to flows at each link when oblivious routing is used, and ensure deadlock freedom for arbitrary minimal routes when two or more virtual channels are available. We then experimentally explore the performance trade-offs of static and dynamic virtual channel allocation for various oblivious routing methods, including DOR, ROMM, Valiant and a novel bandwidth-sensitive oblivious routing scheme (BSORM). Through judicious separation of flows, static allocation schemes often exceed the performance of dynamic allocation schemes

A New Upperbound for the Oblivious Transfer Capacity of Discrete Memoryless Channels

We derive a new upper bound on the string oblivious transfer capacity of discrete memoryless channels. The main tool we use is the tension region of a pair of random variables introduced in Prabhakaran and Prabhakaran (2014) where it was used to derive upper bounds on rates of secure sampling in the source model. In this paper, we consider secure computation of string oblivious transfer in the channel model. Our bound is based on a monotonicity property of the tension region in the channel model. We show that our bound strictly improves upon the upper bound of Ahlswede and Csisz\'ar (2013).Comment: 7 pages, 3 figures, extended version of submission to IEEE Information Theory Workshop, 201