Optimal Error Rates for Interactive Coding I: Adaptivity and Other Settings

We consider the task of interactive communication in the presence of adversarial errors and present tight bounds on the tolerable error-rates in a number of different settings. Most significantly, we explore adaptive interactive communication where the communicating parties decide who should speak next based on the history of the interaction. Braverman and Rao [STOC'11] show that non-adaptively one can code for any constant error rate below 1/4 but not more. They asked whether this bound could be improved using adaptivity. We answer this open question in the affirmative (with a slightly different collection of resources): Our adaptive coding scheme tolerates any error rate below 2/7 and we show that tolerating a higher error rate is impossible. We also show that in the setting of Franklin et al. [CRYPTO'13], where parties share randomness not known to the adversary, adaptivity increases the tolerable error rate from 1/2 to 2/3. For list-decodable interactive communications, where each party outputs a constant size list of possible outcomes, the tight tolerable error rate is 1/2. Our negative results hold even if the communication and computation are unbounded, whereas for our positive results communication and computation are polynomially bounded. Most prior work considered coding schemes with linear amount of communication, while allowing unbounded computations. We argue that studying tolerable error rates in this relaxed context helps to identify a setting's intrinsic optimal error rate. We set forward a strong working hypothesis which stipulates that for any setting the maximum tolerable error rate is independent of many computational and communication complexity measures. We believe this hypothesis to be a powerful guideline for the design of simple, natural, and efficient coding schemes and for understanding the (im)possibilities of coding for interactive communications

Demystifying the Information Reconciliation Protocol Cascade

Cascade is an information reconciliation protocol proposed in the context of secret key agreement in quantum cryptography. This protocol allows removing discrepancies in two partially correlated sequences that belong to distant parties, connected through a public noiseless channel. It is highly interactive, thus requiring a large number of channel communications between the parties to proceed and, although its efficiency is not optimal, it has become the de-facto standard for practical implementations of information reconciliation in quantum key distribution. The aim of this work is to analyze the performance of Cascade, to discuss its strengths, weaknesses and optimization possibilities, comparing with some of the modified versions that have been proposed in the literature. When looking at all design trade-offs, a new view emerges that allows to put forward a number of guidelines and propose near optimal parameters for the practical implementation of Cascade improving performance significantly in comparison with all previous proposals.Comment: 30 pages, 13 figures, 3 table

Low Cost and Compact Quantum Cryptography

We present the design of a novel free-space quantum cryptography system, complete with purpose-built software, that can operate in daylight conditions. The transmitter and receiver modules are built using inexpensive off-the-shelf components. Both modules are compact allowing the generation of renewed shared secrets on demand over a short range of a few metres. An analysis of the software is shown as well as results of error rates and therefore shared secret yields at varying background light levels. As the system is designed to eventually work in short-range consumer applications, we also present a use scenario where the consumer can regularly 'top up' a store of secrets for use in a variety of one-time-pad and authentication protocols.Comment: 18 pages, 9 figures, to be published in New Journal of Physic

Experimental Progress in Computation by Self-Assembly of DNA Tilings

Approaches to DNA-based computing by self-assembly require the use of D. T A nanostructures, called tiles, that have efficient chemistries, expressive computational power: and convenient input and output (I/O) mechanisms. We have designed two new classes of DNA tiles: TAO and TAE, both of which contain three double-helices linked by strand exchange. Structural analysis of a TAO molecule has shown that the molecule assembles efficiently from its four component strands. Here we demonstrate a novel method for I/O whereby multiple tiles assemble around a single-stranded (input) scaffold strand. Computation by tiling theoretically results in the formation of structures that contain single-stranded (output) reported strands, which can then be isolated for subsequent steps of computation if necessary. We illustrate the advantages of TAO and TAE designs by detailing two examples of massively parallel arithmetic: construction of complete XOR and addition tables by linear assemblies of DNA tiles. The three helix structures provide flexibility for topological routing of strands in the computation: allowing the implementation of string tile models