From Information Theory Puzzles in Deletion Channels to Deniability in Quantum Cryptography

by   Arash Atashpendar, et al.

From the output produced by a memoryless deletion channel with a uniformly random input of known length n, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that of the uniform prior measures the amount of information about the channel input which is conveyed by the output of length m. We first conjecture on the basis of experimental data that the entropy of the posterior is minimized by the constant strings 000..., 111... and maximized by the alternating strings 0101..., 1010.... We present related combinatorial theorems involving binary (sub/super)-sequences and prove the minimal entropy conjecture for single and double deletions using clustering techniques. We then prove the minimization conjecture in the asymptotic limit using results from hidden word statistics by showing how the analytic-combinatorial methods of Flajolet, Szpankowski and Vallée, relying on generating functions, can be applied to resolve the case of fixed output length and n→∞. Next, we revisit the notion of deniability in quantum key exchange (QKE). We introduce and formalize the notion of coercer-deniable QKE. We then establish a connection between covert communication and deniability to propose DC-QKE, a simple and provably secure construction for coercer-deniable QKE. We relate deniability to fundamental concepts in quantum information theory and suggest a generic approach based on entanglement distillation for achieving information-theoretic deniability, followed by an analysis of other closely related results such as the relation between the impossibility of unconditionally secure quantum bit commitment and deniability. Finally, we present an efficient coercion-resistant and quantum-secure voting scheme, based on fully homomorphic encryption.


page 1

page 2

page 3

page 4


A Proof of Entropy Minimization for Outputs in Deletion Channels via Hidden Word Statistics

From the output produced by a memoryless deletion channel from a uniform...

From Clustering Supersequences to Entropy Minimizing Subsequences for Single and Double Deletions

A binary string transmitted via a memoryless i.i.d. deletion channel is ...

Revisiting Deniability in Quantum Key Exchange via Covert Communication and Entanglement Distillation

We revisit the notion of deniability in quantum key exchange (QKE), a to...

The Input and Output Entropies of the k-Deletion/Insertion Channel

The channel output entropy of a transmitted word is the entropy of the p...

On quantum channel capacities: an additive refinement

Capacities of quantum channels are fundamental quantities in the theory ...

On a combinatorial generation problem of Knuth

The well-known middle levels conjecture asserts that for every integer n...

Multivariate Analytic Combinatorics for Cost Constrained Channels and Subsequence Enumeration

Analytic combinatorics in several variables is a powerful tool for deriv...

Please sign up or login with your details

Forgot password? Click here to reset