Guessing a password over a wireless channel (on the effect of noise non-uniformity)

TL;DR

This paper analyzes how the statistical properties of a string source and non-uniform noise affect the guesswork needed to reconstruct a string over a noisy channel, revealing counterintuitive insights about noise and guesswork.

Contribution

It characterizes the impact of source and noise statistics on guesswork, showing that average noise does not directly determine guesswork and highlighting potential security implications.

Findings

Average noise level does not determine guesswork.

Recipients with better channels can require more guesses.

Guesswork behavior differs from channel capacity insights.

Abstract

A string is sent over a noisy channel that erases some of its characters. Knowing the statistical properties of the string's source and which characters were erased, a listener that is equipped with an ability to test the veracity of a string, one string at a time, wishes to fill in the missing pieces. Here we characterize the influence of the stochastic properties of both the string's source and the noise on the channel on the distribution of the number of attempts required to identify the string, its guesswork. In particular, we establish that the average noise on the channel is not a determining factor for the average guesswork and illustrate simple settings where one recipient with, on average, a better channel than another recipient, has higher average guesswork. These results stand in contrast to those for the capacity of wiretap channels and suggest the use of techniques such as friendly jamming with pseudo-random sequences to exploit this guesswork behavior.