The Shannon Cipher System with a Guessing Wiretapper: General Sources

TL;DR

This paper investigates the Shannon cipher system with a guessing wiretapper for general sources, deriving tight bounds on guessing moments and linking error exponents with source compression exponents.

Contribution

It introduces bounds on guessing moments for general sources and establishes their tightness for iid, Markov, and unifilar sources, connecting secrecy and source coding exponents.

Findings

Bounds on guessing moments are tight for iid, Markov, and unifilar sources.

A relationship between error exponents and guessing exponents is established.

The work generalizes previous results to broader source classes.

Abstract

The Shannon cipher system is studied in the context of general sources using a notion of computational secrecy introduced by Merhav & Arikan. Bounds are derived on limiting exponents of guessing moments for general sources. The bounds are shown to be tight for iid, Markov, and unifilar sources, thus recovering some known results. A close relationship between error exponents and correct decoding exponents for fixed rate source compression on the one hand and exponents for guessing moments on the other hand is established.