On the Shannon Cipher System With a Wiretapper Guessing Subject to Distortion and Reliability Requirements

TL;DR

This paper analyzes the security of the Shannon cipher system against a guessing attack with constraints on distortion and reliability, providing a single-letter characterization of guess rates based on key rate and system parameters.

Contribution

It extends previous work by incorporating distortion and reliability constraints into the analysis of guessing security, offering a new single-letter characterization of guess rates.

Findings

Derived a single-letter formula for guess rate regions

Extended security analysis to include distortion and reliability

Connected guess rates with key rate and system parameters

Abstract

In this paper we discuss the processes in the Shannon cipher system with discrete memoryless source and a guessing wiretapper. The wiretapper observes a cryptogram of $N$-vector of ciphered messages in the public channel and tries to guess successively the vector of messages within given distortion level $\Delta$ and small probability of error less than $\exp \{-NE\}$ with positive reliability index $E$. The security of the system is measured by the expected number of guesses which wiretapper needs for the approximate reconstruction of the vector of source messages. The distortion, the reliability criteria and the possibility of upper limiting the number of guesses extend the approach studied by Merhav and Arikan. A single-letter characterization is given for the region of pairs $(R_L,R)$ (of the rate $R_L$ of the maximum number of guesses $L(N)$ and the rate $R$ of the average number of guesses) in dependence on key rate $R_K$, distortion level $\Delta$ and reliability $E$.