TL;DR
This paper analyzes the performance of guessing strategies in Shannon cipher systems for sources with memory, establishing relationships between guessing and length functions, and identifying asymptotically optimal strategies for various source types.
Contribution
It introduces a comprehensive framework linking guessing and length functions, and proposes asymptotically optimal encryption and guessing strategies for sources with memory, including unifilar and finite-state sources.
Findings
Optimal strategies are characterized for unifilar sources.
Guessing based on Lempel-Ziv lengths is asymptotically optimal.
Competitive properties of different guessing orders are demonstrated.
Abstract
A guessing wiretapper's performance on a Shannon cipher system is analyzed for a source with memory. Close relationships between guessing functions and length functions are first established. Subsequently, asymptotically optimal encryption and attack strategies are identified and their performances analyzed for sources with memory. The performance metrics are exponents of guessing moments and probability of large deviations. The metrics are then characterized for unifilar sources. Universal asymptotically optimal encryption and attack strategies are also identified for unifilar sources. Guessing in the increasing order of Lempel-Ziv coding lengths is proposed for finite-state sources, and shown to be asymptotically optimal. Finally, competitive optimality properties of guessing in the increasing order of description lengths and Lempel-Ziv coding lengths are demonstrated.
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