Universal Encryption of Individual Sequences Under Maximal Information Leakage

Area of Science:

• Information Theory
• Cryptography
• Computer Science

Background:

• The Shannon cipher system is a foundational model in cryptography.
• Understanding information leakage is crucial for secure communication.
• Finite-state encrypters present unique challenges in information security analysis.

Purpose of the Study:

• To analyze information leakage in Shannon cipher systems using individual sequences and finite-state encrypters.
• To establish bounds on the maximal information leakage.
• To identify methods for achieving asymptotically minimum information leakage.

Main Methods:

• Analysis of Shannon cipher systems within the framework of individual sequences.
• Application of the maximal information leakage metric.
• Derivation of lower and upper bounds for information leakage.

Main Results:

• A lower bound on information leakage was established.
• An asymptotically matching upper bound on information leakage was derived.
• The derived bounds provide insights into the security of finite-state encrypters.

Conclusions:

• Asymptotically minimum information leakage can be achieved.
• Lempel-Ziv compression followed by one-time pad encryption of the compressed bitstream is a method to attain minimal leakage.
• This finding has implications for designing more secure cryptographic systems.