A Cipher Based on Prefix Codes

Area of Science:

• Cryptography
• Information Theory
• Computer Science

Background:

• Prefix codes (P-codes) offer unique structural properties where no codeword is a prefix of another.
• Symmetric ciphers are crucial for secure data transmission, especially in resource-constrained environments like the Internet of Things (IoT).
• Evaluating the security of novel cryptographic systems is essential before deployment.

Purpose of the Study:

• To propose and analyze the security of a novel symmetric cipher based on prefix codes.
• To determine the feasibility of brute-force and statistical attacks against this P-code-based cryptosystem.
• To assess the suitability of the proposed cipher for Internet of Things applications.

Main Methods:

• Detailed analysis of the fundamental properties of P-codes.
• Mathematical derivation of bounds on the number of minimal P-codes containing a given binary word.
• Statistical analysis of the distribution of minimal P-codes over binary words.
• Evaluation of keyspace size against brute-force attack feasibility.
• Assessment of information leakage for statistical attack resistance.

Main Results:

• The keyspace of the P-code-based cipher is demonstrably too large for effective brute-force attacks.
• Bounds were established for the number of minimal P-codes containing pre-defined binary words.
• Statistical attacks are hindered by the limited information available to an attacker regarding the substitution mapping.
• The distribution of minimal P-codes across binary words of fixed length follows a Gaussian distribution.

Conclusions:

• The proposed symmetric cipher utilizing prefix codes exhibits strong security against common cryptanalytic methods.
• Its design simplicity and robust security make it a promising candidate for securing Internet of Things devices and communications.
• Further research into practical implementation and performance metrics is warranted.