Correlation Immunity Analyzer

This Lua script analyzes Boolean functions defined in hexadecimal format for their t-th order correlation immunity. Two algorithms are supported:

• Naive (-n)
• Optimized (-o)

Usage

lua analyzer.lua <hex-binary-function> <correlation-order> [-n | -o]

Parameters

• <hex-binary-function>: Hexadecimal representation of the Boolean function's output.
• <correlation-order>: The order t for correlation immunity.
• -n: Use the naive algorithm.
• -o: Use the optimized algorithm.

Examples

lua analyzer.lua 0xB4 1 -n
lua analyzer.lua 0xDB011464C2F090B41B597D60DD256EE2 2 -o

Sample Inputs

Name	Hexadecimal Function
groundT	0xB4
7-bit	0xDB011464C2F090B41B597D60DD256EE2
8-bit	0xDB011464C2F090B41B597D60DD256EE224FEEB9B3D0F6F4BE4A6829F22DA911D
9-bit	Concatenation of 7-bit and 8-bit values

Output

The analyzer reports:

• Whether the function is balanced (equal number of 0s and 1s).
• Whether it is immune to t-th order correlation.
• Which algorithm was used.

Additional Functionality

The script also includes:

• Hamming weight and Walsh transform utilities.
• A simple Fermat primality test, included for experimentation.

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This analyzer is a practical tool for testing correlation properties of Boolean functions in cryptographic contexts, such as S-box analysis or stream cipher component validation.