LFSR Cryptanalysis

This Python project implements a cryptographic analysis using a Linear Feedback Shift Register (LFSR). The project includes functions to encode and decode text, perform XOR operations, generate keystreams using LFSR, and brute-force search for LFSR seeds to decrypt a given ciphertext. Given the LFSR with feedback polynomial $x^{10} + x^9 + x^7 + x^6 + 1$ and the encrypted message i!))iszwykqnf cyc!?secnncvch, the goal is to find the original plaintext message. Feedback polynomial and encrypted message can be changed to your liking

Features

• Character to Bits Conversion: Maps characters to their corresponding 5-bit binary representation.
• Bits to Character Conversion: Maps 5-bit binary strings back to their corresponding characters.
• Text Encoding/Decoding: Converts text to a binary string and vice versa.
• XOR Operations: Performs bitwise XOR between two binary strings.
• LFSR Keystream Generation: Generates a keystream using an LFSR with a given seed and feedback polynomial.
• Brute-Force LFSR: Attempts to find the correct LFSR seed by brute-forcing all possible seeds and checking the decrypted text.

Functions

list_to_string(l)

Converts a list of integers to a concatenated string.

• Parameters: l (list) - The list to be converted.
• Returns: (str) - The concatenated string.

text_enc(text)

Encodes a given text message to a binary string using a predefined character to binary mapping.

• Parameters: text (str) - The text message to be encoded.
• Returns: (str) - The resulting binary string.

text_dec(binary_string)

Decodes a binary string back to the original text message using a predefined binary to character mapping.

• Parameters: binary_string (str) - The binary string to be decoded.
• Returns: (str) - The resulting text message.

string_xor(btext, key)

Performs bitwise XOR between two binary strings.

• Parameters:
  • btext (str) - The binary string representing the text.
  • key (str) - The binary string representing the key.
• Returns: (str) - The resulting binary string after XOR operation.

sumxor(l)

Calculates the XOR sum of a list of integers.

• Parameters: l (list) - The list of integers.
• Returns: (int) - The resulting XOR sum.

lfsr(seed, feedback, bits, flag)

Generates a keystream using an LFSR with the given seed and feedback polynomial.

• Parameters:
  • seed (list) - The initial seed for the LFSR.
  • feedback (list) - The feedback polynomial coefficients.
  • bits (int) - The number of bits in the generated keystream.
  • flag (int) - Flag to print intermediate states (0 for printing, 1 for silent).
• Returns: (list) - The generated keystream.

brute_force_lfsr(streambits)

Attempts to find the correct LFSR seed by brute-forcing all possible 10-bit seeds and checking the decrypted text.

• Parameters: streambits (str) - The binary string of the ciphertext to be decrypted.
• Returns: None