fmuinos / Quantum-Crypto-Attack

Fundamental quantum simulation to attack symmetric-key cryptography primitives

Quantum-Crypto-Attack

Fundamental quantum simulation to attack symmetric-key cryptography primitives. This project is based on a paper I read about here: Using Simon’s algorithm to attack symmetric-key cryptographic primitives.

The paper describes the use of quantum computers to determine whether a symmetric-key cryptography system is using a Feistel network or a random swapping algorithm.

The paper shows that we can accurately decide whether Feistel networks or random swapping algorithms are used in linear time, technically breaking said symmetric-key cryptography system.

A cryptography system is considered broken when an attacker can tell whether a given output string s is encrypted or a random collection of tokens. When thinking informally about it: If an attacker can see the difference between encrypted strings s and random strings r, there must exist a fundamental, recognizable pattern in s.

Requirements

To compile a binary, you need:

• make
• The libquantum development library (version >= 1.1.1). Note: Some linux distributions have this package in their repositories, usually named libquantum-dev
• A modern C++ compiler capable of compiling C++17

Compilation & Execution

Compile the binary by using the provided Makefile. Simply type make in the project root directory once all requirements are satisfied.

Execute the program by executing the binary, named qa_distinguish.

Program

The program will run 2 tests when booted:

1. Feistel detection routine, which uses a Feistel network as parameter.
2. Feistel detection routine, which uses a random permutation-based encryption routine.
   • Random values will be generated for the alpha and beta values used by the f function.
   • The program outputs one of the following 3 outputs:
     • 3-round Feistel (solved equation): n linearly-independent equations were obtained and the equation was solved. In this case, the program detected the encryption routine is a Feistel network after verifying f(u) = f(u ^ s).
     • 3-round Feistel (more than 2n equations attempted): 2n equations were obtained, containing less than n linearly independent equations. In this case, the program guesses the routine to be a 3-round Feistel network, since random swapping algorithms are unlikely to show this behaviour.
     • random permutation: n linearly independent equations were obtained and the equation was solved. In this case, the program tested f(u) != f(u^s), and as such detected a random swapping algorithm.