Demonstration of Grover’s algorithm for retrieving secret keys in a basic SPN block cipher

In this study, we present in detail the application of Grover's quantum algorithm to the searching problem of the secret key of a simple SPN (Substitution–permutation network) block cipher called Yo-yo. The main goal of the paper is to clarify the construction of the quantum circuit and the operation phases of Grover's algorithm to find the secret key with the condition of knowing at least 1 pair of plaintext-ciphertext. To achieve this goal, we consider 2 cases: the case where there is a unique key that satisfies and the case where there are 2 keys that satisfy at the same time. As a result, our implementation technique, implemented in the Qiskit programming language, requires only 17 qubits to find the key of the Yo-yo block cipher correctly. This technique can be effectively applied on IBM quantum computers for large-scale SPN block ciphers, such as AES and GOST R.34.10.2015, which are widely used today.