In this paper we construct quantum circuit implementing known ciphertext attack on symmetric cipher. We assume that plaintext is in natural language and have known letter distribution. Our method allows to find key using one query to (quantum) decryption oracle and has O( $\sqrt {\left| K \right|} $ ) time complexity, where K—set of possible keys.
In this paper we construct quantum circuit implementing known ciphertext attack on symmetric cipher. We assume that plaintext is in natural language and have known letter distribution. Our method allows to find key using one query to (quantum) decryption oracle and has O( ∣K∣ ) time complexity, where K—set of possible keys.
Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.
Key recovery attack on SPN ciphers such as AES is NP hard in complexity. Previous studies have estimated the quantum resources required for implementing Grover’s key search for AES, but these are largely theoretical in nature. The key challenges to implement Grover’s algorithm on current quantum hardware include the number of available qubits, noise, and decoherence. However, the rapid advancement of hardware has brought us closer to practical realization for the cryptanalysis of light-weight SPN ciphers. This study presents an efficient quantum circuit implementation of Mini-AES, a 16-bit variant of AES, employing standard CNOT and Toffoli gates. To the best of our knowledge, our work provides the first complete quantum implementations of all core Mini-AES components for the quantum oracle. The effects of noise are emulated for each module of the quantum oracle and quantified. Furthermore, Grover’s algorithm is applied to Mini-AES to perform successful key recovery through a known-plaintext attack, demonstrating significant amplitude amplification while using near-optimal Grover’s iterations, thereby reducing the total quantum volume. The optimal Grover’s iterations have been obtained empirically as well as validated with finite-shot analysis. Notably, the application of Grover’s algorithm reveals key clustering behavior in Mini-AES, which has been corroborated through classical simulation.
To evaluate the security of a symmetric cryptosystem against any quantum attack, the symmetric algorithm must be first implemented on a quantum platform. In this study, a quantum implementation of a classical block cipher is presented. A quantum circuit for a classical block cipher of a polynomial size of quantum gates is proposed. The entire work has been tested on a quantum mechanics simulator called libquantum. First, the functionality of the proposed quantum cipher is verified and the experimental results are compared with those of the original classical version. Then, quantum attacks are conducted by using Grover's algorithm to recover the secret key. The proposed quantum cipher is used as a black box for the quantum search. The quantum oracle is then queried over the produced ciphertext to mark the quantum state, which consists of plaintext and key qubits. The experimental results show that for a key of n-bit size and key space of N such that [Formula: see text], the key can be recovered in [Formula: see text] computational steps.
Abstract Quantum Algorithms reduce the computational complexity or solve certain difficult problems that were originally impossible to solve with classical computers. Grover's search algorithm is a Quantum computation algorithm that can find target elements from a set of unstructured data with the best possible, O(√ N) queries. Grover's search Quantum circuits implemented accurately can be used to successfully search and find the keys of Symmetric ciphers. However, very few demonstrations of such practical cryptanalysis are available. In this paper, practical Quantum cryptanalysis circuits for Affine Cipher are proposed and demonstrated, that successfully break the cipher by finding the keys.
With the development of quantum technology, quantum computing has an increasingly significant impact on cryptanalysis. Several quantum algorithms, such as Simon’s algorithm, Grover’s algorithm, the Bernstein–Vazirani algorithm, Shor’s algorithm, and the Grover-meets-Simon algorithm, have been proposed successively. However, almost all cryptanalysis is based on the quantum chosen-plaintext attack (qCPA) model. This paper focuses on a powerful cryptanalytic model, quantum related-key attack (qRKA), and proposes a strategy of qRKAs against symmetric ciphers using Simon’s algorithm. We construct a periodic function to efficiently recover the secret key of symmetric ciphers if the attacked symmetric ciphers satisfy Simon’s promise, and present the complexity analysis on specific symmetric ciphers. Then, we apply qRKA to the Even–Mansour cipher and SoEM construction, recover their secret keys, and show their complexity comparison in the distinct attack models. This work is of great significance for the qRKA cryptanalysis of existing provably secure cryptographic schemes and the design of future quantum secure cryptographic schemes.
Abstract A significant amount of study is being done to review the security promises made for the various ciphers now in use as a result of the development of quantum computing technology. A general attack against symmetric key cryptography primitives that can reduce search costs to the square root is Grover's search algorithm. To implement Grover's algorithm, it is necessary that the target cipher be implemented as a quantum circuit. Despite being relatively new, this area of study has received significant attention from the research community. The authors have estimated the cost of Grover's key search attack against the stream cipher Atom, for the first time, under circuit depth restrictions defined in National Institute of Standards and Technology (NIST) PQC standardisation process. The authors implement the quantum circuit of Atom in QISKIT, (open‐source software development kit for working with quantum computers running on IBM Quantum Experience). The results are also compared with other existing literature on LFSR‐based stream ciphers, such as Grain‐v1, Grain‐128‐AEAD, and Lizard. The authors also find that, to the best of their knowledge, in the existing literature on estimating the cost of Grover's attack on symmetric ciphers, Atom is the only 128‐bit key cipher that meets the threshold of ≈2 170 set by NIST for quantum security of 128‐bit key ciphers. The authors also analyse the security of Atom against quantum TMDTO attacks.