Objective of the study: to study the possibility of reducing quantum resource requirements for Grover's algorithm attack on block ciphers. Simplified-AES is considered as an example. To investigate the possibilities of using a partial key leakage. To estimate the required resources and to simulate a quantum attack on S-AES with reduced requirements. Research methods: algebraic analysis, numerical simulation. Research results: we have demonstrated the possibility of significantly reducing the number of qubits required to attack Simplified-AES by optimizing Grover's oracle. The resource requirements are reduced sufficiently, allowing to study quantum attack on Simplified-AES using numerical simulation on a PC with 400 MB of RAM in about 30 minutes (depending on the CPU configuration). A numerical simulation of a quantum attack on S-AES has been carried out for the case of an ideal leakage configuration, taking into account the elementary quantum noises. Scientific novelty: a new quantum attack algorithm for Simplified-AES cipher with significantly reduced requirements for the qubits number is proposed. Numerical simulation of the attack using this algorithm is carried out, which was practically impossible for previously known approaches. The results illustrate that our ideas about the resource requirements for a quantum attack and, as a consequence, the possible time of its practical implementation can be significantly incorrect if an alternative method for implementing even an already known asymptotically unimprovable quantum attack algorithm is found.
Objective of the study: to study the possibility of reducing quantum resource requirements for Grover's algorithm attack on block ciphers. Simplified-AES is considered as an example. To investigate the possibilities of using a partial key leakage. To estimate the required resources and to simulate a quantum attack on S-AES with reduced requirements. Research methods: algebraic analysis, numerical simulation. Research results: we have demonstrated the possibility of significantly reducing the number of qubits required to attack Simplified-AES by optimizing Grover's oracle. The resource requirements are reduced sufficiently, allowing to study quantum attack on Simplified-AES using numerical simulation on a PC with 400 MB of RAM in about 30 minutes (depending on the CPU configuration). A numerical simulation of a quantum attack on S-AES has been carried out for the case of an ideal leakage configuration, taking into account the elementary quantum noises. Scientific novelty: a new quantum attack algorithm for Simplified-AES cipher with significantly reduced requirements for the qubits number is proposed. Numerical simulation of the attack using this algorithm is carried out, which was practically impossible for previously known approaches. The results illustrate that our ideas about the resource requirements for a quantum attack and, as a consequence, the possible time of its practical implementation can be significantly incorrect if an alternative method for implementing even an already known asymptotically unimprovable quantum attack algorithm is found.
Advanced Encryption Standard is one of the most widely used and important symmetric ciphers for today. It well known, that it can be subjected to the quantum Grover's attack that twice reduces its key strength. But full AES attack requires hundreds of qubits and circuit depth of thousands, that makes impossible not only experimental research but also numerical simulations of this algorithm. Here we present an algorithm for optimized Grover's attack on downscaled Simplifed-AES cipher. Besides full attack we present several approaches that allows to reduce number of required qubits if some nibbles of the key are known as a result of side-channel attack. For 16-bit S-AES the proposed attack requires 23 qubits in general case and 19, 15 or 11 if 4, 8 or 12 bits were leaked in specifc confguration. Comparing to previously known 32-qubits algorithm this approach potentially allows to run the attack on today's NISQ-devices and perform numerical simulations with GPU, that may be useful for further research of problem-specifc error mitigation and error correction techniques.
The Advanced Encryption Standard (AES) is one of the most widely used symmetric block cipher cryptography algorithms. Simplified-AES (S-AES) retains the structural framework of AES, making it an ideal model for elucidating the mechanism of symmetric cryptography. In this paper, we investigate potential quantum attacks on S-AES, utilizing both Grover-based algorithms and variational quantum algorithms (VQAs). For Grover-based attacks, we introduce an optimized oracle for implementing S-AES, reducing the complexity from 160 Toffoli gates to 120 by refining the SubNibble operation. Additionally, we propose a general Variational Quantum Attack Algorithm (VQAA) for any type of symmetric encryption that does not require the quantum implementation of the encryption procedure, which reduces the gate complexity substantially. These improvements enable the implementation of both Grover-based attacks and VQAA on superconducting quantum computers. The results demonstrate the feasibility of cryptographic analysis on currently available quantum hardware. Our findings also underscore the challenges of parameter optimization for S-AES, attributing the difficulty to the design of efficient parameterized quantum circuits, which constrain the effectiveness of variational algorithms. Despite these advancements, significant challenges remain in achieving quantum attacks on AES.
In this work, a quantum design for the Simplified-Advanced Encryption Standard (S-AES) algorithm is presented. Also, a quantum Grover attack is modeled on the proposed quantum S-AES. First, quantum circuits for the main components of S-AES in the finite field F2[x]/(x4 + x + 1), are constructed. Then, the constructed circuits are put together to form a quantum version of S-AES. A C-NOT synthesis is used to decompose some of the functions to reduce the number of the needed qubits. The quantum S-AES is integrated into a black-box queried by Grover's algorithm. A new approach is proposed to uniquely recover the secret key when Grover attack is applied. The entire work is simulated and tested on a quantum mechanics simulator. The complexity analysis shows that a block cipher can be designed as a quantum circuit with a polynomial cost. In addition, the secret key is recovered in quadratic speedup as promised by Grover's algorithm.
NIST(National Institute of Standards and Technology) estimates the Grover key search cost required for symmetric key cryptography as the postquantum security strength. The Grover search algorithm is applicable to key recovery in symmetric key cryptography, and for this, the target encryption process must be implemented as a quantum circuit. In this paper, we present an optimized implementation of Simplified AES as a quantum circuit. Substitution, Mix Columns, and Key Expansion are implemented efficiently, and as a result of resource analysis, qubits, quantum gates, and circuit depth are significantly reduced compared to the previous result.
Grover’s search algorithm allows a quantum adversary to find ak-bit secret key of a block cipher by making O(2k/2) block cipher queries. Resistance of a block cipher to such an attack is evaluated by quantum resources required to implement Grover’s oracle for the target cipher. The quantum resources are typically estimated by theT-depth of its circuit implementation and the number of qubits used by the circuit (width). Since the AES S-box is the only component which requiresT-gates in a quantum implementation of AES, recent research has put its focus on efficient implementation of the AES S-box. However, any efficient implementation with lowT-depth will not be practical in the real world without considering qubit consumption of the implementation. In this work, we propose three methods of trade-off between time and space for the quantum implementation of the AES S-box. In particular, one of our methods turns out to use the smallest number of qubits among the existing methods, significantly reducing itsT-depth.
Quantum computing poses a significant threat to classical cryptographic algorithms, particularly the Advanced Encryption Standard (AES). This study investigates the impact of Grover's algorithm on the AES S-box, a fundamental component of the AES encryption process. By leveraging quantum mechanics, Grover's algorithm can potentially reduce the time required to break AES encryption from 2128operations to 264operations, thus presenting a substantial security risk. This research aims to evaluate the feasibility of such quantum attacks on AES S-box by conducting experiments using virtual quantum simulators. The study examines the resource requirements, including the number of gates and qubits, and assesses the scalability of Grover's algorithm across different data sizes and types. The findings indicate that, while theoretically effective, the practical implementation of Grover's algorithm is currently hindered by significant resource constraints on existing quantum hardware. These results underscore the need for continued advancements in quantum technology and the development of quantum-resistant cryptographic methods to ensure data security in the quantum era. This research contributes to the understanding of quantum vulnerabilities in classical cryptography and supports the development of robust encryption strategies that can withstand future quantum attacks.