Quantum Neural Network Based Distinguisher on SPECK-32/64.

As IoT technology develops, many sensor devices are being used in our life. To protect such sensor data, lightweight block cipher techniques such as SPECK-32 are applied. However, attack techniques for these lightweight ciphers are also being studied. Block ciphers have differential characteristics, which are probabilistically predictable, so deep learning has been utilized to solve this problem. Since Gohr's work at Crypto2019, many studies on deep-learning-based distinguishers have been conducted. Currently, as quantum computers are developed, quantum neural network technology is developing. Quantum neural networks can also learn and make predictions on data, just like classical neural networks. However, current quantum computers are constrained by many factors (e.g., the scale and execution time of available quantum computers), making it difficult for quantum neural networks to outperform classical neural networks. Quantum computers have higher performance and computational speed than classical computers, but this cannot be achieved in the current quantum computing environment. Nevertheless, it is very important to find areas where quantum neural networks work for technology development in the future. In this paper, we propose the first quantum neural network based distinguisher for the block cipher SPECK-32 in an NISQ. Our quantum neural distinguisher successfully operated for up to 5 rounds even under constrained conditions. As a result of our experiment, the classical neural distinguisher achieved an accuracy of 0.93, but our quantum neural distinguisher achieved an accuracy of 0.53 due to limitations in data, time, and parameters. Due to the constrained environment, it cannot exceed the performance of classical neural networks, but it can operate as a distinguisher because it has obtained an accuracy of 0.51 or higher. In addition, we performed an in-depth analysis of the quantum neural network's various factors that affect the performance of the quantum neural distinguisher. As a result, it was confirmed that the embedding method, the number of the qubit, and quantum layers, etc., have an effect. It turns out that if a high-capacity network is needed, we have to properly tune properly to take into account the connectivity and complexity of the circuit, not just by adding quantum resources. In the future, if more quantum resources, data, and time become available, it is expected that an approach to achieve better performance can be designed by considering the various factors presented in this paper.

Quantum Binary Field Multiplication with Optimized Toffoli Depth and Extension to Quantum Inversion.

The Shor's algorithm can find solutions to the discrete logarithm problem on binary elliptic curves in polynomial time. A major challenge in implementing Shor's algorithm is the overhead of representing and performing arithmetic on binary elliptic curves using quantum circuits. Multiplication of binary fields is one of the critical operations in the context of elliptic curve arithmetic, and it is especially costly in the quantum setting. Our goal in this paper is to optimize quantum multiplication in the binary field. In the past, efforts to optimize quantum multiplication have centred on reducing the Toffoli gate count or qubits required. However, despite the fact that circuit depth is an important metric for indicating the performance of a quantum circuit, previous studies have lacked sufficient consideration for reducing circuit depth. Our approach to optimizing quantum multiplication differs from previous work in that we aim at reducing the Toffoli depth and full depth. To optimize quantum multiplication, we adopt the Karatsuba multiplication method which is based on the divide-and-conquer approach. In summary, we present an optimized quantum multiplication that has a Toffoli depth of one. Additionally, the full depth of the quantum circuit is also reduced thanks to our Toffoli depth optimization strategy. To demonstrate the effectiveness of our proposed method, we evaluate its performance using various metrics such as the qubit count, quantum gates, and circuit depth, as well as the qubits-depth product. These metrics provide insight into the resource requirements and complexity of the method. Our work achieves the lowest Toffoli depth, full depth, and the best trade-off performance for quantum multiplication. Further, our multiplication is more effective when not used in stand-alone cases. We show this effectiveness by using our multiplication to the Itoh-Tsujii algorithm-based inversion of F(x8+x4+x3+x+1).