NISQ Security Via Simple Classical Reasoning Achieves Quantum Random Oracle Model Security in Noisy Intermediate-Scale Quantum Settings

The challenge of securing cryptographic systems in the age of near-term quantum computers drives significant research, and Alexandru Cojocaru from University of Edinburgh, Juan Garay from Texas A and M University, Qipeng Liu from UC San Diego, and Fang Song et al. present a new approach to analysing security in these noisy intermediate-scale quantum (NISQ) environments. Their work establishes powerful theorems that simplify the process of proving security, moving away from complex quantum reasoning and towards calculations based solely on classical computation. This breakthrough allows the team to directly demonstrate the hardness of solving multi-instance security games, offering the first direct product theorems within the hybrid quantum-classical setting. Consequently, they establish the difficulty of various cryptographic tasks, including salted games and multiple instance one-wayness, paving the way for more robust security protocols in a future with increasingly powerful quantum computers.

Researchers have developed novel lifting theorems applicable to security games operating under the limitations of near-term quantum computers, including limited coherence and noisy operations. These theorems extend existing security analysis techniques to hybrid algorithms that combine both quantum and classical computations, and to algorithms utilizing imperfect quantum oracles.

Lifting Theorems Prove Cryptographic Game Complexity

This work focuses on establishing the quantum and hybrid complexity of cryptographic games, determining how difficult they are to solve using quantum computers or algorithms combining classical and quantum techniques. The core technique employed is lifting theorems, which reduce the complexity of solving a complex game to solving a simpler one. By demonstrating the security of a simpler game, researchers can then prove the security of the more complex game through a constructed simulator. The team’s results demonstrate that robust security guarantees can be established even with the noise and limitations of NISQ devices, through careful cryptographic design and analysis.

The research considers both purely quantum attacks and hybrid attacks, utilizing random oracles to model underlying cryptographic functions. These theorems are applicable to multi-output games, where an attacker must find multiple solutions, and leverage a technique called coherent reprogramming to construct effective simulators. The theorems provide tighter security bounds for cryptographic games, strengthening confidence in their resistance to quantum and hybrid attacks. This work also improves cryptographic design by providing insights into the complexity of different games, allowing for the development of more robust algorithms. The research provides a foundation for further exploration in quantum and hybrid cryptography, offering a rigorous mathematical framework for analyzing security in the face of advanced computational attacks.

Hybrid Oracle Security Analysis Framework

This work presents new theoretical tools for assessing the security of cryptographic systems in realistic quantum computing environments. A key achievement is the introduction of a “hybrid coherent measure-and-reprogramming” framework, which allows for a refined analysis of how algorithms interact with oracles, functions used to test cryptographic properties. This framework enables the direct calculation of security and complexity, relying on classical reasoning rather than complex quantum calculations. Consequently, the team demonstrated the first direct product theorems in hybrid settings, providing a means to determine the difficulty of solving multiple instances of security games simultaneously.

This advancement facilitates the assessment of the hardness of various cryptographic tasks, including salted games and specific cryptographic protocols. While the results rely on assumptions, such as the absence of duplicate classical queries, they represent a significant step forward in understanding the security of cryptographic systems in the NISQ era. Future research will explore the applicability of these theorems to a wider range of cryptographic systems and investigate the impact of different noise models on security guarantees.