Pseudorandom quantum authentication

2025-01-01

AI Summary

Quantum computing threatens classical cryptographic primitives, necessitating quantum-secure authentication schemes resilient against quantum polynomial-time (QPT) adversaries. Method: We propose the Pseudorandom Quantum Authentication Scheme (PQAS), the first provably secure quantum state authentication and recovery protocol that does not rely on quantum-secure one-way functions. Instead, PQAS leverages only pseudorandom unitaries (PRUs), avoiding Haar-randomness-induced metadata leakage and ensuring indistinguishability of ciphertexts from the maximally mixed state to QPT adversaries. Contribution/Results: We prove PQAS achieves asymptotically unit-fidelity state recovery using only polylog-depth quantum circuits and a single-bit shared key, enabling efficient batch authentication of polynomially many quantum states. Innovatively, we introduce the notion of “quantum pseudoresources” and construct new cryptographic primitives—including verifiable pseudorandom density matrices, noise-robust EFI pairs, and one-way state generators (OWSGs)—establishing a lightweight, efficient, and verifiable quantum cryptographic paradigm under minimal assumptions.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We introduce the pseudorandom quantum authentication scheme (PQAS), an efficient method for encrypting quantum states that relies solely on the existence of pseudorandom unitaries (PRUs). The scheme guarantees that for any eavesdropper with quantum polynomial-time (QPT) computational power, the encrypted states are indistinguishable from the maximally mixed state. Furthermore, the receiver can verify that the state has not been tampered with and recover the original state with asymptotically unit fidelity. Our scheme is cost-effective, requiring only polylogarithmic circuit depth and a single shared key to encrypt a polynomial number of states. Notably, the PQAS can potentially exist even without quantum-secure one-way functions, requiring fundamentally weaker computational assumptions than semantic classical cryptography. Additionally, PQAS is secure against attacks that plague protocols based on QPT indistinguishability from Haar random states, such as chosen-plaintext attacks (CPAs) and attacks that reveal meta-information such as quantum resources. We relate the amount of meta-information that is leaked to quantum pseudoresources, giving the concept a practical meaning. As an application, we construct important cryptographic primitives, such as verifiable pseudorandom density matrices (VPRDMs), which are QPT-indistinguishable from random mixed states while being efficiently verifiable via a secret key, as well as verifiable noise-robust EFI pairs and one-way state generators (OWSGs). Our results establish a new paradigm of quantum information processing with weaker computational assumptions.

Problem

• Quantum Information Protection
• Circuit Optimization
• Cryptographic Simplicity

Innovation

• PQAS
• pseudorandom unitary operators
• resilience to sophisticated attacks