Less is More: On Copy Complexity in Quantum Cryptography

2025-10-06

AI Summary

Quantum cryptographic security often critically depends on the number of copies of the secret key state an adversary can obtain, with a substantial gap existing between single-copy and multi-copy security. Method: We introduce the first general paradigm for provably upgrading security from single-copy to arbitrary polynomial-copy security. Our construction leverages stretch pseudorandom states and single-query pseudorandom unitaries under mild assumptions, and achieves polynomial-copy security for public-key quantum money and quantum copy protection under standard cryptographic assumptions. The approach integrates lightweight key design, indistinguishability obfuscation, and multi-copy security modeling. Contribution/Results: Our framework unifies core quantum cryptographic primitives—including pseudorandom states and unclonable encryption—under a coherent multi-copy security model, thereby bridging the long-standing theoretical gap in “copy complexity” within quantum cryptography and providing a generic, foundational framework for multi-copy security.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Mechanism Design
• Computer Vision: Multi-modal Vision

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies

Abstract

Quantum cryptographic definitions are often sensitive to the number of copies of the cryptographic states revealed to an adversary. Making definitional changes to the number of copies accessible to an adversary can drastically affect various aspects including the computational hardness, feasibility, and applicability of the resulting cryptographic scheme. This phenomenon appears in many places in quantum cryptography, including quantum pseudorandomness and unclonable cryptography. To address this, we present a generic approach to boost single-copy security to multi-copy security and apply this approach to many settings. As a consequence, we obtain the following new results: -One-copy stretch pseudorandom state generators (under mild assumptions) imply the existence of t-copy stretch pseudorandom state generators, for any fixed polynomial t. -One-query pseudorandom unitaries with short keys (under mild assumptions) imply the existence of t-query pseudorandom unitaries with short keys, for any fixed polynomial t. -Assuming indistinguishability obfuscation and other standard cryptographic assumptions, there exist identical-copy secure unclonable primitives such as public-key quantum money and quantum copy-protection.

Problem

• Addressing security degradation from multiple state copies
• Boosting single-copy to multi-copy quantum security
• Establishing copy-secure unclonable cryptographic primitives

Innovation

• Boosts single-copy security to multi-copy security
• Enables t-copy stretch pseudorandom state generators
• Creates identical-copy secure unclonable primitives