Unclonable Cryptography in Linear Quantum Memory
Omri Shmueli, Mark Zhandry
TL;DR
This work initiates a substantial reduction of the long-term quantum memory required for unclonable cryptography, focusing on one-shot signatures (OSS) and quantum signing tokens. It introduces signing techniques that operate on entire messages with a single quantum state and develops a folding coset partition framework to beat the CPF input-size barrier, achieving asymptotically optimal quantum storage in the oracle model. In the standard model, under cryptographic assumptions such as sub-exponential iO, LWE with strong security guarantees, and decomposable trapdoor claw-free functions, the authors obtain $O(oldsymbol{ extlambda})$- or $O(oldsymbol{ extlambda}^2)$-sized quantum secret keys for OSS, significantly reducing memory costs compared to prior work. The paper also develops new information-theoretic and cryptographic hardness results for hidden subspace detection, along with subspace-hiding function concepts, which support the security reductions and have potential applications beyond unclonable cryptography, including quantum copy protection and quantum one-time programs.
Abstract
Quantum cryptography is a rapidly-developing area which leverages quantum information to accomplish classically-impossible tasks. In many of these protocols, quantum states are used as long-term cryptographic keys. Typically, this is to ensure the keys cannot be copied by an adversary, owing to the quantum no-cloning theorem. Unfortunately, due to quantum state's tendency to decohere, persistent quantum memory will likely be one of the most challenging resources for quantum computers. As such, it will be important to minimize persistent memory in quantum protocols. In this work, we consider the case of one-shot signatures (OSS), and more general quantum signing tokens. These are important unclonable primitives, where quantum signing keys allow for signing a single message but not two. Naturally, these quantum signing keys would require storage in long-term quantum memory. Very recently, the first OSS was constructed in a classical oracle model and also in the standard model, but we observe that the quantum memory required for these protocols is quite large. In this work, we significantly decrease the quantum secret key size, in some cases achieving asymptotically optimal size. To do so, we develop novel techniques for proving the security of cryptosystems using coset states, which are one of the main tools used in unclonable cryptography.