Post-Quantum Zero-Knowledge with Space-Bounded Simulation

This chapter explores the concept of post-quantum zero-knowledge proofs with a focus on space-bounded simulation. It delves into the challenges of defining quantum zero-knowledge against malicious quantum verifiers, particularly considering the resource of quantum memory. The chapter introduces new definitions of post-quantum zero-knowledge, such as -space-bounded QZK, and investigates the feasibility of these notions. It presents both positive and negative results, demonstrating the feasibility of space-bounded QZK against logarithmic space verifiers and the impossibility against super-logarithmic space verifiers. The chapter also discusses the technical overview of the techniques employed in the results, including state recovery and the use of subspace states. Additionally, it explores the related work in the field and suggests future directions for research. The chapter concludes with a discussion on the organization of the paper and the definitions of quantum zero-knowledge, providing a comprehensive overview of the current state and future prospects of post-quantum zero-knowledge with space-bounded simulation.