Core Concepts
The authors prove a tight parallel repetition theorem for 3-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. They also show that the security of 4-message computationally secure protocols does not generally decrease under parallel repetition.
Abstract
The paper presents several key results:
Tight Parallel Repetition Theorem for 3-Message Quantum Protocols:
The authors prove that if a 3-message quantum protocol has computational soundness ๐พ, then its ๐-fold parallel repetition has computational soundness ๐พ^๐ + negl(๐), where ๐ is the security parameter. This is tight, as the ๐พ^๐ term is inherent.
The proof combines techniques from quantum rewinding, the quantum singular value transform, and other new ideas to handle the challenges of the quantum setting.
Barriers to Parallel Repetition Beyond 3 Messages:
The authors show that their 3-message parallel repetition theorem cannot extend to 4-message protocols under reasonable cryptographic assumptions, mirroring a classical result.
They construct a 4-message post-quantum protocol whose ๐-fold computational security does not decrease, assuming the existence of post-quantum non-malleable commitments.
Round Compression for Quantum Arguments:
The authors show that all quantum argument systems can be generically compiled into an equivalent 3-message argument system, preserving the communication and verifier complexity.
This allows them to obtain a general round-preserving soundness amplification theorem for quantum arguments.
Applications:
The authors derive hardness amplification theorems for various quantum cryptographic primitives, including quantum bit commitments, EFI pairs, public-key quantum money, and quantum zero-knowledge arguments.
They also obtain a quantum analogue of Yao's XOR lemma as a corollary.
Overall, the paper makes significant advances in the theory of hardness amplification for quantum cryptographic primitives, with applications to a wide range of quantum constructions.
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