Bibliographic Information: Qian, L., Raizes, J., & Zhandry, M. (2024). Hard Quantum Extrapolations in Quantum Cryptography. arXiv preprint arXiv:2409.16516v2.
Research Objective: This paper investigates the existence of a "quantum analog" to one-way functions, a fundamental concept in classical cryptography, to establish a minimal primitive for quantum-resistant cryptography. The authors explore the hardness of "quantum extrapolation" tasks and their potential for building secure quantum commitments.
Methodology: The authors define two types of quantum extrapolation tasks: "classical→quantum" and "quantum→quantum." They then theoretically analyze the relationship between the hardness of these tasks and the existence of other cryptographic primitives like public-key quantum money, quantum signatures, and quantum key distribution protocols.
Key Findings:
Main Conclusions: The hardness of quantum extrapolation, particularly classical→quantum extrapolation, presents a promising avenue for constructing secure quantum cryptographic primitives, especially quantum commitments. This research suggests that quantum extrapolation could serve as a fundamental building block for post-quantum cryptography.
Significance: This work contributes significantly to the field of post-quantum cryptography by exploring new foundational assumptions and their implications for building secure cryptographic systems in a world with quantum computers.
Limitations and Future Research: The authors acknowledge the limitations of their current understanding of quantum→quantum extrapolation and its potential for cryptographic constructions. Further research is needed to explore the full implications of this task and its relationship to other cryptographic primitives. Additionally, investigating the possibility of building EFI pairs from the hardness of quantum extrapolation remains an open question.
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