Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
162 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

One-Way Functions Imply Secure Computation in a Quantum World (2011.13486v3)

Published 26 Nov 2020 in quant-ph and cs.CR

Abstract: We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Furthermore, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commitments based on the black-box use of quantum-hard one-way functions in the standard model. Instantiating the Cr\'epeau-Kilian (FOCS 1988) framework with these commitments yields simulation-secure QOT.

Citations (54)

Summary

  • The paper establishes that quantum-hard one-way functions suffice to construct simulation-secure quantum oblivious transfer.
  • It leverages black-box extraction and equivocal quantum commitments to ensure fairness and lower cryptographic complexity.
  • The findings bridge classical and quantum cryptography, indicating minimal assumptions can secure multi-party quantum computation.

Overview of "One-Way Functions Imply Secure Computation in a Quantum World"

The paper "One-Way Functions Imply Secure Computation in a Quantum World" by Bartusek, Coladangelo, Khurana, and Ma builds a strong theoretical foundation for secure quantum computation based on minimal assumptions. This work leverages the complexity of quantum-hard one-way functions to ensure the secure computation of arbitrary quantum functionalities, specifically focusing on simulation-secure quantum oblivious transfer (QOT).

Main Contribution

The authors establish that the existence of quantum-hard one-way functions suffices to construct simulation-secure QOT, a fundamental building block for secure quantum computation. The research is notable for making only black-box use of these functions, implying a straightforward and practical approach to quantum cryptographic implementations. The construction of QOT serves as a gateway to achieve secure multi-party computations even in the presence of quantum capabilities.

Technical Approach

  • Quantum Bit Commitments: The cornerstone of this paper is the construction of extractable and equivocal quantum bit commitments. Utilizing quantum-hard one-way functions, these commitments enable the realization of simulation-secure QOT. The work generates these commitments in the standard model without exotic assumptions.
  • Extractable and Equivocal Commitments:
    • Extraction: The authors provide a mechanism for extracting committed values from any adversarial committer, which is essential for ensuring that all parties adhere to protocol specifications.
    • Equivocation: Through innovative use of quantum operations and commitments, the scheme ensures that the commitments can later be opened to both potential outcomes without revealing additional information, thereby simulating fairness.

Impact on Cryptographic Complexity

This research achieves an efficient reduction from one-way functions to secure quantum functionalities, driving down the complexity and assumptions required for secure quantum computations. By demonstrating that these minimal assumptions suffice for achieving QOT, the paper challenges and potentially restructures the hierarchy of cryptographic primitives in a quantum world, where classical assumptions are not yet fully understood in terms of their implications on quantum cryptography.

Implications and Future Work

  • Theoretical Significance: This work underscores a potential separation in cryptographic capabilities between classical and quantum worlds. One-way functions, considered the touchstone for classical cryptographic primitives, now have demonstrable equivalence in securing quantum operations.
  • Practical Applications: One-sided statistically secure QOT could revolutionize industries relying on secure quantum communication and computations, offering a level of security assurance with minimal complexity compared to existing quantum cryptographic protocols.
  • Future Directions: The research invites a broader exploration into black-box constructions and the discovery of other fundamental quantum functionalities achievable with minimal assumptions. Moreover, potential implications for quantum communication networks and secure multi-party quantum computing frameworks are profound, as researchers continue to identify and construct primitives that exploit the peculiarities of quantum mechanics.

In summary, this paper is a substantive advancement in the field of quantum cryptography, illustrating that simpler cryptographic assumptions can sufficiently underwrite secure quantum computation frameworks and inviting further research into the black-box applications of quantum one-way functions.

Youtube Logo Streamline Icon: https://streamlinehq.com