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On the obfuscatability of quantum point functions

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Abstract

The goal of this work is to provide a positive result of quantum obfuscation. Point functions have been widely discussed in classical obfuscation theory but yet not formally defined in the quantum setting. To analyze the obfuscatability of quantum point functions, we start with preliminaries on quantum obfuscation, giving out the oracle-implementable relationship of two quantum circuit families and some obfuscations of combined quantum circuits. Then, we present the strict definition of a quantum point function and discuss its variants of multiple points and multiple qubits. Under the quantum-accessible random oracle model, we obtain the obfuscatability of quantum point function families by means of reduction. Finally, we discuss the application of quantum obfuscation in quantum zero-knowledge. As a start of study on quantum point functions, our work will be inspiring in the future development of quantum obfuscation theory.

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References

  1. Hada, S.: Zero-knowledge and code obfuscation. In: Advances in Cryptology-ASIACRYPT, vol. 2000, pp. 443–457 (2000)

  2. Barak, B. et al.: On the (im) possibility of obfuscating programs. In: Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology, pp. 1–18 (2001)

  3. Lynn, B., Prabhakaran, M., Sahai, A.: Positive results and techniques for obfuscation. In: Advances in Cryptology-EUROCRYPT 2004, pp. 20–39 (2004)

  4. Canetti, R., Dakdouk, R.: Obfuscating point functions with multibit output. In: Advances in Cryptology-EUROCRYPT 2008, pp. 489–508 (2008)

  5. Canetti, R., Kalai, Y.T., Varia, M., Wichs, D.: On symmetric encryption and point obfuscation. In: Theory of Cryptography Conference, pp. 52–71 (2010)

  6. Pandey, O., Prabhakaran, M., Sahai, A.: Obfuscation-based non-black-box simulation and four message concurrent zero knowledge for np. In: Theory of Cryptography Conference, pp. 638–667 (2015)

  7. Bellare, M., Stepanovs, I.: Point-function obfuscation: a framework and generic constructions. In: Theory of Cryptography Conference, pp. 565–594 (2016)

  8. Komargodski, I., Yogev, E.: Another step towards realizing random oracles: non-malleable point obfuscation. In: Advances in Cryptology-EUROCRYPT 2018. Lecture Notes in Computer Science, vol. 10820 (2018)

  9. Alagic, G., Jeffery, S., Jordan, S.: Circuit obfuscation using braids. In: Proceedings of 9th Conference on the Theory of Quantum Computation, Communication and Cryptography, vol. 141 (2014)

  10. Alagic, G., Fefferman, B.: On Quantum Obfuscation. (2016). arXiv:1602.01771

  11. Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, pp. 29–34. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  12. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, vol. 62 (1993)

  13. Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26, 1510–1523 (1997)

    Article  MathSciNet  Google Scholar 

  14. Boneh, D. et al.: Random oracles in a quantum world. In: Advances in Cryptology-ASIACRYPT 2011, vol. 41 (2011)

  15. Nir, B., Omer, P.: Point obfuscation and 3-round zero-knowledge. In: International Conference on Theory of Cryptography, pp. 190–208 (2012)

  16. Bookatz, A.D.: QMA-complete problems. Quantum Inf. Comput. 14, 361–383 (2012)

    MathSciNet  Google Scholar 

  17. Kobayashi, H.: General properties of quantum zero-knowledge proofs. In: Conference on Theory of Cryptography, pp. 107–124 (2008)

  18. Dunjko, V. et al.: Composable security of delegated quantum computation. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 406–425 (2014)

  19. Morimae, T.: Verification for measurement-only blind quantum computing. Phys. Rev. A 89, 4085–4088 (2014)

    Article  Google Scholar 

  20. Hayashi, M., Morimae, T.: Measurement-only blind quantum computing with stabilizer testing. Phys. Rev. Lett. 115, 220502 (2015)

    Article  ADS  Google Scholar 

  21. Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 52, 1154–1162 (1996)

    Google Scholar 

Download references

Acknowledgements

This project was supported by the National Natural Science Foundation of China (No. 61571024) and the National Key Research and Development Program of China (No. 2016YFC1000307).

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Authors and Affiliations

  1. School of Cyber Science and Technology, Beihang University, Beijing, 100083, China

    Tao Shang & Jian-wei Liu

  2. School of Electronic and Information Engineering, Beihang University, Beijing, 100083, China

    Ran-yi-liu Chen

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  1. Tao Shang
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  2. Ran-yi-liu Chen
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  3. Jian-wei Liu
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Correspondence to Tao Shang.

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Shang, T., Chen, Ryl. & Liu, Jw. On the obfuscatability of quantum point functions. Quantum Inf Process 18, 55 (2019). https://doi.org/10.1007/s11128-019-2172-2

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