On the obfuscatability of quantum point functions

  • Tao ShangEmail author
  • Ran-yi-liu Chen
  • Jian-wei Liu


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.


Quantum obfuscation Quantum point function Quantum circuit Quantum zero-knowledge 



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).


  1. 1.
    Hada, S.: Zero-knowledge and code obfuscation. In: Advances in Cryptology-ASIACRYPT, vol. 2000, pp. 443–457 (2000)Google Scholar
  2. 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)Google Scholar
  3. 3.
    Lynn, B., Prabhakaran, M., Sahai, A.: Positive results and techniques for obfuscation. In: Advances in Cryptology-EUROCRYPT 2004, pp. 20–39 (2004)Google Scholar
  4. 4.
    Canetti, R., Dakdouk, R.: Obfuscating point functions with multibit output. In: Advances in Cryptology-EUROCRYPT 2008, pp. 489–508 (2008)Google Scholar
  5. 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)Google Scholar
  6. 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)Google Scholar
  7. 7.
    Bellare, M., Stepanovs, I.: Point-function obfuscation: a framework and generic constructions. In: Theory of Cryptography Conference, pp. 565–594 (2016)Google Scholar
  8. 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)Google Scholar
  9. 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)Google Scholar
  10. 10.
    Alagic, G., Fefferman, B.: On Quantum Obfuscation. (2016). arXiv:1602.01771
  11. 11.
    Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, pp. 29–34. Cambridge University Press, Cambridge (2000)Google Scholar
  12. 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)Google Scholar
  13. 13.
    Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26, 1510–1523 (1997)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Boneh, D. et al.: Random oracles in a quantum world. In: Advances in Cryptology-ASIACRYPT 2011, vol. 41 (2011)Google Scholar
  15. 15.
    Nir, B., Omer, P.: Point obfuscation and 3-round zero-knowledge. In: International Conference on Theory of Cryptography, pp. 190–208 (2012)Google Scholar
  16. 16.
    Bookatz, A.D.: QMA-complete problems. Quantum Inf. Comput. 14, 361–383 (2012)MathSciNetGoogle Scholar
  17. 17.
    Kobayashi, H.: General properties of quantum zero-knowledge proofs. In: Conference on Theory of Cryptography, pp. 107–124 (2008)Google Scholar
  18. 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)Google Scholar
  19. 19.
    Morimae, T.: Verification for measurement-only blind quantum computing. Phys. Rev. A 89, 4085–4088 (2014)CrossRefGoogle Scholar
  20. 20.
    Hayashi, M., Morimae, T.: Measurement-only blind quantum computing with stabilizer testing. Phys. Rev. Lett. 115, 220502 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 52, 1154–1162 (1996)Google Scholar

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Authors and Affiliations

  1. 1.School of Cyber Science and TechnologyBeihang UniversityBeijingChina
  2. 2.School of Electronic and Information EngineeringBeihang UniversityBeijingChina

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