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Quantum attribute-based encryption: a comprehensive study

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Abstract

In this work, we study quantum versions of attribute-based encryption schemes. Attribute-based encryption enables fine-grained access control of encrypted data using authorization policies. The secret key of a user and the ciphertext are dependent upon attributes, and the decryption of a ciphertext is possible only if the set of attributes of the user key matches the attributes of the ciphertext. Most of the existing classical attribute-based schemes are based on the hardness of the bilinear Diffie–Hellman problem, which has been proven to be vulnerable against Shor’s algorithm. No efficient quantum attribute-based encryption scheme has been reported till date. In this backdrop, we propose quantum attribute-based encryption schemes exploiting quantum key distribution and quantum error-correcting codes. Attribute-based scheme is a special case of a more general functional encryption scheme whose quantum version we consider next hence giving this work a unifying framework. We present two constructions of quantum functional encryption schemes. The first construction generalizes the traditional notion of functional encryption and can handle multiple functions. The second construction utilizes the quantum query complexities of different Boolean functions. As applications, we present a quantum progressive functional encryption scheme to suitably encrypt an image to be shared among data users with hierarchical relations between them and outline a connection between quantum functional encryption schemes and obfuscated quantum states. In this work, we use weak measurements, which help us to expand our horizon to include encryption schemes in the dishonest model and quantum communication in the presence of an adversary. Our methods are unconditional and do not depend on the known difficulty of problems like lattice-based problems. Finally, we discuss various advantages of our methods and results.

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References

  1. Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Advances in Cryptology—EUROCRYPT 2005: 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, May 22–26, 2005. Proceedings 24, pp. 457–473. Springer (2005)

  2. Zhang, Y., Deng, R.H., Xu, S., Sun, J., Li, Q., Zheng, D.: Attribute-based encryption for cloud computing access control: a survey. ACM Comput. Surv. 53(4), 1–41 (2020)

    Google Scholar 

  3. Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: 2007 IEEE Symposium on Security and Privacy (SP’07), pp. 321–334. IEEE (2007)

  4. Waters, B.: Ciphertext-policy attribute-based encryption: an expressive, efficient, and provably secure realization. In: Public Key Cryptography—PKC 2011: 14th International Conference on Practice and Theory in Public Key Cryptography, Taormina, Italy, March 6–9, 2011. Proceedings 14, pp. 53–70. Springer (2011)

  5. Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, pp. 89–98 (2006)

  6. Chase, M.: Multi-authority attribute based encryption. In: Theory of Cryptography: 4th Theory of Cryptography Conference, TCC 2007, Amsterdam, The Netherlands, February 21–24, 2007. Proceedings 4, pp. 515–534. Springer (2007)

  7. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE (1994)

  8. El Bansarkhani, R., El Kaafarani, A.: Post-quantum attribute-based signatures from lattice assumptions. Cryptology ePrint Archive (2016)

  9. Liu, X., Ma, J., Xiong, J., Li, Q., Zhang, T., Zhu, H.: Threshold attribute-based encryption with attribute hierarchy for lattices in the standard model. IET Inf. Secur. 8(4), 217–223 (2014)

    Article  Google Scholar 

  10. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  11. Blakley, G.R.: Safeguarding cryptographic keys. In: International Workshop On Managing Requirements Knowledge, pp. 313–313. IEEE Computer Society (1979)

  12. Blundo, C., Cresti, A., De Santis, A., Vaccaro, U.: Fully dynamic secret sharing schemes. In: Advances in Cryptology-CRYPTO’93, pp. 110–125. Springer (1994)

  13. Herzberg, A., Jarecki, S., Krawczyk, H., Yung, M.: Proactive secret sharing or: how to cope with perpetual leakage. In: Advances in Cryptology-CRYPT0’95: 15th Annual International Cryptology Conference Santa Barbara, California, USA, August 27–31, 1995 Proceedings 15, pp. 339–352. Springer (1995)

  14. Nojoumian, M., Stinson, D.R.: Sequential secret sharing as a new hierarchical access structure. Cryptology ePrint Archive (2015)

  15. Komargodski, I., Naor, M., Yogev, E.: How to share a secret, infinitely. IEEE Trans. Inf. Theory 64(6), 4179–4190 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  16. Komargodski, I., Paskin-Cherniavsky, A.: Evolving secret sharing: dynamic thresholds and robustness. In: Theory of Cryptography: 15th International Conference, TCC 2017, Baltimore, MD, USA, November 12–15, 2017, Proceedings, Part II 15, pp. 379–393. Springer (2017)

  17. Du, Y.-T., Bao, W.-S.: Dynamic quantum secret sharing protocol based on two-particle transform of bell states. Chin. Phys. B 27(8), 080304 (2018)

    Article  ADS  Google Scholar 

  18. Hsu, J.-L., Chong, S.-K., Hwang, T., Tsai, C.-W.: Dynamic quantum secret sharing. Quantum Inf. Process. 12, 331–344 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Liao, C.-H., Yang, C.-W., Hwang, T.: Dynamic quantum secret sharing protocol based on ghz state. Quantum Inf. Process. 13, 1907–1916 (2014)

    Article  ADS  MATH  Google Scholar 

  20. Qin, H., Dai, Y.: Dynamic quantum secret sharing by using d-dimensional ghz state. Quantum Inf. Process. 16, 1–13 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  21. Samadder Chaudhury, S.: A quantum evolving secret sharing scheme. Int. J. Theor. Phys. 59(12), 3936–3950 (2020)

    Article  MATH  Google Scholar 

  22. Qin, H., Zhu, X., Dai, Y.: (t, n) threshold quantum secret sharing using the phase shift operation. Quantum Inf. Process. 14, 2997–3004 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Guo, L., Yang, X., Yau, W.-C.: Tabe-dac: efficient traceable attribute-based encryption scheme with dynamic access control based on blockchain. IEEE Access 9, 8479–8490 (2021)

    Article  Google Scholar 

  24. Sahai, A., Seyalioglu, H., Waters, B., et al.: Dynamic credentials and ciphertext delegation for attribute-based encryption. In: Crypto, vol. 7417, pp. 199–217. Springer (2012)

  25. Xu, Z., Martin, K.M.: Dynamic user revocation and key refreshing for attribute-based encryption in cloud storage. In: 2012 IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications, pp. 844–849. IEEE (2012)

  26. Shamir, A.: Identity-based cryptosystems and signature schemes. In: Advances in Cryptology: Proceedings of CRYPTO 84 4, pp. 47–53. Springer (1985)

  27. Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Advances in Cryptology-EUROCRYPT 2004: International Conference on the Theory and Applications of Cryptographic Techniques, Interlaken, Switzerland, May 2–6, 2004. Proceedings 23, pp. 506–522. Springer (2004)

  28. Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Theory of Cryptography: 8th Theory of Cryptography Conference, TCC 2011, Providence, RI, USA, March 28–30, 2011. Proceedings 8, pp. 253–273. Springer (2011)

  29. O’Neill, A.: Definitional issues in functional encryption. Cryptology ePrint Archive (2010)

  30. Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Advances in Cryptology—EUROCRYPT 2010: 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, French Riviera, May 30–June 3, 2010. Proceedings 29, pp. 62–91. Springer (2010)

  31. Goldwasser, S., Gordon, S.D., Goyal, V., Jain, A., Katz, J., Liu, F.-H., Sahai, A., Shi, E., Zhou, H.-S.: Multi-input functional encryption. In: EUROCRYPT, vol. 8441, pp. 578–602. Springer (2014)

  32. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. SIAM J. Comput. 45(3), 882–929 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  33. Bitansky, N., Vaikuntanathan, V.: Indistinguishability obfuscation from functional encryption. J. ACM 65(6), 1–37 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  34. Agrawal, S., Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption: new perspectives and lower bounds. In: Advances in Cryptology—CRYPTO 2013: 33rd Annual Cryptology Conference, Santa Barbara, CA, USA, August 18–22, 2013. Proceedings, Part II, pp. 500–518. Springer (2013)

  35. Mascia, C., Sala, M., Villa, I.: A survey on functional encryption. arXiv preprint arXiv:2106.06306 (2021)

  36. Boyen, X.: Attribute-based functional encryption on lattices. In: Theory of Cryptography: 10th Theory of Cryptography Conference, TCC 2013, Tokyo, Japan, March 3–6, 2013. Proceedings, pp. 122–142. Springer (2013)

  37. Debnath, S.K., Mesnager, S., Dey, K., Kundu, N.: Post-quantum secure inner product functional encryption using multivariate public key cryptography. Mediterr. J. Math. 18, 1–15 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  38. Kitagawa, F., Nishimaki, R.: Functional encryption with secure key leasing. In: Advances in Cryptology—ASIACRYPT 2022: 28th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, December 5–9, 2022, Proceedings, Part IV, pp. 569–598. Springer (2023)

  39. Bakas, A., Michalas, A., Frimpong, E., Rabbaninejad, R.: Feel the quantum functioning: instantiating generic multi-input functional encryption from learning with errors (extended version)? Cryptology ePrint Archive (2022)

  40. Ahuja, A.: A quantum-classical scheme towards quantum functional encryption. arXiv preprint arXiv:1703.00207 (2017)

  41. Agrawal, S., Goyal, R., Tomida, J.: Multi-party functional encryption. In: Theory of Cryptography: 19th International Conference, TCC 2021, Raleigh, NC, USA, November 8–11, 2021, Proceedings, Part II, pp. 224–255. Springer (2021)

  42. Aaronson, S., Rothblum, G.N.: Gentle measurement of quantum states and differential privacy. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pp. 322–333 (2019)

  43. Brun, T.A.: A simple model of quantum trajectories. Am. J. Phys. 70(7), 719–737 (2002)

    Article  ADS  Google Scholar 

  44. Gudder, S.: Non-disturbance for fuzzy quantum measurements. Fuzzy Sets Syst. 155(1), 18–25 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  45. Korotkov, A.: Noisy quantum measurement of solid-state qubits: Bayesian approach. Quantum Noise Mesoscopic Phys. 97, 205 (2003)

    Article  Google Scholar 

  46. Beimel, A.: Secret-sharing schemes: a survey. In: Coding and Cryptology: Third International Workshop, IWCC 2011, Qingdao, China, May 30–June 3, 2011. Proceedings 3, pp. 11–46. Springer (2011)

  47. Liu, Z., Cao, Z., Wong, D.S.: Efficient generation of linear secret sharing scheme matrices from threshold access trees. Cryptology ePrint Archive (2010)

  48. Nikov, V., Nikova, S.: New monotone span programs from old. Cryptology ePrint Archive (2004)

  49. Traverso, G., Demirel, D., Buchmann, J.: Dynamic and verifiable hierarchical secret sharing. In: Information Theoretic Security: 9th International Conference, ICITS 2016, Tacoma, WA, USA, August 9–12, 2016, Revised Selected Papers 9, pp. 24–43. Springer (2016)

  50. Ambainis, A.: Understanding quantum algorithms via query complexity. In: Proceedings of the International Congress of Mathematicians: Rio de Janeiro 2018, pp. 3265–3285. World Scientific (2018)

  51. Ambainis, A.: Polynomial degree vs. quantum query complexity. In: 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings, pp. 230–239 (2003)

  52. Reichardt, B.W.: Span programs and quantum query complexity: the general adversary bound is nearly tight for every Boolean function. In: 2009 50th Annual IEEE Symposium on Foundations of Computer Science, pp. 544–551. IEEE (2009)

  53. Laplante, S., Magniez, F.: Lower bounds for randomized and quantum query complexity using Kolmogorov arguments. In: Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004, pp. 294–304 (2004)

  54. Chen, W., Ye, Z., Li, L.: Characterization of exact one-query quantum algorithms. Phys. Rev. A 101(2), 022325 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  55. Ambainis, A.: Quantum lower bounds by quantum arguments. J. Comput. Syst. Sci. 64(4), 750–767 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  56. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Phys. Today 54(2), 60 (2001)

    Google Scholar 

  57. De Wolf, R.: Nondeterministic quantum query and communication complexities. SIAM J. Comput. 32(3), 681–699 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  58. Buhrman, H., De Wolf, R.: Complexity measures and decision tree complexity: a survey. Theor. Comput. Sci. 288(1), 21–43 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  59. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, India, p. 175 (1984)

  60. Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299, 802–803 (1982)

    Article  ADS  MATH  Google Scholar 

  61. Dieks, D.: Communication by epr devices. Phys. Lett. A 92(6), 271–272 (1982)

    Article  ADS  Google Scholar 

  62. Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92(2), 022305 (2015)

    Article  ADS  Google Scholar 

  63. Steane, A.M.: Enlargement of Calderbank–Shor–Steane quantum codes. IEEE Trans. Inf. Theory 45(7), 2492–2495 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  64. Ruhault, S.: Sok: security models for pseudo-random number generators. IACR Trans. Symmetric Cryptol. 2017, 506–544 (2017)

    Article  Google Scholar 

  65. Liu, L., Wang, A., Chang, C.-C., Li, Z.: A novel real-time and progressive secret image sharing with flexible shadows based on compressive sensing. Signal Process. Image Commun. 29(1), 128–134 (2014)

    Article  Google Scholar 

  66. Yan, X., Lu, Y., Liu, L.: A general progressive secret image sharing construction method. Signal Process. Image Commun. 71, 66–75 (2019)

    Article  Google Scholar 

  67. Zhang, Y., Lu, K., Gao, Y., Wang, M.: Neqr: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12, 2833–2860 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  68. Luo, G.-F., Zhou, R.-G., Hu, W.-W.: Novel quantum secret image-sharing scheme. Chin. Phys. B 28(4), 040302 (2019)

    Article  ADS  Google Scholar 

  69. Mosca, M., Tapp, A., de Wolf, R.: Private quantum channels and the cost of randomizing quantum information. arXiv preprint arXiv:quant-ph/0003101 (2000)

  70. Broadbent, A., Jeffery, S.: Quantum homomorphic encryption for circuits of low t-gate complexity. In: Advances in Cryptology—CRYPTO 2015: 35th Annual Cryptology Conference, Santa Barbara, CA, USA, August 16–20, 2015, Proceedings, Part II, pp. 609–629. Springer (2015)

  71. Nayak, A., Wu, F.: The quantum query complexity of approximating the median and related statistics. In: Proceedings of the Thirty-first Annual ACM Symposium on Theory of Computing, pp. 384–393 (1999)

  72. Csirmaz, L.: Complexity of universal access structures. Inf. Process. Lett. 112(4), 149–152 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  73. Harvey, D., Van Der Hoeven, J.: Integer multiplication in time o(nlog\(\backslash \), n). Ann. Math. 193(2), 563–617 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  74. Miller, V.S.: Use of elliptic curves in cryptography. In: Conference on the Theory and Application of Cryptographic Techniques, pp. 417–426. Springer (1985)

  75. Miller, V.S.: The Weil pairing, and its efficient calculation. J. Cryptol. 17(4), 235–261 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  76. Lewko, A., Waters, B.: Decentralizing attribute-based encryption. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 568–588. Springer (2011)

  77. Zhang, J., Zhang, Z., Ge, A.: Ciphertext policy attribute-based encryption from lattices. In: Proceedings of the 7th ACM Symposium on Information, Computer and Communications Security, pp. 16–17 (2012)

  78. Fun, T.S., Samsudin, A.: Lattice ciphertext-policy attribute-based encryption from ring-lwe. In: 2015 International Symposium on Technology Management and Emerging Technologies (ISTMET), pp. 258–262. IEEE (2015)

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Acknowledgements

The first author thanks TCG Centres for Research and Education in Science and Technology (TCG-CREST) for a post-doctoral fellowship which financially supported this work.

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  1. Asmita Samanta and Arpita Maitra have contributed equally to this work.

Authors and Affiliations

  1. Translational Research in Mathematics, TCG Centres for Research and Education in Science and Technology, EP-GP Block, Kolkata, West Bengal, 700091, India

    Shion Samadder Chaudhury

  2. Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, West Bengal, 700108, India

    Asmita Samanta

  3. Institute For Advancing Intelligence, TCG Centres for Research and Education in Science and Technology, EP-GP Block, Kolkata, West Bengal, 700091, India

    Arpita Maitra

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Samadder Chaudhury, S., Samanta, A. & Maitra, A. Quantum attribute-based encryption: a comprehensive study. Quantum Inf Process 22, 335 (2023). https://doi.org/10.1007/s11128-023-04085-z

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