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Inner-Product Functional Encryption from Random Linear Codes: Trial and Challenges

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Abstract

Inner-product encryption scheme is an important branch of functional encryption schemes, which has wide applications in modern society. There have existed many inner-product encryption schemes, but as far as we know, no code-based inner-product functional encryption scheme has been proposed. As one of the most popular post-quantum cryptographic techniques, why code-based cryptosystems are seldom applied in these areas raises our concern. In this paper, we build an inner product encryption scheme from random linear codes and prove its security. Unfortunately, our scheme still suffers from the so large parameter size, which indicates that how to build a practical code-based functional encryption scheme remains a challenging problem.

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References

  1. Abdalla, M., Bourse, F., De Caro, A., Pointcheval, D.: Simple functional encryption schemes for inner products. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 733–751. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_33

    Chapter  Google Scholar 

  2. Agrawal, S., Agrawal, S., Badrinarayanan, S., et al.: Function private functional encryption and property preserving encryption: new de and positive results. Cryptology ePrint Archive, Report 2013/744

    Google Scholar 

  3. Albrecht, M., Bernstein, D.J., Chou, T., et al.: Classic McEliece (2020). https://classic.mceliece.org/

  4. Becker, A., Joux, A., May, A., Meurer, A.: Decoding random binary linear codes in \(2^{n/20}\): how 1 + 1 = 0 improves information set decoding. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 520–536. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_31

    Chapter  MATH  Google Scholar 

  5. Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Trans. Inf. Theory 24(3), 384–386 (1978)

    Article  MathSciNet  Google Scholar 

  6. Bishop, A., Jain, A., Kowalczyk, L.: Function-hiding inner product encryption. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 470–491. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_20

    Chapter  Google Scholar 

  7. Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19571-6_16

    Chapter  Google Scholar 

  8. Debris-Alazard, T., Sendrier, N., Tillich, J.-P.: Wave: a new family of trapdoor one-way preimage sampleable functions based on codes. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 21–51. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_2

    Chapter  Google Scholar 

  9. Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12

    Chapter  Google Scholar 

  10. Katsumata, S., Nishimaki, R., Yamada, S., Yamakawa, T.: Adaptively secure inner product encryption from LWE. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 375–404. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_13

    Chapter  Google Scholar 

  11. Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_9

    Chapter  Google Scholar 

  12. Kim, S., Lewi, K., Mandal, A., Montgomery, H., Roy, A., Wu, D.J.: Function-hiding inner product encryption is practical. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 544–562. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98113-0_29

    Chapter  Google Scholar 

  13. MAGMA Computational Algebra System. http://magma.maths.usyd.edu.au/calc/

  14. May, A., Ozerov, I.: On computing nearest neighbors with applications to decoding of binary linear codes. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 203–228. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_9

    Chapter  Google Scholar 

  15. May, A., Meurer, A., Thomae, E.: Decoding random linear codes in \(\tilde{\cal{O}}(2^{0.054n})\). In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 107–124. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_6

    Chapter  MATH  Google Scholar 

  16. Mceliece, R.J.: A public-key cryptosystem based on algebraic coding theory. DSN Progress Rep. 42(44), 114–116 (1978)

    Google Scholar 

  17. Niederreiter, H.: Knapsack-type cryptosystems and algebraic coding theory. Probl. Contr. Inf. Theory 15(2), 159–166 (1986)

    MathSciNet  MATH  Google Scholar 

  18. Niebuhr, R., Cayrel, P.L., Bulygin, S., et al.: On lower bounds for information set decoding over FQ. In: SCC 2010, pp. 143–157. Springer

    Google Scholar 

  19. Okamoto, T., Takashima, K.: Adaptively attribute-hiding (hierarchical) inner product encryption. IEICE Trans. Fund. Electr. Commun. Comput. Sci. E99.A(1), 92–117 (2016)

    Google Scholar 

  20. Okamoto, T., Takashima, K.: Fully secure unbounded inner-product and attribute-based encryption. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 349–366. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_22

    Chapter  Google Scholar 

  21. Peters, C.: Information-set decoding for linear codes over \(\mathbf{F}_{q}\). In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 81–94. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12929-2_7

    Chapter  Google Scholar 

  22. Prange, E.: The use of information sets in decoding cyclic codes. IRE Trans. Inf. Theory 8(5), 5–9 (1962)

    Article  MathSciNet  Google Scholar 

  23. Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_27

    Chapter  Google Scholar 

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Acknowledgements

This work is supported by Guangdong Major Project of Basic and Applied Basic Research (2019B030302008) and the National Natural Science Foundation of China (No. 61972429).

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Correspondence to Fangguo Zhang .

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Zhang, Z., Zhang, Z., Zhang, F. (2021). Inner-Product Functional Encryption from Random Linear Codes: Trial and Challenges. In: Huang, Q., Yu, Y. (eds) Provable and Practical Security. ProvSec 2021. Lecture Notes in Computer Science(), vol 13059. Springer, Cham. https://doi.org/10.1007/978-3-030-90402-9_14

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  • DOI: https://doi.org/10.1007/978-3-030-90402-9_14

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