Abstract
Non-committing encryption (NCE) is an advanced form of public-key encryption which guarantees the security of a Multi-Party Computation (MPC) protocol in the presence of an adaptive adversary. Brakerski et al. (TCC 2020) recently proposed an intermediate notion, termed Packed Encryption with Partial Equivocality (PEPE), which implies NCE and preserves the ciphertext rate (up to a constant factor). In this work, we propose three new constructions of rate-1 PEPE based on standard assumptions. In particular, we obtain the first constant ciphertext-rate NCE construction from the LWE assumption with polynomial modulus, and from the Subgroup Decision assumption. We also propose an alternative DDH-based construction with guaranteed polynomial running time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
In the proceedings version of [3], a PEPE candidate based on the quadratic residuostity assumption was proposed. Besides a CRS, this construction required oblivious sampling to avoid assuming erasures. In hidden-order groups, it is not clear how to obliviously sample a group element without knowing the group order and while satisfying the requirements of the security proof. The authors of [3] confirmed this issue and removed the QR-based construction in an updated version of their paper.
References
Beaver, D.: Plug and play encryption. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 75–89. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052228
Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_18
Brakerski, Z., Branco, P., Döttling, N., Garg, S., Malavolta, G.: Constant ciphertext-rate non-committing encryption from standard assumptions. In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12550, pp. 58–87. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64375-1_3
Brakerski, Z., Döttling, N., Garg, S., Malavolta, G.: Leveraging linear decryption: rate-1 fully-homomorphic encryption and time-lock puzzles. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11892, pp. 407–437. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36033-7_16
Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehlé, D.: Classical hardness of learning with errors. In: STOC (2013)
Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: STOC (1996)
Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_2
Canetti, R., Poburinnaya, O., Raykova, M.: Optimal-rate non-committing encryption. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10626, pp. 212–241. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_8
Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Improved non-committing encryption with applications to adaptively secure protocols. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 287–302. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_17
Damgård, I., Nielsen, J.B.: Improved non-committing encryption schemes based on a general complexity assumption. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 432–450. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_27
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC (2008)
Hemenway, B., Ostrovsky, R., Richelson, S., Rosen, A.: Adaptive security with quasi-optimal rate. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9562, pp. 525–541. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49096-9_22
Hemenway, B., Ostrovsky, R., Rosen, A.: Non-committing encryption from \(\phi \)-hiding. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9014, pp. 591–608. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46494-6_24
Hofheinz, D., Jager, T., Rupp, A.: Public-key encryption with simulation-based selective-opening security and compact ciphertexts. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 146–168. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53644-5_6
Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)
Libert, B., Passelègue, A., Wee, H., Wu, D.J.: New constructions of statistical NIZKs: dual-mode DV-NIZKs and more. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12107, pp. 410–441. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45727-3_14
Libert, B., Sakzad, A., Stehlé, D., Steinfeld, R.: All-but-many lossy trapdoor functions and selective opening chosen-ciphertext security from LWE. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 332–364. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_12
Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_41
Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: the non-committing encryption case. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 111–126. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45708-9_8
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC (2005)
Yoshida, Y., Kitagawa, F., Tanaka, K.: Non-committing encryption with quasi-optimal ciphertext-rate based on the DDH problem. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 128–158. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_5
Yoshida, Y., Kitagawa, F., Xagawa, K., Tanaka, K.: Non-committing encryption with constant ciphertext expansion from standard assumptions. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 36–65. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64834-3_2
Acknowledgements
We thank the anonymous reviewers for useful comments. This work was supported in part by the French ANR ALAMBIC project (ANR-16-CE39-0006).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Libert, B., Passelègue, A., Riahinia, M. (2022). New and Improved Constructions for Partially Equivocable Public Key Encryption. In: Galdi, C., Jarecki, S. (eds) Security and Cryptography for Networks. SCN 2022. Lecture Notes in Computer Science, vol 13409. Springer, Cham. https://doi.org/10.1007/978-3-031-14791-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-14791-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-14790-6
Online ISBN: 978-3-031-14791-3
eBook Packages: Computer ScienceComputer Science (R0)