nach oben

Erschienen in:

2019 | OriginalPaper | Buchkapitel

New Techniques for Efficient Trapdoor Functions and Applications

verfasst von : Sanjam Garg, Romain Gay, Mohammad Hajiabadi

Erschienen in: Advances in Cryptology – EUROCRYPT 2019

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We develop techniques for constructing trapdoor functions (TDFs) with short image size and advanced security properties. Our approach builds on the recent framework of Garg and Hajiabadi [CRYPTO 2018]. As applications of our techniques, we obtain

The first construction of deterministic-encryption schemes for block-source inputs (both for the CPA and CCA cases) based on the Computational Diffie-Hellman (CDH) assumption. Moreover, by applying our efficiency-enhancing techniques, we obtain CDH-based schemes with ciphertext size linear in plaintext size.
The first construction of lossy TDFs based on the Decisional Diffie-Hellman (DDH) assumption with image size linear in input size, while retaining the lossiness rate of [Peikert-Waters STOC 2008].

Prior to our work, all constructions of deterministic encryption based even on the stronger DDH assumption incurred a quadratic gap between the ciphertext and plaintext sizes. Moreover, all DDH-based constructions of lossy TDFs had image size quadratic in the input size.

At a high level, we break the previous quadratic barriers by introducing a novel technique for encoding input bits via hardcore output bits with the use of erasure-resilient codes. All previous schemes used group elements for encoding input bits, resulting in quadratic expansions.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel On ELFs, Deterministic Encryption, and Correlated-Input Security

Nächstes Kapitel Symbolic Encryption with Pseudorandom Keys

We note that building a TDF providing mere one-wayness with linear-size images is simple: if \(\mathsf {TDF}.\mathsf {F} (\mathsf {ik}, \cdot )\) maps n-bit inputs to \(n^c\)-bit outputs, define \(\mathsf {TDF}.\mathsf {F} '(\mathsf {ik}, \mathsf {x}|| \mathsf {x}')\), where \(|\mathsf {x}| = n\) and \(|\mathsf {x}'| = n^c\), as \(\mathsf {TDF}.\mathsf {F} (\mathsf {ik}, \mathsf {x}) || \mathsf {x}'\). Although this transformation results in TDFs with linear-image size, it destroy more advanced properties such as CCA2 security, deterministic-encryption security and the lossiness rate.

This is the indistinguishability-based, single-message version of their notion, which as they show, is equivalent to the multiple-message version both for the indistinguishability- and simulation-based definitions.

We note that this lossiness property is weaker than the one of [PW08, PW11], but it can be realized under CDH. We will later show efficient DDH-based instantiations of lossiness in the sense of [PW08, PW11].

We mention that the transformation of [RS09] results in CCA-secure PKE schemes which use randomness, but this can be avoided by using the techniques of [KMO10] to get CCA2-secure TDFs.

We have not yet optimized nor tried to get some upper bounds on the constants.

\(\mathsf {ct} \) is assumed to contain (i, b).

The choices of the constants were made as above so to have slackness in proofs—they have not been optimized for efficiency.

For simplicity assume \(g_1 \ne g_{1,b}^r\), hence we will not have a hung situation.

[BBN+09]

Bellare, M., et al.: Hedged public-key encryption: how to protect against bad randomness. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 232–249. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_14CrossRef

[BBO07]

Bellare, M., Boldyreva, A., O’Neill, A.: Deterministic and efficiently searchable encryption. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 535–552. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_30CrossRef

[BCPT13]

Birrell, E., Chung, K.-M., Pass, R., Telang, S.: Randomness-dependent message security. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 700–720. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_39CrossRef

[BFO08]

Boldyreva, A., Fehr, S., O’Neill, A.: On notions of security for deterministic encryption, and efficient constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 335–359. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_19CrossRef

[BFOR08]

Bellare, M., Fischlin, M., O’Neill, A., Ristenpart, T.: Deterministic encryption: definitional equivalences and constructions without random oracles. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 360–378. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_20CrossRef

[BHY09]

Bellare, M., Hofheinz, D., Yilek, S.: Possibility and impossibility results for encryption and commitment secure under selective opening. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 1–35. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01001-9_1CrossRef

[BLSV18]

Brakerski, Z., Lombardi, A., Segev, G., Vaikuntanathan, V.: Anonymous IBE, leakage resilience and circular security from new assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 535–564. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_20CrossRef

[BS11]

Brakerski, Z., Segev, G.: Better security for deterministic public-key encryption: the auxiliary-input setting. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 543–560. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_31CrossRef

[BW10]

Boyen, X., Waters, B.: Shrinking the keys of discrete-log-type lossy trapdoor functions. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 35–52. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13708-2_3CrossRef

[CDG+17]

Cho, C., Döttling, N., Garg, S., Gupta, D., Miao, P., Polychroniadou, A.: Laconic oblivious transfer and its applications. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 33–65. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_2CrossRef

[DG17a]

Döttling, N., Garg, S.: From selective IBE to Full IBE and selective HIBE. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 372–408. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_13CrossRef

[DG17b]

Döttling, N., Garg, S.: Identity-based encryption from the Diffie-Hellman assumption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 537–569. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_18CrossRef

[DGHM18]

Döttling, N., Garg, S., Hajiabadi, M., Masny, D.: New constructions of identity-based and key-dependent message secure encryption schemes. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10769, pp. 3–31. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76578-5_1CrossRefMATH

[DH76]

Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644–654 (1976)MathSciNetCrossRef

[FGK+10]

Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More constructions of lossy and correlation-secure trapdoor functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 279–295. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_17CrossRef

[GH18]

Garg, S., Hajiabadi, M.: Trapdoor functions from the computational Diffie-Hellman assumption. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 362–391. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_13CrossRef

[GMR01]

Gertner, Y., Malkin, T., Reingold, O.: On the impossibility of basing trapdoor functions on trapdoor predicates. In: 42nd FOCS, Las Vegas, NV, USA, 14–17 October 2001, pp. 126–135. IEEE Computer Society Press (2001)

[HO12]

Hemenway, B., Ostrovsky, R.: Extended-DDH and lossy trapdoor functions. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 627–643. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30057-8_37CrossRef

[HO13]

Hemenway, B., Ostrovsky, R.: Building lossy trapdoor functions from lossy encryption. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 241–260. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42045-0_13CrossRef

[ILL89]

Impagliazzo, R., Levin, L.A., Luby, M.: Pseudo-random generation from one-way functions (extended abstracts). In: 21st ACM STOC, Seattle, WA, USA, 15–17 May 1989, pp. 12–24. ACM Press (1989)

[Jus72]

Justesen, J.: Class of constructive asymptotically good algebraic codes. IEEE Trans. Inf. Theory 18(5), 652–656 (1972)MathSciNetCrossRef

[KMO10]

Kiltz, E., Mohassel, P., O’Neill, A.: Adaptive trapdoor functions and chosen-ciphertext security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 673–692. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_34CrossRef

[KW18]

Koppula, V., Waters, B.: Realizing chosen ciphertext security generically in attribute-based encryption and predicate encryption. Cryptology ePrint Archive, Report 2018/847 (2018). https://eprint.iacr.org/2018/847

[MPRS12]

Mironov, I., Pandey, O., Reingold, O., Segev, G.: Incremental deterministic public-key encryption. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 628–644. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_37CrossRef

[MY10]

Mol, P., Yilek, S.: Chosen-ciphertext security from slightly lossy trapdoor functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 296–311. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_18CrossRef

[PVW08]

Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_31CrossRef

[PW08]

Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: 40th ACM STOC, Victoria, British Columbia, Canada, 17–20 May 2008, pp. 187–196. ACM Press (2008)

[PW11]

Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. SIAM J. Comput. 40(6), 1803–1844 (2011)MathSciNetCrossRef

[RS09]

Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00457-5_25CrossRef

[RSA78]

Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signature and public-key cryptosystems. Commun. Assoc. Comput. Mach. 21(2), 120–126 (1978)MathSciNetMATH

[Wee12]

Wee, H.: Dual projective hashing and its applications—lossy trapdoor functions and more. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 246–262. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_16CrossRef

[Wic13]

Wichs, D.: Barriers in cryptography with weak, correlated and leaky sources. In: ITCS 2013, Berkeley, CA, USA, 9–12 January 2013, pp. 111–126. ACM (2013)

Titel: New Techniques for Efficient Trapdoor Functions and Applications
verfasst von: Sanjam Garg
Romain Gay
Mohammad Hajiabadi
Verlag: Springer International Publishing
Buch: Advances in Cryptology – EUROCRYPT 2019
Print ISBN: 978-3-030-17658-7

Electronic ISBN: 978-3-030-17659-4

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-17659-4_2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner