nach oben

Erschienen in:

2020 | OriginalPaper | Buchkapitel

Succinct Functional Commitment for a Large Class of Arithmetic Circuits

verfasst von : Helger Lipmaa, Kateryna Pavlyk

Erschienen in: Advances in Cryptology – ASIACRYPT 2020

Verlag: Springer International Publishing

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

A succinct functional commitment (SFC) scheme for a circuit class \(\mathbf {CC}\) enables, for any circuit \(\mathcal {C}\in \mathbf {CC}\), the committer to first succinctly commit to a vector \(\varvec{\alpha }\), and later succinctly open the commitment to \(\mathcal {C}(\varvec{\alpha }, \varvec{\beta })\), where the verifier chooses \(\varvec{\beta }\) at the time of opening. Unfortunately, SFC commitment schemes are known only for severely limited function classes like the class of inner products. By making non-black-box use of SNARK-construction techniques, we propose a SFC scheme for the large class of semi-sparse polynomials. The new SFC scheme can be used to, say, efficiently (1) implement sparse polynomials, and (2) aggregate various interesting SFC (e.g., vector commitment and polynomial commitment) schemes. The new scheme is evaluation-binding under a new instantiation of the computational uber-assumption. We provide a thorough analysis of the new assumption.

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 Cryptography from One-Way Communication: On Completeness of Finite Channels

Nächstes Kapitel Crowd Verifiable Zero-Knowledge and End-to-End Verifiable Multiparty Computation

As a corollary of independent interest, we also show in the full version [34] that if \(f\not \in {\text {span}}(\mathcal {R})\) then the \((\mathcal {R}, \mathcal {S}, \mathcal {T})\)-uber-assumption follows from HAK and PDL.

Abdolmaleki, B., Baghery, K., Lipmaa, H., Zając, M.: A subversion-resistant SNARK. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part III. LNCS, vol. 10626, pp. 3–33. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_1CrossRef

Abdolmaleki, B., Lipmaa, H., Siim, J., Zając, M.: On QA-NIZK in the BPK model. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020, Part I. LNCS, vol. 12110, pp. 590–620. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_20CrossRef

Barić, N., Pfitzmann, B.: Collision-free accumulators and fail-stop signature schemes without trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 480–494. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_33CrossRef

Bellare, M., Fuchsbauer, G., Scafuro, A.: NIZKs with an untrusted CRS: security in the face of parameter subversion. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part II. LNCS, vol. 10032, pp. 777–804. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_26CrossRefMATH

Benaloh, J., de Mare, M.: One-way accumulators: a decentralized alternative to digital signatures. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 274–285. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48285-7_24CrossRef

Bitansky, N.: Verifiable random functions from non-interactive witness-indistinguishable proofs. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017, Part II. LNCS, vol. 10678, pp. 567–594. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_19CrossRef

Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_26CrossRef

Boneh, D., Bünz, B., Fisch, B.: Batching techniques for accumulators with applications to IOPs and stateless blockchains. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part I. LNCS, vol. 11692, pp. 561–586. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_20CrossRef

Boneh, D., Drake, J., Fisch, B., Gabizon, A.: Efficient polynomial commitment schemes for multiple points and polynomials. Technical report 2020/081, IACR (2020)

10.

Bowe, S., Grigg, J., Hopwood, D.: Halo: recursive proof composition without a trusted setup. Technical report (2019). https://electriccoin.co/wp-content/uploads/2019/09/Halo.pdf

11.

Boyen, X.: The uber-assumption family. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 39–56. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85538-5_3CrossRef

12.

Catalano, D., Fiore, D.: Vector commitments and their applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 55–72. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_5CrossRef

13.

Chase, M., Maller, M., Meiklejohn, S.: Déjà Q all over again: tighter and broader reductions of q-type assumptions. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part II. LNCS, vol. 10032, pp. 655–681. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_22CrossRef

14.

Chase, M., Meiklejohn, S.: Déjà Q: using dual systems to revisit q-type assumptions. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 622–639. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_34CrossRef

15.

Chiesa, A., Hu, Y., Maller, M., Mishra, P., Vesely, N., Ward, N.: Marlin: preprocessing zkSNARKs with universal and updatable SRS. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 738–768. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_26CrossRef

16.

Dent, A.W.: Adapting the weaknesses of the random oracle model to the generic group model. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 100–109. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36178-2_6CrossRef

17.

Fischlin, M.: A note on security proofs in the generic model. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 458–469. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44448-3_35CrossRefMATH

18.

Fuchsbauer, G.: Subversion-zero-knowledge SNARKs. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part I. LNCS, vol. 10769, pp. 315–347. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76578-5_11CrossRef

19.

Fuchsbauer, G., Kiltz, E., Loss, J.: The algebraic group model and its applications. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part II. LNCS, vol. 10992, pp. 33–62. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_2CrossRef

20.

Gennaro, R., Gentry, C., Parno, B., Raykova, M.: Quadratic span programs and succinct NIZKs without PCPs. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 626–645. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_37CrossRef

21.

Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: 43rd ACM STOC, pp. 99–108 (2011)

22.

Gorbunov, S., Reyzin, L., Wee, H., Zhang, Z.: PointProofs: aggregating proofs for multiple vector commitments. Technical report 2020/419, IACR (2020)

23.

Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_19CrossRef

24.

Groth, J.: On the size of pairing-based non-interactive arguments. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016, Part II. LNCS, vol. 9666, pp. 305–326. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_11CrossRef

25.

Izabachène, M., Libert, B., Vergnaud, D.: Block-wise P-signatures and non-interactive anonymous credentials with efficient attributes. In: Chen, L. (ed.) IMACC 2011. LNCS, vol. 7089, pp. 431–450. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25516-8_26CrossRefMATH

26.

Jager, T., Rupp, A.: The semi-generic group model and applications to pairing-based cryptography. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 539–556. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_31CrossRef

27.

Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_11CrossRef

28.

Lai, R.W.F., Malavolta, G.: Subvector commitments with application to succinct arguments. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part I. LNCS, vol. 11692, pp. 530–560. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_19CrossRef

29.

Libert, B., Ramanna, S.C., Yung, M.: Functional commitment schemes: from polynomial commitments to pairing-based accumulators from simple assumptions. In: ICALP 2016. LIPIcs, vol. 55, pp. 30:1–30:14 (2016)

30.

Libert, B., Yung, M.: Concise mercurial vector commitments and independent zero-knowledge sets with short proofs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 499–517. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_30CrossRef

31.

Lipmaa, H.: Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 169–189. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_10CrossRef

32.

Lipmaa, H.: Succinct non-interactive zero knowledge arguments from span programs and linear error-correcting codes. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 41–60. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42033-7_3CrossRef

33.

Lipmaa, H.: Simulation-extractable ZK-SNARKs revisited. Technical report 2019/612, IACR (2019) https://eprint.iacr.org/2019/612. Accessed 8 Feb 2020

34.

Lipmaa, H., Pavlyk, K.: Succinct functional commitment for a large class of arithmetic circuits. Technical Report 2020/?, IACR (2020)

35.

Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: ACM CCS 2019, pp. 2111–2128 (2019)

36.

Papamanthou, C., Shi, E., Tamassia, R.: Signatures of correct computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 222–242. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36594-2_13CrossRefMATH

37.

Shpilka, A., Yehudayoff, A.: Arithmetic circuits: a survey of recent results and open questions. In: Foundations and Trends in Theoretical Computer Science, vol. 5. Now Publishers Inc. (2010)

38.

Tomescu, A., Abraham, I., Buterin, V., Drake, J., Feist, D., Khovratovich, D.: Aggregatable subvector commitments for stateless cryptocurrencies. Technical report 2020/527, IACR (2020)

39.

Valiant, L.G.: Completeness classes in algebra. In: STOC 1979, pp. 249–261 (1979)

40.

Wahby, R.S., Tzialla, I., Shelat, A., Thaler, J., Walfish, M.: Doubly-efficient zkSNARKs without trusted setup. In: IEEE SP 2018, pp. 926–943 (2018)

41.

Zhang, Y., Genkin, D., Katz, J., Papadopoulos, D., Papamanthou, C.: vSQL: verifying arbitrary SQL queries over dynamic outsourced databases. In: IEEE SP 2017, pp. 863–880 (2017)

Titel: Succinct Functional Commitment for a Large Class of Arithmetic Circuits
verfasst von: Helger Lipmaa
Kateryna Pavlyk
Verlag: Springer International Publishing
Buch: Advances in Cryptology – ASIACRYPT 2020
Print ISBN: 978-3-030-64839-8

Electronic ISBN: 978-3-030-64840-4

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-64840-4_23

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