Abstract
Cryptographic objects with updating capabilities have been proposed by Bellare, Goldreich and Goldwasser (CRYPTO’94) under the umbrella of incremental cryptography. They have recently seen increased interest, motivated by theoretical questions (Ananth et al., EC’17) as well as concrete practical motivations (Lehmann et al., EC’18; Groth et al. CRYPTO’18; Klooß et al., EC’19). In this work, the form of updatability we are particularly interested in is that primitives are key-updatable and allow to update “old” cryptographic objects, e.g., signatures or message authentication codes, from the “old” key to the updated key at the same time without requiring full access to the new key (i.e., only via a so-called update token).
Inspired by the rigorous study of updatable encryption by Lehmann and Tackmann (EC’18) and Boyd et al. (CRYPTO’20), we introduce a definitional framework for updatable signatures (USs) and message authentication codes (UMACs). We discuss several applications demonstrating that such primitives can be useful in practical applications, especially around key rotation in various domains, as well as serve as building blocks in other cryptographic schemes. We then turn to constructions and our focus there is on ones that are secure and practically efficient. In particular, we provide generic constructions from key-homomorphic primitives (signatures and PRFs) as well as direct constructions. This allows us to instantiate these primitives from various assumptions such as DDH or CDH (latter in bilinear groups), or the (R)LWE and the SIS assumptions. As an example, we obtain highly practical US schemes from BLS signatures or UMAC schemes from the Naor-Pinkas-Reingold PRF.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See that such large values of \(n \) allow for virtually unbounded number of epochs.
- 2.
We assume that from keys, tokens, and tags, the associated epoch is efficiently extractable.
- 3.
As in UMACs, such large values of \(n \) allow for virtually unbounded number of epochs.
- 4.
\(M =\top \) is a placeholder for “all messages” in \(\mathcal {M} \) and helps us to construct the set \(\mathcal {S}^*\) efficiently.
References
Abdolmaleki, B., Ramacher, S., Slamanig, D.: Lift-and-shift: obtaining simulation extractable subversion and updatable SNARKs generically. In: ACM CCS 20 (2020)
Ananth, P., Cohen, A., Jain, A.: Cryptography with updates. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 445–472. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_15
Apple: code signing. https://developer.apple.com/support/code-signing/
Applebaum, B.: Computationally private randomizing polynomials and their applications. In: Cryptography in Constant Parallel Time. ISC, pp. 79–106. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-17367-7_5
Arch Linux Wiki: pacman/package signing. https://wiki.archlinux.org/index.php/Pacman/Package_signing
Arte, V., Bellare, M., Khati, L.: Incremental cryptography revisited: PRFs, nonces and modular design. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds.) INDOCRYPT 2020. LNCS, vol. 12578, pp. 576–598. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-65277-7_26
Ateniese, G., Chou, D.H., de Medeiros, B., Tsudik, G.: Sanitizable signatures. In: di Vimercati, S.C., Syverson, P., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 159–177. Springer, Heidelberg (2005). https://doi.org/10.1007/11555827_10
Banerjee, A., Peikert, C.: New and improved key-homomorphic pseudorandom functions. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 353–370. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_20
Bellare, M.: New proofs for NMAC and HMAC: security without collision-resistance. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 602–619. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_36
Bellare, M., Goldreich, O., Goldwasser, S.: Incremental cryptography: the case of hashing and signing. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 216–233. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_22
Bellare, M., Goldreich, O., Goldwasser, S.: Incremental cryptography and application to virus protection. In: 27th ACM STOC (1995)
Bichsel, P., Camenisch, J., Neven, G., Smart, N.P., Warinschi, B.: Get shorty via group signatures without encryption. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 381–398. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15317-4_24
Blaze, M., Bleumer, G., Strauss, M.: Divertible protocols and atomic proxy cryptography. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 127–144. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054122
Boneh, D., Eskandarian, S., Kim, S., Shih, M.: Improving speed and security in updatable encryption schemes. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 559–589. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_19
Boneh, D., Lewi, K., Montgomery, H., Raghunathan, A.: Key homomorphic PRFs and their applications. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 410–428. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_23
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_30
Bootle, J., Cerulli, A., Chaidos, P., Ghadafi, E., Groth, J.: Foundations of fully dynamic group signatures. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 117–136. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39555-5_7
Boyd, C., Davies, G.T., Gjøsteen, K., Jiang, Y.: Fast and secure updatable encryption. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12170, pp. 464–493. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56784-2_16
Brzuska, C., Fischlin, M., Freudenreich, T., Lehmann, A., Page, M., Schelbert, J., Schröder, D., Volk, F.: Security of sanitizable signatures revisited. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 317–336. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00468-1_18
Brzuska, C., Fischlin, M., Lehmann, A., Schröder, D.: Unlinkability of sanitizable signatures. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 444–461. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_26
Camenisch, J., Dubovitskaya, M., Haralambiev, K., Kohlweiss, M.: Composable and modular anonymous credentials: definitions and practical constructions. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9453, pp. 262–288. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48800-3_11
Chase, M., Meiklejohn, S., Zaverucha, G.: Algebraic MACs and keyed-verification anonymous credentials. In: ACM CCS 2014 (201)
Derler, D., Slamanig, D.: Key-homomorphic signatures: definitions and applications to multiparty signatures and non-interactive zero-knowledge. Cryptology ePrint Archive, Report 2016/792. https://eprint.iacr.org/2016/792
Derler, D., Slamanig, D.: Highly-efficient fully-anonymous dynamic group signatures. In: ASIACCS 18 (2018)
Derler, D., Slamanig, D.: Key-homomorphic signatures: definitions and applications to multiparty signatures and non-interactive zero-knowledge. Des. Codes Cryptogr. 87, 1373–1413 (2019)
Elenkov, N.: Android Security Internals: An In-Depth Guide to Android’s Security Architecture (2015)
Everspaugh, A., Paterson, K., Ristenpart, T., Scott, S.: Key rotation for authenticated encryption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 98–129. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_4
Fan, X., Liu, F.-H.: Proxy re-encryption and re-signatures from lattices. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 363–382. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_18
Fleischhacker, N., Krupp, J., Malavolta, G., Schneider, J., Schröder, D., Simkin, M.: Efficient unlinkable sanitizable signatures from signatures with re-randomizable keys. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 301–330. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_12
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: 40th ACM STOC (2008)
Google developers: sign your app. https://developer.android.com/studio/publish/app-signing
Groth, J., Kohlweiss, M., Maller, M., Meiklejohn, S., Miers, I.: Updatable and universal common reference strings with applications to ZK-SNARKs. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 698–728. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_24
Ishai, Y., Kushilevitz, E.: Randomizing polynomials: a new representation with applications to round-efficient secure computation. In: 41st FOCS (2000)
Jaeger, J., Stepanovs, I.: Optimal channel security against fine-grained state compromise: the safety of messaging. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 33–62. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_2
Jarecki, S., Krawczyk, H., Resch, J.K.: Updatable oblivious key management for storage systems. In: ACM CCS 2019)
Jiang, Y.: The direction of updatable encryption does not matter much. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 529–558. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_18
Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45760-7_17
Jost, D., Maurer, U., Mularczyk, M.: Efficient ratcheting: almost-optimal guarantees for secure messaging. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 159–188. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_6
Kim, S.: Key-homomorphic pseudorandom functions from LWE with small modulus. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 576–607. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_20
Klooß, M., Lehmann, A., Rupp, A.: (R)CCA secure updatable encryption with integrity protection. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 68–99. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_3
Krafft, M.F.: The Debian System: Concepts and Techniques. No Starch Press Series (2005)
Lehmann, A., Tackmann, B.: Updatable encryption with post-compromise security. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 685–716. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_22
Lipmaa, H.: Key-and-argument-updatable QA-NIZKs. In: Galdi, C., Kolesnikov, V. (eds.) SCN 2020. LNCS, vol. 12238, pp. 645–669. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57990-6_32
Löhr, H., Sadeghi, A., Winandy, M.: Patterns for secure boot and secure storage in computer systems. In: ARES (2010)
Microsoft: sign a windows 10 app package. https://docs.microsoft.com/en-us/windows/msix/package/signing-package-overview
Mykletun, E., Narasimha, M., Tsudik, G.: Authentication and integrity in outsourced databases. TOS (2006)
Naor, M., Pinkas, B., Reingold, O.: Distributed pseudo-random functions and KDCs. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 327–346. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_23
Pointcheval, D., Sanders, O.: Short randomizable signatures. In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 111–126. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29485-8_7
Red hat: how to sign rpms with GPG. https://access.redhat.com/articles/3359321
Sanders, O.: Efficient redactable signature and application to anonymous credentials. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 628–656. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45388-6_22
Steinfeld, R., Bull, L., Zheng, Y.: Content extraction signatures. In: Kim, K. (ed.) ICISC 2001. LNCS, vol. 2288, pp. 285–304. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45861-1_22
Wang, H., Liu, H., Xiao, X., Meng, G., Guo, Y.: Characterizing android app signing issues. In: ASE (2019)
Weintraub, G., Gudes, E.: Data integrity verification in column-oriented NoSQL databases. In: Kerschbaum, F., Paraboschi, S. (eds.) DBSec 2018. LNCS, vol. 10980, pp. 165–181. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-95729-6_11
Zhang, Y., Rajimwale, A., Arpaci-Dusseau, A.C., Arpaci-Dusseau, R.H.: End-to-end data integrity for file systems: a ZFS case study. In: FAST (2010)
Acknowledgements
We thank the anonymous reviewers for their comments. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreements n\(\circ \)830929 (CyberSec4Europe) and n\(\circ \)871473 (KRAKEN), European Union’s Horizon 2020 ECSEL Joint Undertaking project under grant agreement n\(\circ \)783119 (SECREDAS), by the Austrian Science Fund (FWF) and netidee SCIENCE grant P31621-N38 (PROFET) and FWF grant W1255-N23.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 International Association for Cryptologic Research
About this paper
Cite this paper
Cini, V., Ramacher, S., Slamanig, D., Striecks, C., Tairi, E. (2021). Updatable Signatures and Message Authentication Codes. In: Garay, J.A. (eds) Public-Key Cryptography – PKC 2021. PKC 2021. Lecture Notes in Computer Science(), vol 12710. Springer, Cham. https://doi.org/10.1007/978-3-030-75245-3_25
Download citation
DOI: https://doi.org/10.1007/978-3-030-75245-3_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-75244-6
Online ISBN: 978-3-030-75245-3
eBook Packages: Computer ScienceComputer Science (R0)