Abstract
In tandem with recent progress on computing on encrypted data via fully homomorphic encryption, we present a framework for computing on authenticated data via the notion of slightly homomorphic signatures, or P-homomorphic signatures. With such signatures, it is possible for a third party to derive a signature on the object m′ from a signature of m as long as P(m,m′) = 1 for some predicate P which captures the “authenticatable relationship” between m′ and m. Moreover, a derived signature on m′ reveals no extra information about the parent m.
Our definition is carefully formulated to provide one unified framework for a variety of distinct concepts in this area, including arithmetic, homomorphic, quotable, redactable, transitive signatures and more. It includes being unable to distinguish a derived signature from a fresh one even when given the original signature. The inability to link derived signatures to their original sources prevents some practical privacy and linking attacks, which is a challenge not satisfied by most prior works.
Under this strong definition, we then provide generic constructions for all univariate and closed predicates, and specific efficient constructions for a broad class of natural predicates such as quoting, subsets, weighted sums, averages, and Fourier transforms. To our knowledge, these are the first efficient constructions for these predicates (excluding subsets) that provably satisfy this strong security notion.
Chapter PDF
Similar content being viewed by others
References
Ahn, J.H., Boneh, D., Camenisch, J., Hohenberger, S., Shelat, A., Waters, B.: Computing on authenticated data. Cryptology ePrint Archive, Report 2011/096 (2011), http://eprint.iacr.org/
Ateniese, G., Chou, D.H., de Medeiros, B., Tsudik, G.: Sanitizable Signatures. In: di Vimercati, S.d.C., Syverson, P.F., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 159–177. Springer, Heidelberg (2005)
Attrapadung, N., Libert, B.: Homomorphic Network Coding Signatures in the Standard Model. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 17–34. Springer, Heidelberg (2011)
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)
Bellare, M., Micciancio, D., Warinschi, B.: Foundations of Group Signatures: Formal Definitions, Simplified Requirements, and a Construction Based on General Assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 614–629. Springer, Heidelberg (2003)
Bellare, M., Neven, G.: Transitive Signatures Based on Factoring and RSA. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 397–414. Springer, Heidelberg (2002)
Bellare, M., Neven, G.: Transitive signatures: New schemes and proofs. IEEE Transactions on Information Theory 51, 2133–2151 (2005)
Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: IEEE Symposium on Security and Privacy, pp. 321–334 (2007)
Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Boneh, D., Franklin, M.K.: Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3) (2003)
Boneh, D., Freeman, D.M.: Homomorphic Signatures for Polynomial Functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149–168. Springer, Heidelberg (2011); Cryptology ePrint Archive, Report 2011/018
Boneh, D., Freeman, D.M.: Linearly Homomorphic Signatures over Binary Fields and New Tools for Lattice-Based Signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011); Cryptology ePrint Archive, Report 2010/453
Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a Linear Subspace: Signature Schemes for Network Coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 68–87. Springer, Heidelberg (2009)
Boneh, D., Hamburg, M.: Generalized Identity Based and Broadcast Encryption Schemes. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 455–470. Springer, Heidelberg (2008)
Brzuska, C., Busch, H., Dagdelen, O., Fischlin, M., Franz, M., Katzenbeisser, S., Manulis, M., Onete, C., Peter, A., Poettering, B., Schröder, D.: Redactable Signatures for Tree-Structured Data: Definitions and Constructions. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 87–104. Springer, Heidelberg (2010)
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)
Brzuska, C., Fischlin, M., Lehmann, A., Schröder, D.: Santizable signatures: How to partially delegate control for authenticated data. In: BIOSIG 2009, pp. 117–128 (2009)
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)
Camenisch, J., Lysyanskaya, A.: Signature Schemes and Anonymous Credentials from Bilinear Maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004)
Canetti, R., Halevi, S., Katz, J.: A Forward-Secure Public-Key Encryption Scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003)
Chang, E.-C., Lim, C.L., Xu, J.: Short Redactable Signatures Using Random Trees. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 133–147. Springer, Heidelberg (2009)
Charles, D., Jain, K., Lauter, K.: Signatures for network coding. International Journal of Information and Coding Theory 1(1), 3–14 (2009)
Chaum, D., van Heyst, E.: Group Signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991)
Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory 22, 644–654 (1976)
Fragouli, C., Soljanin, E.: Network Coding Fundamentals. Now Publishers Inc., Hanover (2007)
Gennaro, R., Katz, J., Krawczyk, H., Rabin, T.: Secure Network Coding over the Integers. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 142–160. Springer, Heidelberg (2010)
Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009)
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions (extended abstract). In: FOCS, pp. 464–479 (1984)
Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal of Computing 17(2), 281–308 (1988)
Haber, S., Hatano, Y., Honda, Y., Horne, W., Miyazaki, K., Sander, T., Tezoku, S., Yao, D.: Efficient signature schemes supporting redaction, pseudonymization, and data deidentification. In: ASIACCS 2008, pp. 353–362 (2008)
Hevia, A., Micciancio, D.: The Provable Security of Graph-Based One-Time Signatures and Extensions to Algebraic Signature Schemes. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 379–396. Springer, Heidelberg (2002)
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)
Krohn, M., Freedman, M., Mazieres, D.: On-the-fly verification of rateless erasure codes for efficient content distribution. In: Proc. of IEEE Symposium on Security and Privacy, pp. 226–240 (2004)
Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully Secure Functional Encryption: Attribute-Based Encryption and (Hierarchical) Inner Product Encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010)
Micali, S., Rivest, R.L.: Transitive Signature Schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 236–243. Springer, Heidelberg (2002)
Miyazaki, K., Hanaoka, G., Imai, H.: Digitally signed document sanitizing scheme based on bilinear maps. In: ASIACCS 2006: Proceedings of the 2006 ACM Symposium on Information, Computer and Communications Security, pp. 343–354 (2006)
Miyazaki, K., Iwamura, M., Matsumoto, T., Sasaki, R., Yoshiura, H., Tezuka, S., Imai, H.: Digitally signed document sanitizing scheme with disclosure condition control. IEICE Transactions on Fundamentals E88-A(1), 239–246 (2005)
Miyazaki, K., Susaki, S., Iwamura, M., Matsumoto, T., Sasaki, R., Yoshiura, H.: Digital document sanitizing problem. IEICE Technical Report, 103(195(ISEC 2003 12-29)), 61–67 (2003)
Naccache, D.: Is theoretical cryptography any good in practice? CHES 2010 invited talk (2010), http://www.iacr.org/workshops/ches/ches2010
Neven, G.: A simple transitive signature scheme for directed trees. Theoretical Computer Science 396(1-3), 277–282 (2008)
Rivest, R.: Two signature schemes. Slides from talk given at Cambridge University (2000), http://people.csail.mit.edu/rivest/Rivest-CambridgeTalk.pdf
Rivest, R.L., Shamir, A., Tauman, Y.: How to Leak a Secret: Theory and Applications of Ring Signatures. In: Goldreich, O., Rosenberg, A.L., Selman, A.L. (eds.) Theoretical Computer Science. LNCS, vol. 3895, pp. 164–186. Springer, Heidelberg (2006)
Shahandashti, S.F., Salmasizadeh, M., Mohajeri, J.: A Provably Secure Short Transitive Signature Scheme from Bilinear Group Pairs. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 60–76. Springer, Heidelberg (2005)
Smart, N.P., Vercauteren, F.: Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420–443. Springer, Heidelberg (2010)
Steinfeld, R., Bull, L., Zheng, Y.: Content Extraction Signatures. In: Kim, K.-c. (ed.) ICISC 2001. LNCS, vol. 2288, pp. 285–304. Springer, Heidelberg (2002)
van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully Homomorphic Encryption over the Integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)
Waters, B.: Ciphertext-Policy Attribute-Based Encryption: An Expressive, Efficient, and Provably Secure Realization. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 53–70. Springer, Heidelberg (2011)
Wei, L., Coull, S.E., Reiter, M.K.: Bounded vector signatures and their applications. In: ASIACCS 2011, pp. 277–285 (2011)
Yi, X.: Directed Transitive Signature Scheme. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 129–144. Springer, Heidelberg (2006)
Zhao, F., Kalker, T., Médard, M., Han, K.: Signatures for content distribution with network coding. In: Proc. Intl. Symp. Info. Theory (ISIT) (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ahn, J.H., Boneh, D., Camenisch, J., Hohenberger, S., shelat, a., Waters, B. (2012). Computing on Authenticated Data. In: Cramer, R. (eds) Theory of Cryptography. TCC 2012. Lecture Notes in Computer Science, vol 7194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28914-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-28914-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28913-2
Online ISBN: 978-3-642-28914-9
eBook Packages: Computer ScienceComputer Science (R0)Springer Nature Proceedings Computer Science
Keywords
- Signature Scheme
- Network Code
- Random Oracle
- Homomorphic Encryption
- Defense Advance Research Project Agency
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.