Incremental Deterministic Public-Key Encryption

Motivated by applications in large storage systems, we initiate the study of incremental deterministic public-key encryption. Deterministic public-key encryption, introduced by Bellare, Boldyreva, and O’Neill (CRYPTO ’07), provides an alternative to randomized public-key encryption in various scenar...

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Published in:	Journal of cryptology Vol. 31; no. 1; pp. 134 - 161
Main Authors:	Mironov, Ilya, Pandey, Omkant, Reingold, Omer, Segev, Gil
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.01.2018 Springer Nature B.V
Subjects:	Algorithms Coding and Information Theory Combinatorics Communications Engineering Complexity Computational Mathematics and Numerical Analysis Computer Science Cryptography Data encryption Encryption Entropy Extractors Networks Probability Theory and Stochastic Processes Public Key Infrastructure Randomization Security Storage systems Public-key encryption Deterministic encryption Incremental cryptography
ISSN:	0933-2790, 1432-1378
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Abstract	Motivated by applications in large storage systems, we initiate the study of incremental deterministic public-key encryption. Deterministic public-key encryption, introduced by Bellare, Boldyreva, and O’Neill (CRYPTO ’07), provides an alternative to randomized public-key encryption in various scenarios where the latter exhibits inherent drawbacks. A deterministic encryption algorithm, however, cannot satisfy any meaningful notion of security for low-entropy plaintexts distributions, but Bellare et al. demonstrated that a strong notion of security can in fact be realized for relatively high-entropy plaintext distributions. In order to achieve a meaningful level of security, a deterministic encryption algorithm should be typically used for encrypting rather long plaintexts for ensuring a sufficient amount of entropy. This requirement may be at odds with efficiency constraints, such as communication complexity and computation complexity in the presence of small updates. Thus, a highly desirable property of deterministic encryption algorithms is incrementality: Small changes in the plaintext translate into small changes in the corresponding ciphertext. We present a framework for modeling the incrementality of deterministic public-key encryption. Our framework extends the study of the incrementality of cryptography primitives initiated by Bellare, Goldreich and Goldwasser (CRYPTO ’94). Within our framework, we propose two schemes, which we prove to enjoy an optimal tradeoff between their security and incrementality up to lower-order factors. Our first scheme is a generic method which can be based on any deterministic public-key encryption scheme, and, in particular, can be instantiated with any semantically secure (randomized) public-key encryption scheme in the random-oracle model. Our second scheme is based on the Decisional Diffie–Hellman assumption in the standard model. The approach underpinning our schemes is inspired by the fundamental “sample-then-extract” technique due to Nisan and Zuckerman (JCSS ’96) and refined by Vadhan (J. Cryptology ’04), and by the closely related notion of “locally computable extractors” due to Vadhan. Most notably, whereas Vadhan used such extractors to construct private-key encryption schemes in the bounded-storage model, we show that techniques along these lines can also be used to construct incremental public-key encryption schemes.
AbstractList	Motivated by applications in large storage systems, we initiate the study of incremental deterministic public-key encryption. Deterministic public-key encryption, introduced by Bellare, Boldyreva, and O’Neill (CRYPTO ’07), provides an alternative to randomized public-key encryption in various scenarios where the latter exhibits inherent drawbacks. A deterministic encryption algorithm, however, cannot satisfy any meaningful notion of security for low-entropy plaintexts distributions, but Bellare et al. demonstrated that a strong notion of security can in fact be realized for relatively high-entropy plaintext distributions. In order to achieve a meaningful level of security, a deterministic encryption algorithm should be typically used for encrypting rather long plaintexts for ensuring a sufficient amount of entropy. This requirement may be at odds with efficiency constraints, such as communication complexity and computation complexity in the presence of small updates. Thus, a highly desirable property of deterministic encryption algorithms is incrementality: Small changes in the plaintext translate into small changes in the corresponding ciphertext. We present a framework for modeling the incrementality of deterministic public-key encryption. Our framework extends the study of the incrementality of cryptography primitives initiated by Bellare, Goldreich and Goldwasser (CRYPTO ’94). Within our framework, we propose two schemes, which we prove to enjoy an optimal tradeoff between their security and incrementality up to lower-order factors. Our first scheme is a generic method which can be based on any deterministic public-key encryption scheme, and, in particular, can be instantiated with any semantically secure (randomized) public-key encryption scheme in the random-oracle model. Our second scheme is based on the Decisional Diffie–Hellman assumption in the standard model. The approach underpinning our schemes is inspired by the fundamental “sample-then-extract” technique due to Nisan and Zuckerman (JCSS ’96) and refined by Vadhan (J. Cryptology ’04), and by the closely related notion of “locally computable extractors” due to Vadhan. Most notably, whereas Vadhan used such extractors to construct private-key encryption schemes in the bounded-storage model, we show that techniques along these lines can also be used to construct incremental public-key encryption schemes. Motivated by applications in large storage systems, we initiate the study of incremental deterministic public-key encryption. Deterministic public-key encryption, introduced by Bellare, Boldyreva, and O’Neill (CRYPTO ’07), provides an alternative to randomized public-key encryption in various scenarios where the latter exhibits inherent drawbacks. A deterministic encryption algorithm, however, cannot satisfy any meaningful notion of security for low-entropy plaintexts distributions, but Bellare et al. demonstrated that a strong notion of security can in fact be realized for relatively high-entropy plaintext distributions. In order to achieve a meaningful level of security, a deterministic encryption algorithm should be typically used for encrypting rather long plaintexts for ensuring a sufficient amount of entropy. This requirement may be at odds with efficiency constraints, such as communication complexity and computation complexity in the presence of small updates. Thus, a highly desirable property of deterministic encryption algorithms is incrementality: Small changes in the plaintext translate into small changes in the corresponding ciphertext. We present a framework for modeling the incrementality of deterministic public-key encryption. Our framework extends the study of the incrementality of cryptography primitives initiated by Bellare, Goldreich and Goldwasser (CRYPTO ’94). Within our framework, we propose two schemes, which we prove to enjoy an optimal tradeoff between their security and incrementality up to lower-order factors. Our first scheme is a generic method which can be based on any deterministic public-key encryption scheme, and, in particular, can be instantiated with any semantically secure (randomized) public-key encryption scheme in the random-oracle model. Our second scheme is based on the Decisional Diffie–Hellman assumption in the standard model. The approach underpinning our schemes is inspired by the fundamental “sample-then-extract” technique due to Nisan and Zuckerman (JCSS ’96) and refined by Vadhan (J. Cryptology ’04), and by the closely related notion of “locally computable extractors” due to Vadhan. Most notably, whereas Vadhan used such extractors to construct private-key encryption schemes in the bounded-storage model, we show that techniques along these lines can also be used to construct incremental public-key encryption schemes.
Author	Mironov, Ilya Pandey, Omkant Reingold, Omer Segev, Gil
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References	GoldwasserSMicaliSProbabilistic encryptionJournal of Computer and System Sciences198428227029976054810.1016/0022-0000(84)90070-90563.94013 D. Micciancio. Oblivious data structures: applications to cryptography. In Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, pp. 456–464, 1997. RussellAWangHHow to fool an unbounded adversary with a short keyIEEE Transactions on Information Theory200652311301140223807510.1109/TIT.2005.8644381317.94133 PeikertCWatersBLossy trapdoor functions and their applicationsSIAM Journal on Computing201140618031844286319510.1137/0807339541236.94063 VadhanSPConstructing locally computable extractors and cryptosystems in the bounded-storage modelJounal of Cryptology20041714377204284510.1007/s00145-003-0237-x1071.94016 M. Fischlin. Lower bounds for the signature size of incremental schemes. In Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, pp. 438–447, 1997. NisanNZuckermanDRandomness is linear in spaceJournal of Computer and System Sciences19965214352137580310.1006/jcss.1996.00040846.68041 A. Boldyreva, S. Fehr, and A. O’Neill. On notions of security for deterministic encryption, and efficient constructions without random oracles. In Advances in Cryptology—CRYPTO ’08, pp. 335–359, 2008. M. Bellare and D. Micciancio. A new paradigm for collision-free hashing: Incrementality at reduced cost. In Advances in Cryptology—EUROCRYPT ’97, pp. 163–192, 1997. DodisYOstrovskyRReyzinLSmithAFuzzy extractors: how to generate strong keys from biometrics and other noisy dataSIAM Journal on Computing200838197139239952110.1137/0606513801165.94326 ApplebaumBIshaiYKushilevitzECryptography in NC0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{NC}^{{0}}$$\end{document}SIAM Journal on Computing2006364845888227226710.1137/S00975397054469501126.94014 Y. Dodis and A. Smith. Entropic security and the encryption of high entropy messages. In Proceedings of the 2nd Theory of Cryptography Conference, pp. 556–577, 2005. J. R. Douceur, A. Adya, W. J. Bolosky, D. Simon, and M. Theimer. Reclaiming space from duplicate files in a serverless distributed file system. In Proceedings of the 22nd International Conference on Distributed Computing Systems, pp. 617–624, 2002. B. Fuller, A. O’Neill, and L. Reyzin. A unified approach to deterministic encryption: new constructions and a connection to computational entropy. In Proceedings of the 9th Theory of Cryptography Conference, pp. 582–599, 2012. HåstadJImpagliazzoRLevinLALubyMA pseudorandom generator from any one-way functionSIAM Journal on Computing199928413641396168108510.1137/S00975397932447080940.68048 H. Wee. Dual projective hashing and its applications—lossy trapdoor functions and more. In Advances in Cryptology—EUROCRYPT ’12, pp. 246–262, 2012. M. Bellare, M. Fischlin, A. O’Neill, and T. Ristenpart. Deterministic encryption: definitional equivalences and constructions without random oracles. In Advances in Cryptology—CRYPTO ’08, pp. 360–378, 2008. D. Boneh, S. Halevi, M. Hamburg, and R. Ostrovsky. Circular-secure encryption from Decision Diffie–Hellman. In Advances in Cryptology—CRYPTO ’08, pp. 108–125, 2008. A. Raghunathan, G. Segev, and S. Vadhan. Deterministic public-key encryption for adaptively chosen plaintext distributions. In Advances in Crytology—EUROCRYPT ’13, pp. 93–110, 2013. M. Bellare, S. Keelveedhi, and T. Ristenpart. Message-locked encryption and secure deduplication. In Advances in Cryptology—EUROCRYPT ’13, pp. 296–312, 2013. FreemanDMGoldreichOKiltzERosenASegevGMore constructions of lossy and correlation-secure trapdoor functionsJournal of Cryptology20132613974301682210.1007/s00145-011-9112-31291.94083 NaorMSegevGPublic-key cryptosystems resilient to key leakageSIAM Journal on Computing2012414772814297475310.1137/1008134641273.94355 M. Bellare, O. Goldreich, and S. Goldwasser. Incremental cryptography: the case of hashing and signing. In Advances in Cryptology—CRYPTO ’94, pp. 216–233, 1994. Z. Brakerski and G. Segev. Better security for deterministic public-key encryption: The auxiliary-input setting. In Advances in Cryptology—CRYPTO ’11, pp. 543–560, 2011. M. Abadi, D. Boneh, I. Mironov, A. Raghunathan, and G. Segev. Message-locked encryption for lock-dependent messages. In Advances in Cryptology—RYPTO ’13, pp. 374–391, 2013. M. Bellare, Z. Brakerski, M. Naor, T. Ristenpart, G. Segev, H. Shacham, and S. Yilek. Hedged public-key encryption: how to protect against bad randomness. In Advances in Cryptology—ASIACRYPT ’09, pp. 232–249, 2009. M. Bellare, O. Goldreich, and S. Goldwasser. Incremental cryptography and application to virus protection. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pp. 45–56, 1995. M. Fischlin. Incremental cryptography and memory checkers. In Advances in Cryptology—EUROCRYPT ’97, pp. 293–408, 1997. M. Bellare, A. Boldyreva, and A. O’Neill. Deterministic and efficiently searchable encryption. In Advances in Cryptology—CRYPTO ’07, pp. 535–552, 2007. E. Buonanno, J. Katz, and M. Yung. Incremental unforgeable encryption. In Proceedings of the 8th International Workshop on Fast Software Encryption, pp. 109–124, 2001. 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References_xml	– reference: ApplebaumBIshaiYKushilevitzECryptography in NC0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{NC}^{{0}}$$\end{document}SIAM Journal on Computing2006364845888227226710.1137/S00975397054469501126.94014 – reference: H. Wee. Dual projective hashing and its applications—lossy trapdoor functions and more. In Advances in Cryptology—EUROCRYPT ’12, pp. 246–262, 2012. – reference: M. Fischlin. Lower bounds for the signature size of incremental schemes. In Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, pp. 438–447, 1997. – reference: A. Raghunathan, G. Segev, and S. Vadhan. Deterministic public-key encryption for adaptively chosen plaintext distributions. In Advances in Crytology—EUROCRYPT ’13, pp. 93–110, 2013. – reference: J. R. Douceur, A. Adya, W. J. Bolosky, D. Simon, and M. Theimer. Reclaiming space from duplicate files in a serverless distributed file system. In Proceedings of the 22nd International Conference on Distributed Computing Systems, pp. 617–624, 2002. – reference: B. Fuller, A. O’Neill, and L. Reyzin. A unified approach to deterministic encryption: new constructions and a connection to computational entropy. In Proceedings of the 9th Theory of Cryptography Conference, pp. 582–599, 2012. – reference: M. Bellare, O. Goldreich, and S. Goldwasser. Incremental cryptography and application to virus protection. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pp. 45–56, 1995. – reference: FreemanDMGoldreichOKiltzERosenASegevGMore constructions of lossy and correlation-secure trapdoor functionsJournal of Cryptology20132613974301682210.1007/s00145-011-9112-31291.94083 – reference: D. Boneh, S. Halevi, M. Hamburg, and R. Ostrovsky. Circular-secure encryption from Decision Diffie–Hellman. In Advances in Cryptology—CRYPTO ’08, pp. 108–125, 2008. – reference: M. Bellare, S. Keelveedhi, and T. Ristenpart. Message-locked encryption and secure deduplication. In Advances in Cryptology—EUROCRYPT ’13, pp. 296–312, 2013. – reference: DodisYOstrovskyRReyzinLSmithAFuzzy extractors: how to generate strong keys from biometrics and other noisy dataSIAM Journal on Computing200838197139239952110.1137/0606513801165.94326 – reference: PeikertCWatersBLossy trapdoor functions and their applicationsSIAM Journal on Computing201140618031844286319510.1137/0807339541236.94063 – reference: M. Bellare, M. Fischlin, A. O’Neill, and T. Ristenpart. Deterministic encryption: definitional equivalences and constructions without random oracles. In Advances in Cryptology—CRYPTO ’08, pp. 360–378, 2008. – reference: M. Bellare, A. Boldyreva, and A. O’Neill. Deterministic and efficiently searchable encryption. In Advances in Cryptology—CRYPTO ’07, pp. 535–552, 2007. – reference: E. Buonanno, J. Katz, and M. Yung. Incremental unforgeable encryption. In Proceedings of the 8th International Workshop on Fast Software Encryption, pp. 109–124, 2001. – reference: M. Bellare, O. Goldreich, and S. Goldwasser. Incremental cryptography: the case of hashing and signing. In Advances in Cryptology—CRYPTO ’94, pp. 216–233, 1994. – reference: M. Bellare and D. Micciancio. A new paradigm for collision-free hashing: Incrementality at reduced cost. In Advances in Cryptology—EUROCRYPT ’97, pp. 163–192, 1997. – reference: Y. Dodis and A. Smith. Entropic security and the encryption of high entropy messages. In Proceedings of the 2nd Theory of Cryptography Conference, pp. 556–577, 2005. – reference: GoldwasserSMicaliSProbabilistic encryptionJournal of Computer and System Sciences198428227029976054810.1016/0022-0000(84)90070-90563.94013 – reference: VadhanSPConstructing locally computable extractors and cryptosystems in the bounded-storage modelJounal of Cryptology20041714377204284510.1007/s00145-003-0237-x1071.94016 – reference: A. Boldyreva, S. Fehr, and A. O’Neill. On notions of security for deterministic encryption, and efficient constructions without random oracles. In Advances in Cryptology—CRYPTO ’08, pp. 335–359, 2008. – reference: Z. Brakerski and G. Segev. Better security for deterministic public-key encryption: The auxiliary-input setting. In Advances in Cryptology—CRYPTO ’11, pp. 543–560, 2011. – reference: RussellAWangHHow to fool an unbounded adversary with a short keyIEEE Transactions on Information Theory200652311301140223807510.1109/TIT.2005.8644381317.94133 – reference: M. Bellare, Z. Brakerski, M. Naor, T. Ristenpart, G. Segev, H. Shacham, and S. Yilek. Hedged public-key encryption: how to protect against bad randomness. In Advances in Cryptology—ASIACRYPT ’09, pp. 232–249, 2009. – reference: M. Fischlin. Incremental cryptography and memory checkers. In Advances in Cryptology—EUROCRYPT ’97, pp. 293–408, 1997. – reference: M. Abadi, D. Boneh, I. Mironov, A. Raghunathan, and G. Segev. Message-locked encryption for lock-dependent messages. In Advances in Cryptology—RYPTO ’13, pp. 374–391, 2013. – reference: D. Micciancio. Oblivious data structures: applications to cryptography. 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Snippet	Motivated by applications in large storage systems, we initiate the study of incremental deterministic public-key encryption. Deterministic public-key...
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SubjectTerms	Algorithms Coding and Information Theory Combinatorics Communications Engineering Complexity Computational Mathematics and Numerical Analysis Computer Science Cryptography Data encryption Encryption Entropy Extractors Networks Probability Theory and Stochastic Processes Public Key Infrastructure Randomization Security Storage systems
Title	Incremental Deterministic Public-Key Encryption
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