Reproducible Circularly Secure Bit Encryption: Applications and Realizations

We give generic constructions of several fundamental cryptographic primitives based on a new encryption primitive that combines circular security for bit encryption with the so-called reproducibility property (Bellare et al. in Public key cryptography—PKC 2003, vol. 2567, pp. 85–99, Springer, 2003). At the heart of our constructions is a novel technique which gives a way of de-randomizing reproducible public-key bit encryption schemes and also a way of reducing one-wayness conditions of a constructed trapdoor function family (TDF) to circular security of the base scheme. The main primitives that we build from our encryption primitive include k-wise one-way TDFs (Rosen and Segev in SIAM J Comput 39(7):3058–3088, 2010), chosen-ciphertext-attack-secure encryption and deterministic encryption. Our results demonstrate a new set of applications of circularly secure encryption beyond fully homomorphic encryption and symbolic soundness. Finally, we show the plausibility of our assumptions by showing that the decisional Diffie–Hellman-based circularly secure scheme of Boneh et al. (Advances in cryptology—CRYPTO 2008, vol. 5157, Springer, 2008) and the subgroup indistinguishability-based scheme of Brakerski and Goldwasser (Advances in cryptology—CRYPTO 2010, vol. 6223, pp. 1–20, Springer, 2010) are both reproducible.

[1]  Russell Impagliazzo,et al.  Limits on the provable consequences of one-way permutations , 1988, STOC '89.

[2]  Leonid A. Levin,et al.  A hard-core predicate for all one-way functions , 1989, STOC '89.

[3]  Proceedings of the 21st Annual ACM Symposium on Theory of Computing, May 14-17, 1989, Seattle, Washigton, USA , 1989, STOC.

[4]  Noam Nisan,et al.  Randomness is Linear in Space , 1996, J. Comput. Syst. Sci..

[5]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[6]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[7]  Jan Camenisch,et al.  An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation , 2001, IACR Cryptol. ePrint Arch..

[8]  Tal Malkin,et al.  On the impossibility of basing trapdoor functions on trapdoor predicates , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[9]  John Black,et al.  Encryption-Scheme Security in the Presence of Key-Dependent Messages , 2002, Selected Areas in Cryptography.

[10]  Mihir Bellare,et al.  Randomness Re-use in Multi-recipient Encryption Schemeas , 2003, Public Key Cryptography.

[11]  Luca Trevisan,et al.  Notions of Reducibility between Cryptographic Primitives , 2004, TCC.

[12]  Jonathan Katz,et al.  Chosen-Ciphertext Security from Identity-Based Encryption , 2004, SIAM J. Comput..

[13]  Steven Myers,et al.  Towards a Separation of Semantic and CCA Security for Public Key Encryption , 2007, TCC.

[14]  Brent Waters,et al.  Lossy trapdoor functions and their applications , 2008, SIAM J. Comput..

[15]  Mihir Bellare,et al.  Deterministic and Efficiently Searchable Encryption , 2007, CRYPTO.

[16]  Adam O'Neill,et al.  Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles , 2008, CRYPTO.

[17]  Rafail Ostrovsky,et al.  Circular-Secure Encryption from Decision Diffie-Hellman , 2008, CRYPTO.

[18]  David Wagner,et al.  Advances in Cryptology - CRYPTO 2008, 28th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 17-21, 2008. Proceedings , 2008, CRYPTO.

[19]  Rafail Ostrovsky,et al.  Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data , 2004, SIAM J. Comput..

[20]  Jan Camenisch,et al.  A public key encryption scheme secure against key dependent chosen plaintext and adaptive chosen ciphertext attacks , 2009, IACR Cryptol. ePrint Arch..

[21]  Serge Fehr,et al.  On Notions of Security for Deterministic Encryption, and Efficient Constructions without Random Oracles , 2008, CRYPTO.

[22]  Yuval Ishai,et al.  Bounded Key-Dependent Message Security , 2010, IACR Cryptol. ePrint Arch..

[23]  Steven Myers,et al.  Bit Encryption Is Complete , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[24]  Gil Segev,et al.  Chosen-Ciphertext Security via Correlated Products , 2009, SIAM J. Comput..

[25]  Vinod Vaikuntanathan,et al.  Simultaneous Hardcore Bits and Cryptography against Memory Attacks , 2009, TCC.

[26]  David Cash,et al.  Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems , 2009, CRYPTO.

[27]  Yael Tauman Kalai,et al.  Black-Box Circular-Secure Encryption beyond Affine Functions , 2011, TCC.

[28]  Zvika Brakerski,et al.  Circular and Leakage Resilient Public-Key Encryption Under Subgroup Indistinguishability (or: Quadratic Residuosity Strikes Back) , 2010, IACR Cryptol. ePrint Arch..

[29]  Daniele Micciancio.  Theory of Cryptography , 2010, Lecture Notes in Computer Science.

[30]  Yevgeniy Vahlis,et al.  Two Is a Crowd? A Black-Box Separation of One-Wayness and Security under Correlated Inputs , 2010, TCC.

[31]  Yael Tauman Kalai,et al.  Public-Key Encryption Schemes with Auxiliary Inputs , 2010, TCC.

[32]  Rafail Ostrovsky,et al.  Building Injective Trapdoor Functions From Oblivious Transfer , 2010, Electron. Colloquium Comput. Complex..

[33]  Moti Yung,et al.  Efficient Circuit-Size Independent Public Key Encryption with KDM Security , 2011, EUROCRYPT.

[34]  Oded Goldreich,et al.  More Constructions of Lossy and Correlation-Secure Trapdoor Functions , 2010, Journal of Cryptology.

[35]  Zvika Brakerski,et al.  Better Security for Deterministic Public-Key Encryption: The Auxiliary-Input Setting , 2011, Journal of Cryptology.

[36]  Hoeteck Wee,et al.  Lossy trapdoor functions from homomorphic reproducible encryption , 2012, Inf. Process. Lett..

[37]  Hoeteck Wee,et al.  Dual Projective Hashing and Its Applications - Lossy Trapdoor Functions and More , 2012, EUROCRYPT.

[38]  Moni Naor,et al.  Public-Key Cryptosystems Resilient to Key Leakage , 2012, SIAM J. Comput..

[39]  Adam O'Neill,et al.  A Unified Approach to Deterministic Encryption: New Constructions and a Connection to Computational Entropy , 2012, Journal of Cryptology.

[40]  Rafail Ostrovsky,et al.  Building Lossy Trapdoor Functions from Lossy Encryption , 2013, ASIACRYPT.

[41]  Dennis Hofheinz,et al.  Circular Chosen-Ciphertext Security with Compact Ciphertexts , 2013, EUROCRYPT.

[42]  Benny Applebaum,et al.  Key-Dependent Message Security: Generic Amplification and Completeness , 2011, Journal of Cryptology.

[43]  Ron Rothblum,et al.  On the Circular Security of Bit-Encryption , 2013, TCC.

[44]  Kai-Min Chung,et al.  Randomness-Dependent Message Security , 2013, TCC.

[45]  Bruce M. Kapron,et al.  Reproducible Circularly-Secure Bit Encryption: Applications and Realizations , 2015, CRYPTO.

[46]  Editor , 2015, The Journal of Private Equity.