Towards Attribute-Based Encryption for RAMs from LWE: Sub-linear Decryption, and More

Attribute based encryption (ABE) is an advanced encryption system with a built-in mechanism to generate keys associated with functions which in turn provide restricted access to encrypted data. Most of the known candidates of attribute based encryption model the functions as circuits. This results in significant efficiency bottlenecks, especially in the setting where the function associated with the ABE key is represented by a random access machine (RAM) and a database, with the runtime of the RAM program being sublinear in the database size. In this work we study the notion of attribute based encryption for random access machines (RAMs), introduced in the work of Goldwasser, Kalai, Popa, Vaikuntanathan and Zeldovich (Crypto 2013). We present a construction of attribute based encryption for RAMs satisfying sublinear decryption complexity assuming learning with errors; this is the first construction based on standard assumptions. Previously, Goldwasser et al. achieved this result based on non-falsifiable knowledge assumptions. We also consider a dual notion of ABE for RAMs, where the database is in the ciphertext and we show how to achieve this dual notion, albeit with large attribute keys, also based on learning with errors.

[1]  Fuyuki Kitagawa,et al.  Adaptively Secure and Succinct Functional Encryption: Improving Security and Efficiency, Simultaneously , 2019, IACR Cryptol. ePrint Arch..

[2]  Brent Waters,et al.  Functional Encryption: Definitions and Challenges , 2011, TCC.

[3]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2005, STOC '05.

[4]  Craig Gentry,et al.  Fully Secure Attribute Based Encryption from Multilinear Maps , 2014, IACR Cryptol. ePrint Arch..

[5]  Brent Waters,et al.  Efficient Identity-Based Encryption Without Random Oracles , 2005, EUROCRYPT.

[6]  Shweta Agrawal,et al.  Reusable Garbled Deterministic Finite Automata from Learning With Errors , 2017, ICALP.

[7]  Daniel Wichs,et al.  Leveled Fully Homomorphic Signatures from Standard Lattices , 2015, IACR Cryptol. ePrint Arch..

[8]  David Cash,et al.  Targeted Homomorphic Attribute-Based Encryption , 2016, TCC.

[9]  Rafail Ostrovsky,et al.  Garbled RAM Revisited , 2014, EUROCRYPT.

[10]  Brent Waters,et al.  Fuzzy Identity-Based Encryption , 2005, EUROCRYPT.

[11]  Vinod Vaikuntanathan,et al.  Anonymous IBE, Leakage Resilience and Circular Security from New Assumptions , 2018, IACR Cryptol. ePrint Arch..

[12]  Hoeteck Wee,et al.  Dual System Encryption via Predicate Encodings , 2014, TCC.

[13]  Yael Tauman Kalai,et al.  Reusable garbled circuits and succinct functional encryption , 2013, STOC '13.

[14]  Brent Waters,et al.  New Negative Results on Differing-Inputs Obfuscation , 2016, EUROCRYPT.

[15]  Dan Boneh,et al.  Efficient Lattice (H)IBE in the Standard Model , 2010, EUROCRYPT.

[16]  Brent Waters,et al.  Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based , 2013, CRYPTO.

[17]  Vinod Vaikuntanathan,et al.  Attribute-based encryption for circuits , 2013, STOC '13.

[18]  Sanjam Garg,et al.  A Simple Construction of iO for Turing Machines , 2018, IACR Cryptol. ePrint Arch..

[19]  Allison Bishop,et al.  Decentralizing Attribute-Based Encryption , 2011, IACR Cryptol. ePrint Arch..

[20]  Nico Döttling,et al.  Identity-Based Encryption from the Diffie-Hellman Assumption , 2017, CRYPTO.

[21]  Melissa Chase,et al.  A Study of Pair Encodings: Predicate Encryption in Prime Order Groups , 2016, TCC.

[22]  Jonathan Katz,et al.  Predicate Encryption Supporting Disjunctions, Polynomial Equations, and Inner Products , 2008, Journal of Cryptology.

[23]  Chris Peikert,et al.  Faster Bootstrapping with Polynomial Error , 2014, CRYPTO.

[24]  Allison Bishop,et al.  Fully Secure Functional Encryption: Attribute-Based Encryption and (Hierarchical) Inner Product Encryption , 2010, EUROCRYPT.

[25]  Yael Tauman Kalai,et al.  How to Run Turing Machines on Encrypted Data , 2013, CRYPTO.

[26]  Brent Waters,et al.  Attribute-Based Encryption for Circuits from Multilinear Maps , 2012, CRYPTO.

[27]  Adam O'Neill,et al.  Definitional Issues in Functional Encryption , 2010, IACR Cryptol. ePrint Arch..

[28]  A. Sahai,et al.  Indistinguishability Obfuscation from Functional Encryption for Simple Functions Prabhanjan Ananth , 2015 .

[29]  Chris Peikert,et al.  Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller , 2012, IACR Cryptol. ePrint Arch..

[30]  Rafail Ostrovsky,et al.  Attribute-based encryption with non-monotonic access structures , 2007, CCS '07.

[31]  Rafail Ostrovsky,et al.  Black-Box Garbled RAM , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[32]  Vinod Vaikuntanathan,et al.  Private Constrained PRFs (and More) from LWE , 2017, TCC.

[33]  Chris Peikert,et al.  Public-key cryptosystems from the worst-case shortest vector problem: extended abstract , 2009, STOC '09.

[34]  Brent Waters,et al.  Functional Encryption for Regular Languages , 2012, CRYPTO.

[35]  Nuttapong Attrapadung,et al.  Dual System Encryption via Doubly Selective Security: Framework, Fully-secure Functional Encryption for Regular Languages, and More , 2014, IACR Cryptol. ePrint Arch..

[36]  Rafael Pass,et al.  Limits of Extractability Assumptions with Distributional Auxiliary Input , 2015, ASIACRYPT.

[37]  Rafail Ostrovsky,et al.  Garbled RAM From One-Way Functions , 2015, STOC.

[38]  Prabhanjan Vijendra Ananth,et al.  Succinct Garbling Schemes from Functional Encryption through a Local Simulation Paradigm , 2018, IACR Cryptol. ePrint Arch..

[39]  Daniele Micciancio,et al.  Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions , 2011, CRYPTO.

[40]  Brent Waters,et al.  Constrained Pseudorandom Functions for Unconstrained Inputs , 2016, EUROCRYPT.

[41]  Amit Sahai,et al.  Functional Encryption for Turing Machines , 2016, TCC.

[42]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[43]  Nir Bitansky,et al.  Time-Lock Puzzles from Randomized Encodings , 2016, IACR Cryptol. ePrint Arch..

[44]  Craig Gentry,et al.  Trapdoors for hard lattices and new cryptographic constructions , 2008, IACR Cryptol. ePrint Arch..

[45]  Vinod Vaikuntanathan,et al.  Circuit-ABE from LWE: Unbounded Attributes and Semi-adaptive Security , 2016, CRYPTO.

[46]  Vinod Vaikuntanathan,et al.  Constrained Key-Homomorphic PRFs from Standard Lattice Assumptions - Or: How to Secretly Embed a Circuit in Your PRF , 2015, TCC.

[47]  Brent Waters,et al.  Dual System Encryption: Realizing Fully Secure IBE and HIBE under Simple Assumptions , 2009, IACR Cryptol. ePrint Arch..

[48]  Brent Waters,et al.  Attribute-based encryption for fine-grained access control of encrypted data , 2006, CCS '06.

[49]  David Cash,et al.  Bonsai Trees, or How to Delegate a Lattice Basis , 2010, Journal of Cryptology.

[50]  Vinod Vaikuntanathan,et al.  How to Delegate and Verify in Public: Verifiable Computation from Attribute-based Encryption , 2012, IACR Cryptol. ePrint Arch..

[51]  Craig Gentry,et al.  On the Implausibility of Differing-Inputs Obfuscation and Extractable Witness Encryption with Auxiliary Input , 2014, CRYPTO.

[52]  Amit Sahai,et al.  Bounded Ciphertext Policy Attribute Based Encryption , 2008, ICALP.

[53]  Shweta Agrawal,et al.  FE and iO for Turing Machines from Minimal Assumptions , 2018, IACR Cryptol. ePrint Arch..

[54]  Craig Gentry,et al.  Fully Key-Homomorphic Encryption, Arithmetic Circuit ABE and Compact Garbled Circuits , 2014, EUROCRYPT.

[55]  Vinod Vaikuntanathan,et al.  Predicate Encryption for Circuits from LWE , 2015, CRYPTO.

[56]  Damien Stehlé,et al.  Classical hardness of learning with errors , 2013, STOC '13.