Compressible FHE with Applications to PIR

Homomorphic encryption (HE) is often viewed as impractical, both in communication and computation. Here we provide an additively homomorphic encryption scheme based on (ring) LWE with nearly optimal rate (\(1-\epsilon \) for any \(\epsilon >0\)). Moreover, we describe how to compress many Gentry-Sahai-Waters (GSW) ciphertexts (e.g., ciphertexts that may have come from a homomorphic evaluation) into (fewer) high-rate ciphertexts.

[1]  Amit Sahai,et al.  Homomorphic Encryption Standard , 2019, IACR Cryptol. ePrint Arch..

[2]  Craig Gentry,et al.  Homomorphic Evaluation of the AES Circuit , 2012, IACR Cryptol. ePrint Arch..

[3]  Matthew Green,et al.  Outsourcing the Decryption of ABE Ciphertexts , 2011, USENIX Security Symposium.

[4]  Markku-Juhani O. Saarinen.  Ring-LWE Ciphertext Compression and Error Correction: Tools for Lightweight Post-Quantum Cryptography , 2017, IACR Cryptol. ePrint Arch..

[5]  Craig Gentry,et al.  (Leveled) fully homomorphic encryption without bootstrapping , 2012, ITCS '12.

[6]  Ian Goldberg,et al.  Revisiting the Computational Practicality of Private Information Retrieval , 2011, Financial Cryptography.

[7]  Eyal Kushilevitz,et al.  Private information retrieval , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[8]  Masahiro Yagisawa,et al.  Fully Homomorphic Encryption without bootstrapping , 2015, IACR Cryptol. ePrint Arch..

[9]  Sanjeev Arora,et al.  New Algorithms for Learning in Presence of Errors , 2011, ICALP.

[10]  Hugo Krawczyk,et al.  On Compression of Data Encrypted With Block Ciphers , 2012, IEEE Transactions on Information Theory.

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

[12]  Srinath T. V. Setty,et al.  PIR with Compressed Queries and Amortized Query Processing , 2018, 2018 IEEE Symposium on Security and Privacy (SP).

[13]  Yuval Ishai,et al.  Limits of Practical Sublinear Secure Computation , 2018, IACR Cryptol. ePrint Arch..

[14]  Julien P. Stern.  A New Efficient All-Or-Nothing Disclosure of Secrets Protocol , 1998, ASIACRYPT.

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

[16]  Vinod Vaikuntanathan,et al.  Efficient Fully Homomorphic Encryption from (Standard) LWE , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[17]  Craig Gentry,et al.  Homomorphic Encryption for Finite Automata , 2019, IACR Cryptol. ePrint Arch..

[18]  Steven D. Galbraith,et al.  Computing pairings using x-coordinates only , 2009, Des. Codes Cryptogr..

[19]  Frederik Vercauteren,et al.  Fully homomorphic SIMD operations , 2012, Designs, Codes and Cryptography.

[20]  Craig Gentry,et al.  Fully Homomorphic Encryption with Polylog Overhead , 2012, EUROCRYPT.

[21]  Vinod Vaikuntanathan,et al.  Can homomorphic encryption be practical? , 2011, CCSW '11.

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

[23]  Helger Lipmaa,et al.  A Simpler Rate-Optimal CPIR Protocol , 2017, Financial Cryptography.

[24]  Rafail Ostrovsky,et al.  Trapdoor Hash Functions and Their Applications , 2019, IACR Cryptol. ePrint Arch..

[25]  Brent Waters,et al.  A Framework for Efficient and Composable Oblivious Transfer , 2008, CRYPTO.

[26]  Anat Paskin-Cherniavsky,et al.  Evaluating Branching Programs on Encrypted Data , 2007, TCC.

[27]  Marc-Olivier Killijian,et al.  XPIR : Private Information Retrieval for Everyone , 2016, Proc. Priv. Enhancing Technol..

[28]  Tatsuaki Okamoto,et al.  Packing Messages and Optimizing Bootstrapping in GSW-FHE , 2015, Public Key Cryptography.

[29]  Aggelos Kiayias,et al.  Optimal Rate Private Information Retrieval from Homomorphic Encryption , 2015, Proc. Priv. Enhancing Technol..

[30]  Yuval Ishai,et al.  Two-Message Witness Indistinguishability and Secure Computation in the Plain Model from New Assumptions , 2017, ASIACRYPT.

[31]  Radu Sion,et al.  On the Practicality of Private Information Retrieval , 2007, NDSS.

[32]  Julien P. Stern.  A new and efficient all-or-nothing disclosure of secrets protocol , 1998 .

[33]  Craig Gentry,et al.  How to Compress Rabin Ciphertexts and Signatures (and More) , 2004, CRYPTO.

[34]  Craig Gentry,et al.  Fully Homomorphic Encryption over the Integers , 2010, EUROCRYPT.

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

[36]  Julian D. Laderman,et al.  A noncommutative algorithm for multiplying $3 \times 3$ matrices using 23 multiplications , 1976 .

[37]  Shai Halevi,et al.  Algorithms in HElib , 2014, CRYPTO.

[38]  Zvika Brakerski,et al.  Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles , 2019, IACR Cryptol. ePrint Arch..

[39]  Vinod Vaikuntanathan,et al.  Efficient Fully Homomorphic Encryption from (Standard) LWE , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[40]  Shai Halevi,et al.  Homomorphic Encryption , 2017, Tutorials on the Foundations of Cryptography.

[41]  Craig Gentry,et al.  Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

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

[43]  Rafail Ostrovsky,et al.  Replication is not needed: single database, computationally-private information retrieval , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[44]  Ivan Damgård,et al.  A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System , 2001, Public Key Cryptography.

[45]  Vinod Vaikuntanathan,et al.  Lattice-based FHE as secure as PKE , 2014, IACR Cryptol. ePrint Arch..

[46]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[47]  Craig Gentry,et al.  Packed Ciphertexts in LWE-Based Homomorphic Encryption , 2013, Public Key Cryptography.

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

[49]  Chris Peikert,et al.  On Ideal Lattices and Learning with Errors over Rings , 2010, JACM.