Feasibility and Infeasibility of Adaptively Secure Fully Homomorphic Encryption

Fully homomorphic encryption (FHE) is a form of public-key encryption that enables arbitrary computation over encrypted data. The past few years have seen several realizations of FHE under different assumptions, and FHE has been used as a building block in many cryptographic applications.

[1]  Ron Steinfeld,et al.  Faster Fully Homomorphic Encryption , 2010, ASIACRYPT.

[2]  Tal Malkin,et al.  Improved Non-committing Encryption with Applications to Adaptively Secure Protocols , 2009, ASIACRYPT.

[3]  A. Yao.  How to generate and exchange secrets , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[4]  Donald Beaver,et al.  Plug and Play Encryption , 1997, CRYPTO.

[5]  Craig Gentry,et al.  Non-interactive Verifiable Computing: Outsourcing Computation to Untrusted Workers , 2010, CRYPTO.

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

[7]  Stanislaw Jarecki,et al.  Adaptively Secure Threshold Cryptography: Introducing Concurrency, Removing Erasures , 2000, EUROCRYPT.

[8]  Rafail Ostrovsky,et al.  Round-Optimal Secure Two-Party Computation , 2004, CRYPTO.

[9]  Craig Gentry,et al.  Implementing Gentry's Fully-Homomorphic Encryption Scheme , 2011, EUROCRYPT.

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

[11]  Mihir Bellare,et al.  Garbling Schemes , 2012, IACR Cryptol. ePrint Arch..

[12]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[13]  Yehuda Lindell,et al.  A Proof of Security of Yao’s Protocol for Two-Party Computation , 2009, Journal of Cryptology.

[14]  Yael Tauman Kalai,et al.  Smooth Projective Hashing and Two-Message Oblivious Transfer , 2005, Journal of Cryptology.

[15]  Mihir Bellare,et al.  Foundations of garbled circuits , 2012, CCS.

[16]  Ivan Damgård,et al.  Improved Non-committing Encryption Schemes Based on a General Complexity Assumption , 2000, CRYPTO.

[17]  Yehuda Lindell,et al.  Universally composable two-party and multi-party secure computation , 2002, STOC '02.

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

[19]  Jonathan Katz,et al.  Adaptively-Secure, Non-interactive Public-Key Encryption , 2005, TCC.

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

[21]  Yael Tauman Kalai,et al.  Improved Delegation of Computation using Fully Homomorphic Encryption , 2010, IACR Cryptol. ePrint Arch..

[22]  Vinod Vaikuntanathan,et al.  Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages , 2011, CRYPTO.

[23]  Ronald Cramer,et al.  Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption , 2001, EUROCRYPT.

[24]  Ronald L. Rivest,et al.  ON DATA BANKS AND PRIVACY HOMOMORPHISMS , 1978 .

[25]  Moni Naor,et al.  Adaptively secure multi-party computation , 1996, STOC '96.

[26]  Frederik Vercauteren,et al.  Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes , 2010, Public Key Cryptography.

[27]  Donald Beaver,et al.  Cryptographic Protocols Provably Secure Against Dynamic Adversaries , 1992, EUROCRYPT.

[28]  Craig Gentry,et al.  A fully homomorphic encryption scheme , 2009 .

[29]  Jesper Buus Nielsen,et al.  Separating Random Oracle Proofs from Complexity Theoretic Proofs: The Non-committing Encryption Case , 2002, CRYPTO.

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

[31]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[32]  Craig Gentry,et al.  i-Hop Homomorphic Encryption and Rerandomizable Yao Circuits , 2010, IACR Cryptol. ePrint Arch..

[33]  Jonathan Katz,et al.  Efficient, Adaptively Secure, and Composable Oblivious Transfer with a Single, Global CRS , 2013, Public Key Cryptography.

[34]  Zvika Brakerski,et al.  Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP , 2012, CRYPTO.