Homomorphic Authenticated Encryption Secure Against Chosen-Ciphertext Attack

We study homomorphic authenticated encryption, where privacy and authenticity of data are protected simultaneously. We define homomorphic versions of various security notions for privacy and authenticity, and investigate relations between them. In particular, we show that it is possible to give a natural definition of IND-CCA for homomorphic authenticated encryption, unlike the case of homomorphic encryption. Also, we construct a simple homomorphic authenticated encryption scheme supporting arithmetic circuits, which is chosen-ciphertext secure both for privacy and authenticity. Our scheme is based on the error-free approximate GCD assumption.

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

[2]  Jean-Sébastien Coron,et al.  Scale-Invariant Fully Homomorphic Encryption over the Integers , 2014, Public Key Cryptography.

[3]  Rosario Gennaro,et al.  Fully Homomorphic Message Authenticators , 2013, IACR Cryptol. ePrint Arch..

[4]  Mihir Bellare,et al.  A concrete security treatment of symmetric encryption , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[5]  Jean-Sébastien Coron,et al.  Fully Homomorphic Encryption over the Integers with Shorter Public Keys , 2011, IACR Cryptol. ePrint Arch..

[6]  Vinod Vaikuntanathan,et al.  (Leveled) Fully Homomorphic Signatures from Lattices , 2014, IACR Cryptol. ePrint Arch..

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

[8]  Morris J. Dworkin.  SP 800-38C. Recommendation for Block Cipher Modes of Operation: the CCM Mode for Authentication and Confidentiality , 2004 .

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

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

[11]  Bogdan Warinschi,et al.  Homomorphic Signatures with Efficient Verification for Polynomial Functions , 2014, CRYPTO.

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

[13]  Jean-Sébastien Coron,et al.  Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers , 2012, EUROCRYPT.

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

[15]  Mihir Bellare,et al.  Subtleties in the Definition of IND-CCA: When and How Should Challenge Decryption Be Disallowed? , 2013, Journal of Cryptology.

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

[17]  Phillip Rogaway,et al.  The Software Performance of Authenticated-Encryption Modes , 2011, FSE.

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

[19]  Mihir Bellare,et al.  OCB: a block-cipher mode of operation for efficient authenticated encryption , 2001, CCS '01.

[20]  Jung Hee Cheon,et al.  Batch Fully Homomorphic Encryption over the Integers , 2013, EUROCRYPT.

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

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

[23]  Mihir Bellare,et al.  The Power of Verification Queries in Message Authentication and Authenticated Encryption , 2004, IACR Cryptol. ePrint Arch..

[24]  Dan Boneh,et al.  Homomorphic Signatures for Polynomial Functions , 2011, EUROCRYPT.

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

[26]  Chanathip Namprempre,et al.  Authenticated Encryption: Relations among Notions and Analysis of the Generic Composition Paradigm , 2000, Journal of Cryptology.

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

[28]  Morris J. Dworkin,et al.  SP 800-38D. Recommendation for Block Cipher Modes of Operation: Galois/Counter Mode (GCM) and GMAC , 2007 .

[29]  Dario Fiore,et al.  Practical Homomorphic MACs for Arithmetic Circuits , 2013, IACR Cryptol. ePrint Arch..