### Homomorphic Encryption with CCA Security

Manoj Prabhakaran and Mike Rosulek

##### Abstract

We address the problem of constructing public-key encryption schemes that meaningfully combine useful {\em computability features} with {\em non-malleability}. In particular, we investigate schemes in which anyone can change an encryption of an unknown message $m$ into an encryption of $T(m)$ (as a {\em feature}), for a specific set of allowed functions $T$, but the scheme is non-malleable'' with respect to all other operations. We formulate precise definitions that capture these intuitive requirements and also show relationships among our new definitions and other more standard ones (IND-CCA, gCCA, and RCCA). We further justify our definitions by showing their equivalence to a natural formulation of security in the Universally Composable framework. We also consider extending the definitions to features which combine {\em multiple} ciphertexts, and show that a natural definition is unattainable for a useful class of features. Finally, we describe a new family of encryption schemes that satisfy our definitions for a wide variety of allowed transformations $T$, and which are secure under the standard Decisional Diffie-Hellman (DDH) assumption.

Note: Changes in May 24 version: Simplified description of our construction's parameters and its allowed transformations. Changes in May 1 version: More details added to proof of Theorem 3.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Full version of an extended abstract presented at ICALP 2008
Keywords
homomorphic encryption
Contact author(s)
rosulek @ uiuc edu
History
2008-05-24: last of 3 revisions
See all versions
Short URL
https://ia.cr/2008/079

CC BY

BibTeX

@misc{cryptoeprint:2008/079,
author = {Manoj Prabhakaran and Mike Rosulek},
title = {Homomorphic Encryption with CCA Security},
howpublished = {Cryptology ePrint Archive, Paper 2008/079},
year = {2008},
note = {\url{https://eprint.iacr.org/2008/079}},
url = {https://eprint.iacr.org/2008/079}
}

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