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Homomorphic Encryption with CCA Security

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Automata, Languages and Programming (ICALP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5126))

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Abstract

We address the problem of constructing public-key encryption schemes that meaningfully combine useful computability features with 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 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 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.

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Authors and Affiliations

  1. University of Illinois, Urbana-Champaign,  

    Manoj Prabhakaran & Mike Rosulek

Authors
  1. Manoj Prabhakaran
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  2. Mike Rosulek
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Editor information

Luca Aceto Ivan Damgård Leslie Ann Goldberg Magnús M. Halldórsson Anna Ingólfsdóttir Igor Walukiewicz

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Prabhakaran, M., Rosulek, M. (2008). Homomorphic Encryption with CCA Security. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70583-3_54

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  • DOI: https://doi.org/10.1007/978-3-540-70583-3_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70582-6

  • Online ISBN: 978-3-540-70583-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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