Paper 2024/1545

Fully Composable Homomorphic Encryption

Daniele Micciancio, University of California, San Diego
Abstract

The traditional definition of fully homomorphic encryption (FHE) is not composable, i.e., it does not guarantee that evaluating two (or more) homomorphic computations in a sequence produces correct results. We formally define and investigate a stronger notion of homomorphic encryption which we call "fully composable homomorphic encryption", or "composable FHE". The definition is both simple and powerful: it does not directly involve the evaluation of multiple functions, and yet it supports the arbitrary composition of homomorphic evaluations. On the technical side, we compare the new definition with other definitions proposed in the past, proving both implications and separations, and show how the "bootstrapping" technique of (Gentry, STOC 2009) can be formalized as a method to transform a (non-composable, circular secure) homomorphic encryption scheme into a fully composable one. We use this formalization of bootstrapping to formulate a number of conjectures and open problems.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
Fully homomorphic encryptioncomposabilitycircular securityfunctional bootstrapping
Contact author(s)
daniele @ cs ucsd edu
History
2024-10-04: approved
2024-10-02: received
See all versions
Short URL
https://ia.cr/2024/1545
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/1545,
      author = {Daniele Micciancio},
      title = {Fully Composable Homomorphic Encryption},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1545},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1545}
}
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