Paper 2023/1895

The Patching Landscape of Elisabeth-4 and the Mixed Filter Permutator Paradigm

Clément Hoffmann, Université Catholique de Louvain
Pierrick Méaux, University of Luxembourg
François-Xavier Standaert, Université Catholique de Louvain

Filter permutators are a family of stream cipher designs that are aimed for hybrid homomorphic encryption. While originally operating on bits, they have been generalized to groups at Asiacrypt 2022, and instantiated for evaluation with the TFHE scheme which favors a filter based on (negacyclic) Look Up Tables (LUTs). A recent work of Gilbert et al., to appear at Asiacrypt 2023, exhibited (algebraic) weaknesses in the Elisabeth-4 instance, exploiting the combination of the 4-bit negacyclic LUTs it uses as filter. In this article, we explore the landscape of patches that can be used to restore the security of such designs while maintaining their good properties for hybrid homomorphic encryption. Starting with minimum changes, we observe that just updating the filter function (still with small negacyclic LUTs) is conceptually feasible, and propose the resulting Elisabeth-b4 design with three levels of NLUTs. We then show that a group permutator combining two different functions in the filter can simplify the analysis and improve performances. We specify the Gabriel instance to illustrate this claim. We finally propose to modify the group filter permutator paradigm into a mixed filter permutator, which considers the permutation of the key with elements in a group and a filter outputting elements in a different group. We specify the Margrethe instance as a first example of mixed filter permutator, with key elements in $\mathbb{F}_2$ and output in $\mathbb{Z}_{16}$, that we believe well-suited for recent fully homomorphic encryption schemes that can efficiently evaluate larger (not negacyclic) LUTs.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. Minor revision. Indocrypt 2023
stream-cipherhheboolean functions
Contact author(s)
clement hoffmann @ uclouvain be
pierrick meaux @ uni lu
francois-xavier standaert @ uclouvain be
2023-12-11: approved
2023-12-09: received
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      author = {Clément Hoffmann and Pierrick Méaux and François-Xavier Standaert},
      title = {The Patching Landscape of Elisabeth-4 and the Mixed Filter Permutator Paradigm},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1895},
      year = {2023},
      note = {\url{}},
      url = {}
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