1. Faster Homomorphic Linear Transformations in HElib 2018 Crypto HomomorphicEncryption
    Shai Halevi and Victor Shoup
    [View PDF on eprint.iacr.org]
    [Show BibTex Citation]

    @misc{cryptoeprint:2018:244,
    author = {Shai Halevi and Victor Shoup},
    title = {Faster Homomorphic Linear Transformations in HElib},
    howpublished = {Cryptology ePrint Archive, Report 2018/244},
    year = {2018},
    note = {\url{https://eprint.iacr.org/2018/244}},
    }

HElib is a software library that implements homomorphic encryption (HE), with a focus on effective use of “packed” ciphertexts. An important operation (which is used in bootstrapping, as well as in other applications) is applying a known linear map to a vector of encrypted data. In this paper, we describe several algorithmic improvements that significantly speed up this operation: in our experiments, our new algorithms were 30-75 times faster than those currently implemented in HElib for typical parameters.

Our techniques also reduce the size of the large public evaluation key, often using 33%-50% less space than the previous HElib implementation. We also implemented a new tradeoff that enables a drastic reduction in size, maybe a 25x factor or more for some parameters, paying only a 2-4x factor in runtime (and giving up some parallelization opportunities).

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