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Journal of Cryptology

, Volume 31, Issue 3, pp 885–916 | Cite as

Stream Ciphers: A Practical Solution for Efficient Homomorphic-Ciphertext Compression

  • Anne Canteaut
  • Sergiu Carpov
  • Caroline Fontaine
  • Tancrède Lepoint
  • María Naya-Plasencia
  • Pascal Paillier
  • Renaud Sirdey
Article
  • 371 Downloads

Abstract

In typical applications of homomorphic encryption, the first step consists for Alice of encrypting some plaintext m under Bob’s public key \(\mathsf {pk}\) and of sending the ciphertext \(c = \mathsf {HE}_{\mathsf {pk}}(m)\) to some third-party evaluator Charlie. This paper specifically considers that first step, i.e., the problem of transmitting c as efficiently as possible from Alice to Charlie. As others suggested before, a form of compression is achieved using hybrid encryption. Given a symmetric encryption scheme \(\mathsf {E}\), Alice picks a random key k and sends a much smaller ciphertext \(c' = (\mathsf {HE}_{\mathsf {pk}}(k), \mathsf {E}_k(m))\) that Charlie decompresses homomorphically into the original c using a decryption circuit \(\mathcal {C}_{{\mathsf {E}^{-1}}}\). In this paper, we revisit that paradigm in light of its concrete implementation constraints, in particular \(\mathsf {E}\) is chosen to be an additive IV-based stream cipher. We investigate the performances offered in this context by Trivium, which belongs to the eSTREAM portfolio, and we also propose a variant with 128-bit security: Kreyvium. We show that Trivium, whose security has been firmly established for over a decade, and the new variant Kreyvium has excellent performance. We also describe a second construction, based on exponentiation in binary fields, which is impractical but sets the lowest depth record to \(8\) for \(128\)-bit security.

Keywords

Stream ciphers Homomorphic cryptography Trivium 

Notes

Acknowledgements

We thank Yannick Seurin for informing us about the complete characterization of secure hybrid encryption.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Anne Canteaut
    • 1
  • Sergiu Carpov
    • 2
  • Caroline Fontaine
    • 3
    • 4
  • Tancrède Lepoint
    • 5
  • María Naya-Plasencia
    • 1
  • Pascal Paillier
    • 6
  • Renaud Sirdey
    • 2
  1. 1.InriaParisFrance
  2. 2.CEA LISTSaclayFrance
  3. 3.Lab-STICC, CNRSBrestFrance
  4. 4.IMT AtlantiqueBrestFrance
  5. 5.SRI InternationalNew YorkUSA
  6. 6.CryptoExpertsParisFrance

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