Paper 2021/1624

On the IND-CCA1 Security of FHE Schemes

Prastudy Fauzi, Martha Norberg Hovd, and Håvard Raddum


Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first. There are numerous FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice. However, while these FHE schemes are semantically (IND-CPA) secure, the question of their IND-CCA1 security is much less studied. In this paper, we group SHE schemes into broad categories based on their similarities and underlying hardness problems. For each category, we show that the SHE schemes are susceptible to either known adaptive key recovery attacks, a natural extension of known attacks, or our proposed attacks. Finally, we discuss the known techniques to achieve IND-CCA1 secure FHE and SHE schemes.

Available format(s)
Publication info
Preprint. MINOR revision.
FHE schemesIND-CCAcryptanalysis
Contact author(s)
prastudy fauzi @ gmail com
martha @ simula no
haavardr @ simula no
2021-12-17: received
Short URL
Creative Commons Attribution


      author = {Prastudy Fauzi and Martha Norberg Hovd and Håvard Raddum},
      title = {On the IND-CCA1 Security of FHE Schemes},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1624},
      year = {2021},
      note = {\url{}},
      url = {}
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