Marina Checri
Université Paris-Saclay

Renaud Sirdey
Université Paris-Saclay

Aymen Boudguiga
Université Paris-Saclay

Jean-Paul Bultel
Université Paris-Saclay

Keywords: FHE, CPAD, threshold FHE, CCA security

Abstract

In their 2021 seminal paper, Li and Micciancio presented a passive attack against the CKKS approximate FHE scheme and introduced the notion of CPA^D security. The current status quo is that this line of attacks does not apply to "exact" FHE. In this paper, we challenge this status quo by exhibiting a CPA^D key recovery attack on the linearly homomorphic Regev cryptosystem which easily generalizes to other xHE schemes such as BFV, BGV and TFHE showing that these cryptosystems are not CPA^D secure in their basic form. We also show that existing threshold variants of BFV, BGV and CKKS are particularily exposed to CPA^D attackers and would be CPA^D-insecure without smudging noise addition after partial decryption. Finally we successfully implement our attack against several mainstream FHE libraries and discuss a number of natural countermeasures as well as their consequences in terms of FHE practice, security and efficiency. The attack itself is quite practical as it typically takes less than an hour on an average laptop PC, requiring a few thousand ciphertexts as well as up to around a million evaluations/decryptions, to perform a full key recovery.