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A Practical Full Key Recovery Attack on TFHE and FHEW by Inducing Decryption Errors
Authors: Bhuvnesh Chaturvedi, Anirban Chakraborty, Ayantika Chatterjee, Debdeep MukhopadhyayAbstract:
Fully Homomorphic Encryption (FHE) promises to
secure our data on the untrusted cloud, while allowing arbitrary
computations. Present research shows that while there are pos-
sibilities of side channel exploitations on the client side targeting
the encryption or key-generation processes, the encrypted data on
the cloud is secure against practical attacks. The current paper
shows that it is possible for adversaries to inject perturbations in
the ciphertexts stored in the cloud to result in decryption errors.
Most importantly, we highlight that when the client reports of
such aberrations to the cloud service provider the complete
secret key can be extracted in few attempts. Technically, this
implies a break of the IND-CVA (Indistinguishability against
Ciphertext Verification Attacks) security of the FHE schemes.
The underlying core methodology of the attack is to exploit
the dependence of the error in the ciphertexts to the timing
of homomorphic computations. These correlations can lead to
timing templates which when used in conjunction with the error-
induced decryption errors as reported by the client can lead to
an accurate estimation of the ciphertext errors. As the security
of the underlying Learning with Errors (LWE) collapse with the
leakage of the errors, the adversary is capable of ascertaining the
secret keys. We demonstrate this attack on two well-known FHE
libraries, namely FHEW and TFHE, where we need 7, 23 and
28 queries to the client for each error recovery respectively. We
mounted full key recovery attack on TFHE (without and with
bootstrapping) and FHEW with key sizes 630 and 500 bits with
1260, 703 and 1003 correct errors and 31948, 21273 and 9073
client queries respectively.
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