Leaking secrets in homomorphic encryption with side-channel attacks

Abstract

Homomorphic encryption (HE) allows computing encrypted data in the ciphertext domain without knowing the encryption key. It is possible, however, to break fully homomorphic encryption (FHE) algorithms by using side channels. This article demonstrates side-channel leakages of the Microsoft SEAL HE library. The proposed attack can steal encryption keys during the key generation phase by abusing the leakage of ternary value assignments that occurs during the number theoretic transform (NTT) algorithm. We propose two attacks, one for -O0 flag non-optimized code implementation which targets addition and subtraction operations, and one for -O3 flag compiler optimization which targets guard and mul root operations. In particular, the attacks can steal the secret key coefficients from a single power/electromagnetic measurement trace of SEAL's NTT implementation. To achieve high accuracy with a single-trace, we develop novel machine-learning side-channel profilers. On an ARM Cortex-M4F processor, our attacks are able to extract secret key coefficients with an accuracy of 98.3% when compiler optimization is disabled, and 98.6% when compiler optimization is enabled. We finally demonstrate that our attack can evade an application of the random delay insertion defense.