A Complete and Optimized Key Mismatch Attack on NIST Candidate NewHope

In CT-RSA 2019, Bauer et al. have analyzed the case when the public key is reused for the NewHope key encapsulation mechanism (KEM), a second-round candidate in the NIST Post-quantum Standard process. They proposed an elegant method to recover coefficients ranging from \(-6\) to 4 in the secret key. We repeat their experiments but there are two fundamental problems. First, even for coefficients in [−6, 4] we cannot recover at least 262 of them in each secret key with 1024 coefficients. Second, for the coefficient outside [−6, 4], they suggested an exhaustive search. But for each secret key on average there are 10 coefficients that need to be exhaustively searched, and each of them has 6 possibilities. This makes Bauer et al.’s method highly inefficient. We propose an improved method, which with \(99.22\%\) probability recovers all the coefficients ranging from \(-6\) to 4 in the secret key. Then, inspired by Ding et al.’s key mismatch attack, we propose an efficient strategy which with a probability of \(96.88\%\) succeeds in recovering all the coefficients in the secret key. Experiments show that our proposed method is very efficient, which completes the attack in about 137.56 ms using the NewHope parameters.