  After three rounds of post-quantum cryptography (PQC) strict evaluations
conducted by the national institute of standards and technology (NIST),
CRYSTALS-Kyber has successfully been selected and drafted for standardization
from the mid of 2022. It becomes urgent to further evaluate Kyber's physical
security for the upcoming deployment phase. In this paper, we present an
improved two-step attack on Kyber to quickly recover the full secret key, s, by
using much fewer energy traces and less time. In the first step, we use the
correlation power analysis (CPA) attack to obtain a portion of guess values of
s with a small number of energy traces. The CPA attack is enhanced by utilizing
both the Pearson and Kendall's rank correlation coefficients and modifying the
leakage model to improve the accuracy. In the second step, we adopt the lattice
attack to recover s based on the results of CPA. The success rate is largely
built up by constructing a trail-and-error method. We implement the proposed
attack for the reference implementation of Kyber512 (4 128-value groups of s)
on ARM Cortex-M4 and successfully recover a 128-value group of s in about 9
minutes using a 16-core machine. Additionally, in that case, we only cost at
most 60 CPA guess values for a group and 15 power traces for a guess.
