  TLS is extensively utilized for secure data transmission over networks.
However, with the advent of quantum computers, the security of TLS based on
traditional public-key cryptography is under threat. To counter quantum
threats, it is imperative to integrate post-quantum algorithms into TLS. Most
PQ-TLS research focuses on integration and evaluation, but few studies address
the improvement of PQ-TLS performance by optimizing PQC implementation. For the
TLS protocol, handshake performance is crucial, and for post-quantum TLS
(PQ-TLS) the performance of post-quantum key encapsulation mechanisms (KEMs)
directly impacts handshake performance. In this work, we explore the impact of
post-quantum KEMs on PQ-TLS performance. We explore how to improve ML-KEM
performance using the latest Intel's Advanced Vector Extensions instruction set
AVX-512. We detail a spectrum of techniques devised to parallelize polynomial
multiplication, modular reduction, and other computationally intensive modules
within ML-KEM. Our optimized ML-KEM implementation achieves up to 1.64x speedup
compared to the latest AVX2 implementation. Furthermore, we introduce a novel
batch key generation method for ML-KEM that can seamlessly integrate into the
TLS protocols. The batch method accelerates the key generation procedure by
3.5x to 4.9x. We integrate the optimized AVX-512 implementation of ML-KEM into
TLS 1.3, and assess handshake performance under both PQ-only and hybrid modes.
The assessment demonstrates that our faster ML-KEM implementation results in a
higher number of TLS 1.3 handshakes per second under both modes. Additionally,
we revisit two IND-1-CCA KEM constructions discussed in Eurocrypt22 and
Asiacrypt23. Besides, we implement them based on ML-KEM and integrate the one
of better performance into TLS 1.3 with benchmarks.
