In today’s digital landscape, cryptography plays a vital role in ensuring communication security through encryption and authentication algorithms. While traditional cryptographic methods rely on hard mathematical problems for security, the rise of quantum computing threatens their effectiveness. Post-Quantum Cryptography (PQC) algorithms, like CRYSTALSKyber, aim to withstand quantum attacks. Recently standardized, CRYSTALS-Kyber is a lattice-based algorithm designed to resist quantum attacks. However, its implementation faces computational challenges, particularly with Keccak-based functions, which are crucial for security and upon which the FIPS 202 standard is based. Our paper addresses this technological challenge by designing a FIPS 202 hardware accelerator to enhance CRYSTALS-Kyber efficiency and security. We chose to implement the entire FIPS 202 standard in hardware in order to widen the applicability of the accelerator to all possible algorithms that rely on such hash functions, taking care to provide realistic assumptions on system-level integration inside a System-on-Chip (SoC). We provide results in terms of area, frequency, and clock cycles for both ASIC and FPGA targets. An area reduction of up to 22.3% is achieved with respect to state-ofthe-art solutions. In addition, we integrated the accelerator inside a 32-bit RISC-V based security-oriented SoC, where we show a strong performance gain on CRYSTALS-Kyber execution. The design presented in this paper performs better in all Kyber1024 primitives, with an improvement up to 3.21× in Kyber-KeyGen.