This page lists some figures for ML-KEM-768 (which is the PQ key exchange algorithm that's most widely deployed today): https://blog.cloudflare.com/pq-2025/#ml-kem-versus-x25519 This one is actually faster than X25519 (a highly optimized ECC algorithm) by about double but requires 1,184 bytes of data to be exchanged per keyshare vs 32 for X25519. In practice everyone today is using a hybrid algorithm (where you do both ECC and PQ in case the PQ algorithm has an undiscovered weakness) so an ECC+PQ key exchange will be strictly slower than an ECC-only key exchange.

This page lists some numbers for different PQ signature algorithms: https://blog.cloudflare.com/another-look-at-pq-signatures/#t... Right now the NIST has selected three different ones (ML-DSA, SLH-DSA, and Falcon a.k.a. FN-DSA) which each have different trade-offs.

SLH-DSA is slow and requires a large amount of data for signatures, however it's considered the most secure of the algorithms (since it's based on the well-understood security properties of symmetric hash algorithms) so it was selected primarily as a "backup" in case the other two algorithms are both broken (which may be possible as they're both based on the same mathematical structure).

ML-DSA and Falcon are both fairly fast (within an order of magnitude of Ed25519, the X25519 curve signature algorithm), but both require significantly larger keys (41x/28x) and signatures (38x/10x) compared to Ed25519. Falcon has the additional constraint that achieving the listed performance in that table requires a hardware FPU that implements IEEE-754 with constant-time double-precision math. CPUs that do not have such an FPU will need to fall back to software emulation of the required floating point math (most phone, desktop, and server CPUs have such an FPU but many embedded CPUs and microcontrollers do not).

The net result is that TLS handshakes with PQ signatures and key exchange may balloon to high single- or double-digit kilobytes in size, which will be especially impactful for users on marginal connections (and may break some "middle boxes" https://blog.cloudflare.com/nist-post-quantum-surprise/#dili...).