Securing bandwidth-constrained Internet of Things (IoT) and edge networks during post-quantum migration creates an authentication trade-off: ML-KEM provides post-quantum key establishment, whereas post-quantum signatures increase certificate-chain size, verification cost, and handshake latency. We present HPQ-AKE, a sign-less hybrid authenticated key exchange for RSA-enabled IoT gateways and edge/cloud services that replaces transcript signatures with dual KEMs. HPQ-AKE combines ML-KEM-768 for post-quantum session secrecy and forward secrecy with RSA-OAEP for implicit mutual authentication, preserving existing RSA-enabled infrastructure during migration. We analyze HPQ-AKE in an extended Bellare-Rogaway model, separating classical authentication in the Random Oracle Model from session-key secrecy in the Quantum Random Oracle Model. Under the Module-LWE and RSA assumptions, it establishes AKE security, forward secrecy, and conditional KCI resistance under the long-term-key-only exposure assumptions. Evaluation combines x86 micro-benchmarking, analytical latency modeling, and 10,000-iteration Monte Carlo simulation. HPQ-AKE reduces modeled handshake transmission from 13,009 to 5,668 Bytes, a 56.4% reduction relative to a Hybrid TLS 1.3 Full handshake, while requiring 7.11 ms of total local computation on the measured x86 testbed. Under a simulated 50 kbps satellite-like link with 600 ms RTT and stochastic jitter, median latency is 1,914 ms, 31.4% below the 2,791 ms baseline. At 20 ms RTT, modeled break-even thresholds are 0.31 Mbps against the pre-cached baseline and 4.08 Mbps against the full baseline; both decrease as RTT increases. These x86-based results motivate evaluation on gateway-class IoT and edge platforms; performance on ARM gateways and unaccelerated microcontrollers remains unvalidated.

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