Public key algorithms based on quasi-cyclic binary moderate-density parity-check codes (QC-MDPCs) and QC low-density parity-check codes (QC-LDPCs) codes for key encapsulation and encryption submitted to the NIST post-quantum competition (Bit Flipping Key Encapsulation (BIKE), QC-MDPC KEM, LEDA) are vulnerable against reaction attacks based on decoding failures. To protect algorithms, authors propose to limit the key usage, in the extreme (BIKE) to only use ephemeral public keys. In some authenticated protocols, we need to combine each key with a signature, which can lead to increased traffic overhead, especially given the large signature sizes of some of the proposed post-quantum signature schemes. We propose to combine ephemeral public keys with a simple Merkle tree to obtain a server authenticated key encapsulation/transport suitable for TLS-like handshake protocols. This allows a very simple public key verification on the client, leading to efficient protocols suitable for Internet of Things applications.
Keywords: Merkle tree; authenticated KEM; ephemeral keys.