A post-quantum hybrid encryption based on QC-LDPC codes in the multi-user setting

The encryption schemes based on coding theory are one of the most accredited choices in post-quantum scenario, where QC-LDPC codes are usually employed to construct concrete schemes due to the well security and good efficiency. In this work, we introduce a new IND-CCA secure multi-instance framework for code-based hybrid encryption primitive in the random oracle model, which is derived from our new multi-instance KEM and DEM building modules. We note that previous multi-instance KEM and DEM are usually derived from single-instance KEM and DEM, and hence suffers from large parameter sizes and security loss. Nevertheless, our multi-instance KEM is a direct construction based on a key generation function and a one-way trapdoor function, and our multi-instance DEM is constructed from a standard DEM and MAC with a tag in the input to achieve a tighter security loss. Finally, we present a IND-CCA secure multi-instance hybrid encryption scheme based on QC-LDPC codes in the random oracle model, where the scheme achieves small private key size and only consumes addition and multiplication operations over F₂[x].