Bidirectional Proxy Re-encryption Based on Isogenies

Proxy re-encryption (PRE) enables a semi-trusted entity, known as a proxy, to convert a ciphertext under one public key into a ciphertext under another public key without learning the underlying plaintext. This functionality has numerous applications, including e-mail forwarding and encrypted file systems. Most existing post-quantum PRE schemes are based on lattice assumptions. In this paper, we propose a novel post-quantum PRE scheme based on isogenies. Our scheme is multi-hop bidirectional PRE and provides security against chosen plaintext attacks. We construct the PRE using a natural public key encryption (PKE) derived from CSIDH group actions.