Cryptographic system, encryption device, decryption device, and key generation device

Abstract

A cryptographic system () performs a cryptographic process in which a Richelot isogeny sequence φwhose starting point is an abelian surface Aand whose end point is an abelian surface Ais a secret key and the abelian surface Ais a public key. An encryption device () computes an abelian surface Aby transitioning the abelian surface A, which is the public key, by a Richelot isogeny sequence φgenerated by encoding a plaintext m, and sets the abelian surface Aas a ciphertext. A decryption device () computes a Richelot isogeny φwhose starting point is the abelian surface A, which is the public key, and whose end point is the abelian surface A, which is the ciphertext, based on the Richelot isogeny sequence φ, which is the secret key.