Encryption device, decryption device, key generation device, encryption method, decryption method, key generation method, computer program product for encryption, computer program product for decryption, and computer program product for key generation

Abstract

According to one embodiment, an encryption device includes a memory and one or more processors. The one or more processors are configured to: acquire, as a public key, an n-variable symmetric indeterminate equation having an element not more than a constant degree of F[t] and being symmetric for at least two variables; embed the plaintext into coefficients of an n-variable plaintext polynomial having an element not more than a constant degree of F[t]; randomly generate an n-variable polynomial having an element not more than a constant degree of F[t], randomly generate an n-variable symmetric polynomial having an element not more than a constant degree of F[t] and being symmetric for at least two variables, and randomly generate a noise polynomial having an element not more than a constant degree of F[t]; and generate a ciphertext from the three polynomials and the equation for the n-variable plaintext polynomial.