Cryptographic system, cryptographic method, cryptographic program, and decryption device

Abstract

In a functional encryption scheme where a decryption key dk can decrypt a ciphertext encrypted by an encryption key ek, when decrypting the encryption key in which a parameter Φ is set, by the decryption key dk in which a parameter Ψ is set, if and only if a relation R(Φ, Ψ) holds, a wider range as a relation R is expressed. Of first information including a polynomial d(x), plural polynomials D(x), and predicate information, and second information including attribute information, a cryptographic system treats one as a ciphertext and a remaining one as a decryption key. A decryption device, based on the predicate information and attribute information, selects at least one of polynomials D(x), and calculates a coefficient Δenabling a polynomial constituted based on a polynomial ΔD(x) to be divided out by a polynomial d(x), the polynomial ΔD(x) obtained by multiplying the selected polynomial D(x) by coefficient Δ.