Key sharing system, public key cryptosystem, signature system, key sharing apparatus, encryption apparatus, decryption apparatus, signature apparatus, authentication apparatus, key sharing method, encryption method, decryption method, signature method, authentication method, and programs

Abstract

A key sharing system is disclosed which uses a public key XεGF(n) (2≦X<n) which belongs to a Galois finite field GF(n) for an integer n (n≧2), and a polynomial T(•, •) defined in GF(n) by T(a, x)≡S(a, x)mod n where S(•, •) is a Chebyshev polynomial defined by S(a, cos θ)=cos(aθ) where a is an integer (a≧2). In a key sharing apparatus of this system, an integer obtaining unit obtains an integer p (2≦p<n), a transmission key calculation unit calculates a transmission key YεGF(n) using the integer p based on Y=T(p, X), a transmission key sending unit sends the transmission key Y to another key sharing apparatus, a transmission key reception unit receives a transmission key W from another key sharing apparatus, and a common key calculation unit calculates a common key ZεGF(n) using the transmission key W based on Z=T(p, W).