PROBLEM TO BE SOLVED: To provide a key share system or the like suitable for a public key encryption system and a signature system.;SOLUTION: In the key share system 101 for using a polynomial T(., .) defined by T(a, x)S(a, x) mod n on a Galois field GF(n) with respect to a Chebychev polynomial S(., .) defined by S(a, cos)=cos(a) with respect to public key X belongs to GF(n) of 2 or more and less than n belonging to the Galois field GF(n) with respect to an integer n(n2) and an integer a(a2), an integer acquisition section 103 of a key share device 102 acquires an integer p being 2 or more and less than n, a transmission key calculation section 104 calculates a transmission key Y belongs to GF(n) by Y=T(p, X) from the acquired integer p, a transmission key section 105 transmits a calculated transmission key Y to other key share device 102, a transmission key reception section 106 receives a transmission key W sent from other key share device 102 and a common key calculation section 107 calculates a share key Z belongs to GF(n) by Z=T(p, W) from the received transmission key W.;COPYRIGHT: (C)2003,JPO
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