1. A measurement device comprising: a first measurement unit configured to measure first biological data at least k times, where k≧2, to obtain any k first measurement values; a distributed-signature generation unit configured to execute signature operations for the k first measurement values using any various k distributed-signature keys, respectively, to generate k distributed signatures, the k distributed-signature keys being capable of reconstructing a signature generation key only when all of the k distributed-signature keys are available; a signature synthesis unit configured to synthesize the k distributed signatures together to reconstruct a signature; and a steady state verification unit configured to verify, using a signature verification key corresponding to the signature generation key, whether or not the signature reconstructed by said signature synthesis unit is correct, where the correctness of the signature means that the k first measurement values are same values, wherein a result of a multiplication of the signature generation key and the signature verification key is a predetermined value, each of the signature operations is exponentiation where a corresponding one of the k distributed-signature keys or the signature generation key is an exponent, the signature generation key is generated by summing values of respective multiplications of the k distributed-signature keys by respective predetermined coefficients, said distributed-signature generation unit is configured to generate the k distributed signatures by executing the exponentiation for the k first measurement values, respectively, a base of the exponentiation being each of the k first measurement values, and an exponent of the exponentiation being a distributed-signature key corresponding to the each of the k first measurement values among the k distributed-signature keys, said signature synthesis unit is configured to calculate the signature by raising the k distributed signatures respectively to power of the respective predetermined coefficients to generate k exponentiation results, and multiplying the k exponentiation results together, and said steady state verification unit is configured to determine by the verification that the signature reconstructed by said signature synthesis unit is correct, when a predetermined verification equation is satisfied, a left-hand side of the predetermined verification equation being exponentiation where the signature is a base and the signature verification key is an exponent, and a right-hand side of the predetermined verification equation being a target first measurement value from among the k first measurement values.