SUBSTITUTION CALCULATION SYSTEM CALCULATION APPARATUS CAPABILITY PROVIDING APPARATUS SUBSTITUTION CALCULATION METHOD CAPABILITY PROVIDING METHOD PROGRAM AND RECORDING MEDIUM

摘要

When G and H are groups, f(x) is a function for obtaining the source of group G for x ?H, X1 and X2 are random variables having values in group G, x1 is an observed value of the random variable X1, and x2 is an observed value of the random variable X2, a calculation apparatus outputs t1 and t2 that correspond to a cryptogram (x), and a capability providing apparatus calculates f(t1) properly, using t1, with a probability higher than a certain probability and puts the result of the calculation as z1, and calculates f(t2) properly, using t2, with a probability higher than a certain probability and puts the result of the calculation as z2. The calculation apparatus then generates a calculation result u = f(x)bx1 from z1, generates a calculation result v = f(x)ax2 from z2, and outputs ubva when the calculation results u and v satisfy a specific relationship.