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

摘要

A computing apparatus outputs τ1 and τ2 corresponding to a ciphertext x, a capability providing apparatus uses τ1 to correctly compute f(τ1) with a probability greater than a certain probability and sets the result of the computation as z1, uses τ2 to correctly compute f(τ2) with a probability greater than a certain probability and sets the result of the computation as z2, the computing apparatus generates a computation result u = f(x)bx1 from z1, generates a computation result v = f(x)ax2 from z2, and outputs ub'va' if the computation results u and v satisfy a particular relation, where G and H are groups, f(x) is a function for obtaining an element of the group G for x ∈ H, X1 and X2 are random variables having values in the group G, x1 is a realization of the random variable X1, and x2 is a realization of the random variable X2.