Provided is an information processing apparatus including a number acquisition unit configured to acquire a number used for a coefficient of each term constituting a set of a multi-order multivariate polynomial F=(f1, . . . , fm), the number generated using a predetermined function from information shared between entities that execute an algorithm of a public-key authentication scheme or a digital signature scheme that uses a public key including the set of the multi-order multivariate polynomial F, and a polynomial calculation unit configured to calculate a multi-order multivariate polynomial for an input value of a variable by allocating the number acquired by the number acquisition unit to coefficients of the multi-order multivariate that includes the set of the multi-order multivariate polynomial F as a structural element. The polynomial calculation unit skips a calculation process for a term in which an input value of at least one variable is 0