To provide a modular multiplication method and a calculating device that do not rely on the Montgomery technique, wherein the number of times of multiply-add calculations is reduced to shorten a calculation time for calculation speed-up, there is no limitation in input value, and it is possible to execute a remainder calculation exceeding the calculable maximum bit length of a multiply-add unit that is used. Assuming that N=2.sup.n-M and X=.alpha..times.2.sup.n+.beta., a relation of XmodN=(.alpha..times.M+.beta.)modN is derived, which is utilized. n represents a maximum bit number where "1" is assigned in N, a solution of 2.sup.n+1modN is set as b, A.times.B is set as X, XmodN is transferred to (X/2.sup.n+1.times.b+Xmod2.sup.n+1)modN and further transferred to (Xn/2.sup.n+1.times.b+Xnmod2.sup.n+1)modN, calculations of Xn/2.sup.n+1.times.b+Xnmod2.sup.n+1 are repeated until a bit length of Xn becomes n+1, Xn-N is derived and a derived result is set as a solution of "A.times.BmodN".