A method for calculating a conversion parameter of the Montgomery modular multiplication to improve the efficiency of software installation, comprising a first step for calculating H0=2v×R (mod n) (where v is an integer, v≧1, and (m×k)/v is an integer), a second step for calculating Hp=2v×2^p×R (mod n) from H0=2v×R (mod n) by repeating Hi=REDC(Hi−1, Hi−1)n with respect to i=1, 2, . . . , p (where p represents an integer satisfying the condition 2p≧(m×k)/v>2p−1, REDC represents the Montgomery modular multiplication REDC(a, b)n=a×b×R−1 (mod n), and x^i represents exponential computation xi); and a third step for calculating Hp=R2 (mod n) by calculating Hp=REDC(Hp, g)n with respect to Hp obtained in the second step when 2p>(m×k)/v (where g=2k×E(p,m,k), E(p, m, k)=2×m−(v×2p)/k) and finally outputting Hp as R2 (mod n).