An elliptic curve cryptosystem apparatus performing an elliptic curve cryptosystem process has a coordinate transforming unit for transforming coordinates (X:Y:Z) on a point P on an elliptic curve over a finite field GF(p^m) to coordinates (r1.times.(X-s1):r2.times.(Y-s2):r3.times.(Z-s3)) (where, p is a prime number, m is an integer not less than 1, r1, r2 and r3 are integers not less than 1 and not larger than (p-1), s1, s2 and s3 are integer not less than 0 and not larger than (p-1), and a code "^" represents power), and a scalar multiplication operating unit for performing scalar multiplication on the point on the elliptic curve transformed by the coordinate transforming unit, wherein at least one of the parameters s1, s2 and s3 has a value other than 0. The apparatus can perform the scalar multiplication in the elliptic curve cryptosystem, with resistance to side channel attacks.