A method and an apparatus capable of realizing at a high speed an elliptic
curve cryptography in a finite field of characteristic 2, in which the
elliptic curve is given by y.sup.2 +xy=x.sup.3 +ax.sup.2 +b (b.noteq.0)
and an elliptic curve cryptography method which can protect private key
information against leaking from deviation information of processing time
to thereby defend a cipher text against a timing attack and a differential
power analysis attack are provided. To this end, an arithmetic process for
executing scalar multiplication arithmetic d(x, y) a constant number of
times per bit of the private key d is adopted. Further, for the scalar
multiplication d(x, y), a random number k is generated upon transformation
of the affine coordinates (x, y) to the projective coordinates for thereby
effectuating the transformation (x, y).fwdarw.[kx, ky, k] or alternatively
(x, y).fwdarw.[k.sup.2 x, k.sup.3 y, k]. Thus, object for the arithmetic
is varied by the random number (k).
