Method of privacy communication using elliptic curves

DETAILED DESCRIPTION Accordingly, the present invention has an object to provide a method of privacy communication using elliptic curves which define an EDLP unsolvable by the reducing method.
The above object is fulfilled by a method of privacy communication in which an elliptic curve E and an element thereof are notified to all parties who wish to communicate, and data are transmitted from one party to another by using a calculation of the element and coded data made in secret by each party, the method is characterized by a construction of E(GF(p)) whose number of elements has exactly p, assuming that p is a prime number and E(GF(p)) is a group of elements of GF(p) on the elliptic curve E.
Further, E(GF(p)) is constructed by an algorithm : let d be a positive integer such that it gives an imaginary quadratic field Q((-d.
sup.
1/2)) with a small class number; then find a prime number p such that 4.
multidot.
p-1=d.
multidot.
square number; and find a solution of a class polynomial H.
sub.
d (x)=0 modulo p such that is defined by d and given with a j-invariant.
The elliptic curve may be given 1 as the class number.
According to the above mentioned method, the number of the elements of E(GF(p)) has exactly p with the elliptic curve E, and the order of an element other than the zero element is not prime to p.
Therefore, EDLP on such an elliptic curve E can not be solved by the reducing method, hence the privacy communication using such an elliptic curve E is highly secure.