A method of elliptic curve encryption includes, (a) selecting an elliptic curve E.sub.p (a,b) of the form y.sup.2=x.sup.3+ax+b mod (p) wherein a and b are non-negative integers less than p satisfying the formula 4 a.sup.3+27b.sup.2 mod (p) not equal to 0; (b) generating a large 160 bit random number by a method of concatenation of a number of smaller random numbers; (c) generating a well hidden point G (x,y) on the elliptic curve E.sub.p (a,b) by scalar multiplication of a point B (x,y) on the elliptic curve with a large random integer which further includes the steps: (i) converting the large random integer into a series of powers of 2.sup.31; (ii) converting each coefficient of 2.sup.31 obtained from above step into a binary series; (iii) multiplication of binary series obtained from steps (i) and (ii) above with the point B (x,y) on the elliptic curve; (d) generating a private key n.sub.A (of about >=160 bit length); (e) generating a public key P.sub.A (x,y) given by the formula P.sub.A (x,y)=(n.sub.A-G (x,y)) mod (p); (f) encrypting the input message MSG; (g) decrypting the ciphered text.