Patent ID: 8345863

Claim:
A method of countering side-channel attacks on an elliptic curve cryptosystem (ECC), the method comprising: providing a system for message communication between a pair of correspondents, a message being exchanged in accordance with ECC instructions executable on computer processors of the respective correspondents, the ECC instructions including: extending a definition field of an elliptic curve of the ECC to an extension ring in a first field by defining a first elliptic curve equation and converting the first elliptic curve equation to a second elliptic curve equation, wherein the second elliptic curve equation includes a term for checking if there is a sign change fault attack on the ECC; generating a temporary ciphertext in the extension ring and countering attacks on the ECC; and generating a final ciphertext for the first field, wherein the first elliptic curve equation becomes Y 2 *Z+p*YZ 3 =X 3 +a*X*Z 4 +b*Z 6 when represented in Jacobian coordinate and becomes y 2 +p*y=x 3 +a*x+b when represented in Affine coordinate, and wherein the converting of the first elliptic curve equation to the second elliptic curve equation comprises converting b to B (=s 2 +p*s−t 3 −a*t mod p*r) so as to obtain the second elliptic curve equation, Y 2 *Z+p*Y*Z 3 =X 3 a*X*Z 4 +B*Z 6 , when the coordinates of the input point P of the ECC is (t, s), wherein: X is a Jacobian variable X coordinate; each a and b is one of a finite field Fq having elements q (q is a prime), x and y are Affine variable x and y coordinates, B is a converted value of b from the first elliptic curve equation to the second elliptic curve equation, s and t are the coordinates of the input point P of the ECC.