Elliptic curve encryption method and system

An elliptic curve encryption method using an elliptic curve over a prime field, comprising the steps of:

• defining a prime p as an order of a prime field, which has a form of p=Abn+B where 0<A<2w, 0<B<2w, b=2w, w, A, B, b are positive integers;
• performing a finite field arithmetic using said p;
• performing scalar multiplication using said finite field arithmetic;
• and
• performing encryption or decryption using the performance result of said scalar multiplication.

An encryption system for executing an elliptic curve encryption method using an elliptic curve over a prime field, comprising:

• means for expressing different points on the elliptic curve in a homogeneous coordinate system [X, Y, Z], which using [X3, Y3, Z3] and [X1, Y1, Z1, (Z1)2, (Z1)3];
• means for adding said different points using [X3, Y3, Z3]=[X1, Y1, Z1, (Z1)2, (Z1)3]+[X2, Y2, Z2];
• and
• means for doubling said different points using [X3, Y3, Z3]=2[X1, Y1, Z1].

An encryption system for executing an elliptic curve encryption method using an elliptic curve over a prime field, comprising:

• means for defining a prime p as an order of a prime field, which has a form of p=Abn+B where 0<A<2w, 0<B<2w, b=2w, and w, A, B and b are positive integers;
• means for performing a finite field arithmetic using said prime p;
• means for performing a scalar multiplication using said finite field arithmetic;
• and
• means for performing encryption or decryption using the performance result of said scalar multiplication.

An elliptic curve encryption method of receiving elliptic curve information to generate a public key and enciphering a plain text in accordance with the elliptic curve information and the public key, comprising the steps of:

• providing different points on the elliptic curve in a homogeneous coordinate system [X, Y, Z] which are expressed by [X3, Y3, Z3] and [X1, Y1, Z1, (Z1)2, (Z1)3];
• using [X3, Y3, Z3]=[X1, Y1, Z1, (Z1)2, (Z1)3]+[X2, Y2, Z2] in a point addition process;
• and
• using [X3, Y3, Z3]=2[X1, Y1, Z1] in a point doubling process.

An elliptic curve encryption method of receiving elliptic curve information to generate a private key and deciphering an enciphered text in accordance with the elliptic curve information and the private key, comprising the steps of:

• providing different points on the elliptic curve in a homogeneous coordinate system [X, Y, Z] which are expressed by [X3, Y3, Z3] and [X1, Y1, Z1, (Z1)2, (Z1)3];
• using [X3, Y3, Z3]=[X1, Y1, Z1, (Z1)2, (Z1)3]+[X2, Y2, Z2] in a point addition process;
• and
• using [X3, Y3, Z3]=2[X1, Y1, Z1] in a point doubling process.

A computer-readable storage device for storing a program for implementing a method for an elliptic curve encryption method using an elliptic curve in a prime field, comprising the steps of:

• providing different points on the elliptic curve in a homogeneous coordinate system [X, Y, Z] which are expressed by [X3, Y3, Z3] and [X1, Y1, Z1, (Z1)2, (Z1)3];
• using [X3, Y3, Z3]=[X1, Y1, Z1, (Z1)2, (Z1)3]+[X2, Y2, Z2] in a point addition process;
• and
• using [X3, Y3, Z3]=2[X1, Y1, Z1] in a point doubling process.

A computer-readable storage device for storing a program for implementing an elliptic curve encryption method of receiving elliptic curve information to generate a private key and deciphering an enciphered text in accordance with the elliptic curve information and the private key, comprising the steps of:

• providing different points on the elliptic curve in a homogeneous coordinate system [X, Y, Z] which are expressed by [X3, Y3, Z3] and [X1, Y1, Z1, (Z1)2, (Z1)3];
• using [X3, Y3, Z3]=[X1, Y1, Z1, (Z1)2, (Z1)3]+[X2, Y2, Z2] in a point addition process;
• and
• using [X3, Y3, Z3]=2[X1, Y1, Z1] in a point doubling process.