Reference no: EM13286769

In this project you need to write a program called "ECC.java"to implement Elliptic Curve encryption/decryption.

Specifically, your program will read parameters, plaintext and ciphertextfrom a file named "input.txt" (under the same directory).Then your program needs tocreate a file named "output.txt" (under the same directory) and prints the public key, private key, encryption and decryption results to "output.txt". (Please check the attached sample files "input.txt" and "output.txt".)

In "input.txt":

1.     First line is aprime number q. Thus GF(q) is the ground field.

2.     Second line are two integers a and b,separated by one blank space. Thus the elliptic curve E_q(a, b) is: y² = x³ + ax + b.

3.     Thirdline are two integers x₁ and y₁,separated by one blank space. Thus the base point is: G = (x₁, y₁).

4.     Fourth line is an integer n_A. Thus private key is n_A.

5.     Fifth line are two integers m₁ and m₂,separated by one blank space. Thus the point of the plaintext is P_m = (m₁, m₂).

6.     Sixth line is the randomly generated positive integer k.

7.     Seventh line arefour integers c₁₁, c₁₂,c₂₁, and c₂₂, separated by one blank space. Thus the point of the ciphertext is C_m = (c₁=(c₁₁, c₁₂),c₂=(c₂₁,c₂₂)).

In "output.txt":

1.     First line (two integers) is the public key.

2.     Second line (one integer) is the private key.

3.     Third line (four integers)is the point of the ciphertextencrypted fromP_musing public key and k in input.txt. Suppose the point of the ciphertext C_m = (kG, P_m+kP_B), then the first two integers are the coordinates ofkG and the latter two integers are the coordinates ofP_m+kP_B.

4.     Fourth line (two integers)is the point of the plaintext decrypted fromC_musing private key in input.txt.

The program will be tested usingcommand line. I will type "javacECC.java" to compile it and type "java ECC" to run it.