java programing

GF2 In this project you are required to write the java program “[login to view URL]” to implement the second type of finite field GF(pn) where p is a prime number and n is a positive integer, and four operations “+”, “-”, “*”, and “/”, respectively. Specifically, your program will read parameters and polynomials from a file named “[login to view URL]” (under the same directory of the program). Then your program should create a file named “[login to view URL]” (under the same directory of the program) and write the results to “[login to view URL]”. Please check the attached sample files “[login to view URL]” and “[login to view URL]”. In “[login to view URL]”: 1. First line is the prime number p. 2. Second line is the degree n of the irreducible polynomial m(x) over Zp, which can be any positive integer. 3. Third line is the coefficients of m(x), from the leading coefficient to the constant term, separated by one blank space. 4. Fourth line is the degree u of f(x) over Zp, where u can be any integer satisfying 0 < u < n. 5. Fifth line is the coefficients of f(x), from the leading coefficient to the constant term, separated by one blank space. 6. Sixth line is the degree v of g(x) over Zp, where v can be any integer satisfying 0 < v < n. 7. Seventh line is the coefficients of g(x), from the leading coefficient to the constant term, separated by one blank space. Example: If the [login to view URL] file contains the following seven lines: 3 2 1 0 1 1 1 1 1 2 1 Then p = 3 (i.e. base field is Z3), m(x) = x2 + 1, f(x) = x + 1, and g(x) = 2x + 1. In “[login to view URL]”: 1. First line is the coefficients of f(x) + g(x) in GF(pn), from the leading coefficient to the constant term, separated by one blank space. 2. Second line is the coefficients of f(x) - g(x) in GF(pn), from the leading coefficient to the constant term, separated by one blank space. 3. Third line is the coefficients of f(x) * g(x) in GF(pn), from the leading coefficient to the constant term, separated by one blank space. 4. Fourth line is the coefficients of f(x) / g(x) in GF(pn), from the leading coefficient to the constant term, separated by one blank space (don’t forget to handle the case of g(x) = 0). Example: Given the preceding [login to view URL] file, f(x) + g(x) = (x + 1) + (2x + 1) = 3x + 2 = 2 Explain: since 3 is not in Zp = Z3, perform 3 mod 3 = 0. f(x) - g(x) = (x + 1) - (2x + 1) = - x = 2x Explain: since − 1 is not in Zp = Z3, perform −1 mod 3 = 2. f(x) * g(x) = (x + 1) * (2x + 1) = 2x2 + 3x + 1 = 2x2 + 1 = PLDA(2x2 + 1, x2 + 1)[1] = 2 Explain: since 3 is not in Zp = Z3, perform 3 mod 3 = 0; since the degree of 2x2+ 1 >= the degree of m(x), perform 2x2 + 1 mod x2+ 1 = PLDA(2x2+ 1, x2 + 1)[1] = 2. f(x) / g(x) = (x + 1) / (2x + 1) = (x + 1) * EEAP(2x + 1, x2 + 1)[0] = (x + 1) * (2x + 2) = 2x2 + 4x + 2 = 2x2+ x + 2 = PLDA(2x2 + x + 2, x2 + 1)[1] = x Therefore, the [login to view URL] file should contain the following four lines: 2 2 0 2 1 0 Remark 1: The leading coefficient should not be 0 unless the polynomial is 0. Example 1: Let p = 3, m(x) = x2+ 1, f(x) = 2x, g(x) = x + 1, then f(x) + g(x) = 1 rather than 0x + 1 or 3x + 1. Thus the first line of “[login to view URL]” should be 1 rather than 0 1 or 3 1. Example 2: Let p = 3, m(x) = x2 + 1, f(x) = x + 2, g(x) = 2x + 1, then f(x) + g(x) = 0 rather than 0x + 0 or 3x + 3. Thus the first line of “[login to view URL]” should be 0 rather than 0 0 or 3 3. Remark 2: The coefficient (that after the leading coefficient) should be outputted even if it is 0. Example 1: Let p = 3, m(x) = x2 + 1, f(x) = 1, g(x) = x + 2, then f(x) + g(x) = x. Thus the first line of “[login to view URL]” should be 1 0 rather than 1 or 1 3. “javac [login to view URL]” will be entered to the command line to compile the java file and then “java GF2” will be entered to the command line to run the program Your program should output the file “[login to view URL]” to the same directory