ff_sample.out:

001,110->001 001,111->011 010,000->000 010,001->000 010,010->100 010,011->000 010,100->011 010,101->001 010,110->100 010,111->010 011,000->000 011,001->000 011,010->000 011,011->100 011,100->001 011,101->011 011,110->010 011,111->100 100,000->000 100,001->110 100,010->111 100,011->101 100,100->000 100,101->100 100,110->100 100,111->100 101,000->000 101,001->110 101,010->011 101,011->001 101,100->010 101,101->110 101,110->010 101,111->010 110,000->000 110,001->010 110,010->111 110,011->001 110,100->011 110,101->011 110,110->111 110,111->011 111,000->000 111,001->010 111,010->011 111,011->101 111,100->001 111,101->001 111,110->001 111,111->101

Problem 2. 30% Consider the finite field F26 generated by the primitive polynomial p(x)=x6+x+1. Suppose that we have a function F(x,k)=x3+(x+k)3+k where the operations used are finite field addition, multiplication, and exponentiation. The inputs x and k are 6-bit blocks, and the output of the function is another 6-bit block. Write a program that will compute the value of the function for any inputs x and k, e.g. which for x=(0,0,0,0,0,0) and k=(0,0,0,0,0,0) will output (0,0,0,0,0,0). 1 Use this program to generate a lookup table of the function, i.e. a file containing a list of pairs of the form x,k>f(x) for all possible 6-bit inputs x and k. Sample output: See ff_sample. out for a file containing the truth table of the same function F(x,k)=x3+(x+k)3+k but for the field F23 (and therefore for 3-bit input and output blocks)