The MixColumn transformation of AES consists of a matrixvector multiplication in the field GF(2^8) with P(x)=x^8 +x^4 +x^3 +x +1. Let b =(b7 x^7 +...+b0) be one of the (four) input bytes to the vectormatrix multiplication. Each input byte is multiplied with the constants 01, 02 and 03. Your task is to provide exact equations for calculating the results of those three constant multiplications. We denote the result by d =(d7 x^7 +...+d0). 1. Write expressions for computing the 8 bits of d=01 b as functions of the bi`s: d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . 2. Write expressions for computing the 8 bits of d=02 b as functions of the bi's. If a XOR operation of two bits is required write it as, for example, b0+b1. d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . 3. Repeat for d =03 b: d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . Note: The AES specification uses 01 to represent the polynomial 1, 02 to represent the polynomial x, and 03 to represent x +1

Problem 4.11 in the textbook: The MixColumn transformation of AES consists of a matrix-vector multiplication in the field GF(2^8) with P(x)=x8+x4+x3+x+1 Let b=(b7x7++b0) be one of the (four) input bytes to the vector-matrix multiplication. Each input byte is multiplied with the constants 01, 02 and 03. Your task is to provide exact equations for calculating the results of those three constant multiplications. We denote the result by d=(d7x7++d0). 1. Write expressions for computing the 8 bits of d=01b as functions of the bi's: d0=,d1=,d2=,d3=,d5=d6= and d7= example, b0+b1. d0= d1=,d2= , d4= , d5= , d6= and 3. Repeat for d=03b