The InvMixColumns transformation of AES consists of a matrix–vector multiplication in the field GF(2^8) with irreducible polynomial P(x) = x^8+x^4+x^3+x+1 as well during the decryption of AES. Let b = (b7x7+. . .+b0) be one of the (four) input bytes to the vector– matrix multiplication. Each input byte is multiplied with the constants 0E, 0B, 0D and 09. Your task is to provide exact equations for computing those three constant multiplications after reductions. We denote the result by d = (d7x7+. . .+d0).

At steady state, air at 200 kpa, 325 k, and mass flow rate of 0.5 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. the inlet cross-sectional area is 6 cm2. at the duct exit, the pressure of the air is 100 kpa and the velocity is 250 m/s. neglecting potential energy effects and modeling air as an 1.008 kj/kg k, determine ideal gas with constant cp = (a) the velocity of the air at the inlet, in m/s. (b) the temperature of the air at the exit, in k. (c) the exit cross-sectional area, in cm2