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).

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Water at 55c flows across a flat plate whose surface temperature is held constant at 95c. if the temperature gradient at the plate's surface for a given value of x is 18 c/mm, find a) local heat transfer coefficient. b) heat flux

Which of the following components of a pid controlled accumulates the error over time and responds to system error after the error has been accumulated? a)- proportional b)- derivative c)- integral d)- on/off.