Let n be a large integer and let k = m = c = z/nz. for each of the
functions

e : k×m→c

listed in (a), (b), and (c), answer the following questions:
• is e an encryption function?
• if e is an encryption function, what is its associated decryption function d?
• if e is not an encryption function, can you make it into an encryption function
by using some smaller, yet reasonably large, set of keys?
(a) ek(m) ≡ k − m (mod n).
(b) ek(m) ≡ k · m (mod n).
(c) ek(m) ≡ (k + m)2 (mod n).

Afour cylinder four-stroke in-line engine has a stroke of 160mm, connecting rod length of 150mm, a reciprocating mass of 3kg and its firing order is 1-3-4-2. the spacing between cylinders is 100mm. i. show that the engine is in balance with regard to the primary inertia forces and primary 3. a and secondary inertia couples. li determine the out of balance secondary inertia force ii. propose ways of balancing this out of balance force and discuss the challenges that will arise

Shafts are machine elements that are used to a) carry axial loads b) direct shear loads c) transmit power d) rotate at constant speed e) none of the above circular and square shafts subjected to the same torque under the same circum behave a) the same way b) almost the same way

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?