In rsa digital signature, suppose bob wants to send a signed message (x = 4) to alice. the first steps are exactly t eps are exactly the same as it is done for an rsa encryption: bob computes his rsa parameters and sends the public key to alice. we know p = 3, q=11, and bob choose e=3. (hint: we learn rsa algorithm and key generation in week 7) (1) what is the public key pair bob sends to alice? (2) what is the value of signature s? (3) what is the value of verkpuba(x, s)? show all intermediate steps clearly.

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?