Consider the RSA algorithm. Let the two prime numbers, p=11 and q=31. You need to derive appropriate public key (e,n) and private key (d,n).    Can we pick e=5? If yes, what will be the corresponding (d,n)? Can we pick e=17? If yes, what will be the corresponding (d,n)? Calculation Reference is given as follows.   17*51=867 17*52=884 17*53=901 17*54=918     Use e=17, how to encrypt the number 3? You do not need to provide the encrypted value.

Find the equivalent postfix, prefix, and prefix expressions for the following infix expression. Then, using the algorithm EVAL_POSTFIX() and the values A = 1, B = 10, C = 1, D = 2, G = -1, and H = 6, evaluate the corresponding postfix expression found in (i). (−(? + ? + ?) ↑ ?) ∗ (? + ?)

Let's count ternary digit strings, that is, strings in which each digit can be 0, 1, or 2. a. How many ternary digit strings contain exactly ʼn digits? b. How many ternary digit strings contain exactly n digits and n 2's. c. How many ternary digit strings contain exactly n digits and n - 1 2's. (Hint: where can you put the non-2 digit, and then what could it be?) d. How many ternary digit strings contain exactly n digits and n - 2 2's. (Hint: see previous hint) e. How many ternary digit strings contain exactly n digits and n – k 2's. f. How many ternary digit strings contain exactly n digits and no 2's. (Hint: what kind of a string is this?) g. Use the above parts to give a combinatorial proof for the identity (1) + ²(7) + 2² (2) + 2³ (3) +... 2² (1) +2 = 3¹. =

The following table shows the frequency of expressions in different textbooks. We have a New Doc and would like to find its neighbors (similar textbooks). a. Measure the distance between the new document and each textbook by using Manhattan technique b. Rank textbooks according to the Manhattan values Documents T1 T2 T3 T4 T5 Textbook1 4 Textbook2 3 2 Textbook3 1 4 4 Textbook4 2 2 3 1 New Doc 3 3 4

Write Algorithm to Conversion from an Arabic number to a modern Roman number.in: decimal number n (0 ≤ n)out: sequence R =
s0, s1,...,s12 representing the structure of the Roman number (Ri = number of primitives Vi in n for i ∈ [0, 12])constant: sequence P =
1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1 of primitive Roman numberslocal: remainder x to be converted (0 ≤ x ≤ n); coefficient c for a primitive Romannumbers (for other than P0, 0 ≤ c ≤ 3)