Messages are to be encoded using the RSA method, and the primes chosen are p “ 17 and q “ 19, so that n “ pq “ 323, and e “ 19. Thus, the public key is p323, 19q.   (a) Show that the decryption exponent d (your private key) is 91.

A cryptanalyst has determined that the three most common trigraphs in a ciphertext are LME, WRI, and ZYC, and guesses that these ciphertext trigraphs correspond to the three most common trigraphs in English text, THE, AND, and THA. If the plaintext was encrypted using a Hill trigraphic cipher described by C ≡ AP (mod 26), what are the entries of the 3 × 3 encrypting matrix A?

Solve on paper

EXM.1.AHL.TZ0.37 IB [Maximum mark: 8] In this part, marks will only be awarded if you show the correct application of the required algorithms, and show all your working. In an offshore drilling site for a large oil company, the distances between the planned wells are given below in metres. 1 2 3 4 5 6 7 8 9 10 2 30 3 40 60 4 90 190 130 5 80 200 10 160 6 70 40 20 40 40 130 7 60 120 50 90 30 60 8 50 140 90 70 70 140 70 40 9 40 170 140 60 50 90 50 70 10 200 200 80 150 110 90 30 190 90 100 11 150 30 200 120 190 120 60 190 150 200 + It is intended to construct a network of paths to connect the different wells in a way that minimises the sum of the distances between them. Use Prim's algorithm, starting at vertex 3, to find a network of paths of minimum total length that can span the whole site. [8]

Let x and y be integers such that x = 3 (mod 10) and y = 5 (mod 10). Find the integer z such that 97x + 3y³ z (mod 10) and 0 ≤ z ≤9.

Is b correct? It's calculated differently than a. The paths from a to d should be C(9,4) or C(9,5).

For any integer x, x2-x will always result in an even value

. Consider the alphabet Σ = {0,1}. Give regular expressions generating the following lan- guages. (a) {w ¤ Σ* | w begins with a 0 and ends with a 1} (b) {w € Σ* | w contains at least four Os} 1* (c) {w € Σ* | w contains the substring 1101} (d) {w € Σ* | w has length at least 4 and its third symbol is a 0} (e) {w € Σ* | w begins with a 0 and has even length, or begins with a 1 and has odd length} (f) {€,0} (g) The empty set (h) All strings over Σ (i) All strings over Σ except the empty string

Please help me to solve problem 28

Q2. Given, F(w,x,y,z) = II M(0,4,8,12) ; (here M means Maxterms) a) Complete the truth table for F W X F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 b) Write the minimum expression of F