Parameter Scenario Bob chooses p, a large prime 17 3 Bob chooses a, primitive element in Z*, Bob chooses Kpr = d E {2,3, ..., p-2} 5 Bob computes Kpub = ß = aª mod p p, a, and ß are sent to Alice Alice chooses i in {2,3,..., p-2} 7 Alice computes KE = a' mod p Alice computes KM=B*mod p 3 Alice's message to send is x € Z*, Alice encrypts message x, y=x*KM mod p Alice sends KĘ and y to Bob Bob computes KM=Kg°mod p Bob computes KM' mod p Bob computes x = y* KM¯' mod p
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A: Given DFA is
For the given scenario where Alice is trying to send encrypted data to Bob, and Bob is trying to decrypt it, using Elgamal encryption scheme, fill the values in the table
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- To have random-access lookup, a grid should have a scheme for numbering the tiles.For example, a square grid has rows and columns, which give a natural numberingfor the tiles. Devise schemes for triangular and hexagonal grids. Use the numberingscheme to define a rule for determining the neighbourhood (i.e. adjacent tiles) of agiven tile in the grid. For example, if we have a four-connected square grid, wherethe indices are i for rows and j for columns, the neighbourhood of tile i, j can bedefined asneighbourhood(i, j) = {i ± 1, j,i, j ± 1}Consider eight points on the Cartesian two-dimensional xx-yy plane. For each pair of vertices uu and vv, the weight of edge uvuv is the Euclidean (Pythagorean) distance between those two points. For example, dist(a,h) = \sqrt{4^2 + 1^2} = \sqrt{17}dist(a,h)=42+12=17 and dist(a,b) = \sqrt{2^2 + 0^2} = 2dist(a,b)=22+02=2. Using the algorithm of your choice, determine one possible minimum-weight spanning tree and compute its total distance, rounding your answer to one decimal place. Clearly show your steps.The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm Euclid(a,b)Require: a, b ≥ 0Ensure: a = GCD(a, b) while b ̸= 0 do t ← b b ← a mod b a ← tend whilereturn a We want to estimate its worst case running time using the big-Oh notation. Answer the following questions: a. Let x be a integer stored on n bits. How many bits will you need to store x/2? b. We note that if a ≥ b, then a mod b < a/2. Assume the values of the input integers a and b are encoded on n bits. How many bits will be used to store the values of a and b at the next iteration of the While loop? c. Deduce from this observation, the maximal number iterations of the While loop the algorithm will do.
- Let s = σ1. . . σk be a binary string of length k > 0. We say that a binary string w = w1 . . . wn contains s as a subsequence if there are k indices 1 ≤ i1 < i2, . . . < ik ≤ n such that wik = sr for every 1 ≤ r ≤ k. For example, if s = 11 then 10001, 1010 and 110 contain s as a subsequence whereas 000 and 1000 do not. Prove that the language of all binary strings containing a fixed binary string s of length k as a subsequence is a regular language.Given a set of n types of rectangular 3-D boxes, where the ith box has height hi, width wi and depth di (all real numbers). Create a stack of boxes which is as tall as possible, but you can only stack a box on top of another box if the dimensions of the 2-D base of the lower box are each strictly larger than those of the 2-D base of the higher box. It is possible to rotate a box so that any side functions as its base. It is also allowable to use multiple instances of the same type of box. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.The Virtual Weight (VW) of an integer number (which consists of more than 1 digit) is the sumof the individual digits that are composing the number. For example, consider the followingtwo numbers; 5638 and 1145, then the VW of each is calculated as following:VW(5638) = 5+6+3+8 = 22VW(1145) = 1+1+4+5 = 11Then, the VW can be classified as L (mean Low) or H (means High) using a specific cut-offvalue. For example, if the cut-off value is 15, then the VW of the number 5638 is H (High),and the VW of the number 1145 is L because 22 > 15 and 11 ≤ 15 respectivelyWrite a C++ program that: reads a positive integer n (where 5≤n≤20) from the user. If the user enters invalidnumber, then the program should continue prompting until he/she enters a valid numberwithin the specified range. Then, the program should generate n random numbers using the built-in rand()function. Every time a random number is generated, the program will classify that number as Lor H using the above method. Use a…
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- Problem Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w. Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal. In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized. All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap. You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line. Input format The first line of the input contains an integer, n - denoting the range of numbers…Which one of the following statements about Kruskal’s algorithm is false? A. It can produce a minimum spanning tree that contains a cycle. B. It is a greedy algorithm. C. It starts by sorting the edges in non-decreasing order. D. It uses a union-find data structure.Q. Given a 2d grid map of '1's (land) and '0's (water),count the number of islands.An island is surrounded by water and is formed byconnecting adjacent lands horizontally or vertically.You may assume all four edges of the grid are all surrounded by water. Example 1: 11110110101100000000Answer: 1 Example 2: 11000110000010000011Answer: 3""" def num_islands(grid): count = 0 for i in range(len(grid)): for j, col in enumerate(grid[i]): if col == 1: dfs(grid, i, j) count += 1 Please code it. .