given as, [10 18 1 A = 17 1 3 4 7 21. If the key matrix is then Compute A-1 mod 26. (Hint: Row reduce the augmented matrix using modulo 26 calculations. Recall that the modulus of a number N is the reminder after dividing by the modulus M. For example, 55 is equal to (we say "congruent to") 3 modulo (or “mod 26") since 55 = 2(26) + 3.)

Q: Show that the permutations (12) and (12345) generate S5.

A: We have to show that the permutation 12 and 12345 generates S5. Suppose H=12,12345. We know that…

Q: True or False. Provide justification. The system x ≡ 3 mod 18 and x ≡ 7 mod 20 has a unique solution…

A: We see, possible solutions to x ≡ 7 mod 20 modulo 180 are     x ≡ 7, 27, 47, 67, 87, 107, 127, 147,…

Q: 1. modular arithmetic is the basis of many crypto-systems. Compute the result without a calculator.…

A:

Q: 7. Without performing actual division, determine whether 1 010 908 899 is divisible by 7, 11 and 13.

A: As per rule I need to solve only first question.

Q: 4444 is divided by a 1.19) find the remainder when 4444 * 2?=-1 (mod a).

A: 1.19 We have 4444  ≡  7 (mod 9). So, 44444444 ≡ 7 4444 (mod 9) Now,       73 ≡1 (mod 9) Or,…

Q: Use A-¹ to decode the cryptogram. 1 2 2 3 7 9 -4 -2 11 -2 29 100 -55 3 247 -9 6 58 -8 9 63 -29 -9 97…

A:

Q: Consider the product of cycles (1 2)(4 7 8)(2 1)(7 2 8 1 5) that are permutations of {1, 2, 3, 4, 5,…

A:

Q: Use the inverse of the matrix to decode the cryptogram 13 −26 21 33 −53 −12 18 −23 −42 5 −20 56 −24…

A: The given matrix, A=1-22-1131-1-4 using the inverse matrix to decode the cryptogram 13  -26  21  33…

Q: Find the four solutions of x* = 1 (mod 13).

A: Since you have asked multiple questions we will solve the first question for you .To get any…

Q: C1. A. 32 B. 234 C. 238 The multiplicative inverse of 177 mod 260 is D. 37 E. does not exist F. none…

A: To find the multiplicative inverse of 177(mod260).

Q: 3. Show that ifn = 2 (mod 4), then 9" + 8" is divisible by 5.

A: Here we will prove the given statement.

Q: # In this excercise 6, write B combination if possible. 6. B A3 alpheap. of the other matrices - =…

A: It is given that the four matrices are B=23-42, A1=1001,A2=0-110,A3=1101. Objective is to check…

Q: Let -1 9 -1 1 1 2 0 |and P =| 0 0 1 1 0 5 A = 1 %3D 0 15 -2 Given that P diagonalizes A, then…

A:

Q: If a = 8(mod19) and b = 6(mod19), which of the following is the least residue of a × b modulo 19? ●…

A:

Q: 5. Solve x³x+15= 0 (mod 63). (Don't just list solutions! Consider modulo 7 and 9 then use the…

A: As given in the hint we use the Chinese Remainder Theorem to solve this question. The details…

Q: a60 = a(mod 1001) a61 = a (mod 1001) This option This option

A:

Q: Problem 3 (1) Show carefully that gcd(71, 97) = 1. (2) Is 71 a unit modulo 97? If yes, explain why…

A:

Q: Consider the pseudorandom number generator given in our lessons: with Uf +1 = (auf + b) mod m…

A:

Q: if a-1 is the inverse of a mod m and b-1 is the inverse of b mod m then a-1b-1 is the inverse of ab…

A:

Q: Informal Exercise 20. Observe that 4| 102. Show that to find Rem(n, 4), you just need to replace n e…

A: We need to find the remainder when n is divided by 4 .

Q: How many ways can the letters in BIBBIBIA be arranged so that the 3 I's appear in consecutive…

A:

Q: côngri 8.8. Use the technique of the previous problem to solve the following systems of congru-…

A:

Q: #5. Suppose that a = 2 (mod 113), and b = 5 (mod 113) What is (a b + 56b + 155) mod 113?

A: given a≡2(mod113),b=5(mod113)a3≡23(mod113)a3b≡235(mod113)56b≡280(mod113)56b≡54(mod113)155≡15mod113)

Q: 2. Make a table for each of and ®: 1 3 1 4 1 2 3 4 4 3. 2. 4. 2. 1. 2. 3.

A:

Q: 4. Convert (101001000)2 from binary to decimal notation and (1984)j10 from decimal to binary…

A:

Q: given matrices to compute the given expression. 9 8 -3 3 -7 5 and B: 8 1 1 O Let A = -2 4 -2 Find…

A:

Q: Define the following operation on Zn: { [1] if a = b (mod 5) [0] if a zb (mod 5) (a] * (b] = (a) Is…

A: Binary Operation : Let S be a non-empty set, then a map f : S×S →S defines a binary operation.…

Q: Consider a 3 by 3 matrix A, where a11, a22, a33 and are all zero and a₁1 = a31. Suppose |A| ‡ 0, how…

A: Given: Let us consider a 3×3 matrix. Here a11,a22,a33 =0 and a11=a31 To show: Suppose A≠0 then find…

Q: Theorem 5.3. Let a be an odd integer. If a3 we have (29) a 2 = 1 (mod 2º), so there are no primitive…

A: Proof:                 We shall prove by induction on α. First we consider α=3. Let α be an odd…

Q: Exercise 6.3.4. Find all solutions modulo 10 to x² + 3x = 0 (mod 10). There are two distinct…

A: We employ the chinese remainder theorem to find the four solutions. Details typeset in latex in step…

Q: QUESTION 7 1.5 Consider the linear congruence 6x = 5 mod 7 The multiplicative inverse of 6 is mod…

A: All the sub-parts of the given question has been solved in step 2.

Q: 22. Which of the following integers are the possible one's digits of a fourth power of any 0, 1, 5…

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Let a = (17 3)(5 9 4 2) and B = (2 3)(7 4)(5 1 8) be elements of S10. Then, a'B is O (1 4)( 27 58 9…

A: Alpha square beta inverse is : (1 4)(2 7 5 8 3 9) Third option is correct.

Q: Consider the system of linear congruences 4x +9y= 2 (mod 11) 2x+2y = 7 (mod 11) V Suppose that the…

A: “Since you have posted multiple questions, we will provide the solution   only to the first question…

Q: 2. Show that 1184 – 534 is divisible by 7. -

A:

Q: p = 39 is not prime. Find a number a that has no inverse z ( mod 39). This means that az = 1 (mod…

A:

Q: a. Find the inverse of 43 (mod 256) b. Solve the linear congruence 43x=7(mod 256)

A:

Q: duce the expression for u to 2(5 ,Y = (1+5P) +4 (mod 2p - 1) or simply, to 2u, = 1+5P-1(mod 2p - 1).…

A:

Q: Please answer very soon will give rating surely

A: To perform the MixColumns steps of SAES if the current state of the encryption process is given by…