(b) The affine cipher E is given by E(x) = 17x - 3 (mod 26). The conversion table for letters and numbers is shown below. A C E F H J K M 2 3 4 8. 9. 10 11 12 Q R T U V W Y 13 14 15 16 17 18 19 20 21 22 23 24 25 (i) Show that -3 is a multiplicative inverse of 17 modulo 26. (ii) Suppose that you receive the enciphered message 8, 23, 10, 11. Decipher the message and deduce the word that was sent.

Q: 1 -1 0 1. Let A=(23¹), B(4). 3 -5 (a) Compute AB and BA. (b) Compute A + B and B + A. (c) If c = 3,…

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Q: (d) (x² + 2x + 1)q(x) = 1 (mod x³ + x² + 1) over Z3

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Q: 8. Find the remainder of x2021 + x2020 + 1 modulo x2 – 1 in Q[x].

A: Remainder of the Polynomial

Q: Show that x2 = Y mod p has

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Q: et x, y E Z. We have (x+y)³ = (x+y)² (x+y) = (x² +2xy+y?)(x+y) = (x³+3x?y+3xy² + y³) = x³ + y3 od 3.

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Q: The affine cipher E is given by E(x) ≡ 15x − 7 (mod 26). The conversion table for letters and…

A: E(x) = 15x - 7 (mod 26) Therefore, the decryption is given by D(y) = 7•(y+7) (mod 26)

Q: 4. Find the principal representative of each of the following: x³ -x + 1 mod x + 2 in Q[x] i. x3 ii.…

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

A: Here we will prove the given statement.

Q: 3. Let h: Z→ Z be the function h(r) = = x mod 4. Find h-¹(0), h-¹({0, 1, 2, 3}), and h-¹(4). Explain…

A: In this question we can easily observe that that output of the function is the remainder when any…

Q: (2) (a) Find all of the solutions modulo 15 to 6x = 15 mod 18. Express your answer in terms of the…

A: Given, 6x≡15 mod 18. As it is known that, an≡bn mod cn ⇔ a≡b mod c. Therefore, we have 6x≡15 mod 18…

Q: The product of 3371 and 1259 is 4244089. What is the gcd of 3371 and 4244089? 01 O 1259 O 3371…

A: Topic - Greatest Common divisor We are given, Product of 3371 and 1279 is 4244089

Q: 1.42. Encode the following phrase (including capitalization, spacing and punctua- tion) into a…

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Q: The affine cipher E is given by E(x) ≡ 15x − 7 (mod 26). The conversion table for letters and…

A:

Q: -3 Let A = -1 -12 -5 5 20 -47] -21 80 Use the fact that det (A) = 5 to compute -6 -2 10 -10 40 -94…

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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.

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

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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: SetS = round(10 ∗ rand(5));S = triu(S, 1) + eye(5)S = S' ∗ ST = inv(S) The exact inverse of S should…

A: These are basic MATLAB commands, this is done on the MATLAB window and results are shown below:

Q: 2 19) Find the value(s) of k such that A = [13] has an inverse. What is the inverse of A?

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