Encrypt the message STOP using the RSA cryptosystem with key (2537, 13). Note that 2537 = 43 ⋅ 59, p = 43 and q = 59 are primes, and gcd(e, (p − 1)(q − 1)) = gcd(13, 42 ⋅ 58) = 1.

Q: 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678).

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Q: A. 5x = -127 mod 15.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Q1: Given that totient (337) is 336, what is 69^673 (mod 337)?

A: Here in question totient function is used it is nothing but same as eular phi(∅(n)) function which…

Q: Solve the quadratic congruence, 6x²-7x+2 ≡ 0 mod 31.

A: We have to solve the above quadratic congurence.

Q: Q16

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Q: 31 = 10 mod 3. :Select one True False

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Q: Solve 34X=77 mod 89 3. Solve

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Q: ions of the congruence 15x^2 + 19

A: Given:- 15x2+19x≡5 mod 55

Q: Solve 271044 = ... (mod59)

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Q: congruences 4* = 13 (mod_17) and 54 (mod 19).

A: Given congruences are: 4x≡13mod 175x≡4mod 19 We have to solve the given exponential congruences.

Q: Solve the linear congruence 2370x ≡ 69 (mod 2517) or say why no solutions exist

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Q: y = 3x - 5 mod 26 СРHТXT

A: Let us consider the equation y≡ax+b(mod 26) To decrypt the message  Convert the equation in terms…

Q: Fill in the following blanks. Suppose you are finding 15^-1 (mod 131). This problem is equivalent to…

A: Answer follows

Q: DONT USE AI, USE PENCIL AND PAPER WHILE DOING IT. SHOW ANSWER AND RESULTS An RSA cipher has public…

A: Step 1 The given information is as follows:public key pq = 65e = 7 Step 2 (a) Encrypting the message…

Q: Solve the congruence 11x = 45 (mod 97) where x is an integer in the interval [0,97).

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Q: Which of the following linear congruence has 1 incongruent solution? (a) 3x = 9 (mod21) (b) 14x = 12…

A: The solution is given as

Q: 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678).

A: We need to find the GCD(12345,678)=?

Q: (d) (e) (f) Assume that a 15 = 1 Find the value of ord41a. mod 41 and a #1 mod 41. How many…

A: As per the question we have to find : ord41(a) , where a15 ≡ 1 mod 41 but a ≠ 1 mod 41 total number…

Q: Does x2 +3x+7=0 mod 31 have solutions? IF

A: This follows in the same way as we study quadratic equations. Here we use facts about quadratic…

Q: If you multiply n whole numbers (even or odd) when is the answer odd? Translate into multiplication…

A: If we multiply whole numbers, the pattern is as follows: Even × Even=Even Even × Odd=Even Odd ×…

Q: Find all solutions for x, up to congruence. (b) x ≡ 11 mod 142 and x ≡ 25 mod 86.

A: Given: (b) x≡11 mod 142 and x≡25 mod 86 To find: All solutions for x, up to convergence.

Q: SorvE THモ CONGROEモNしE 626 X Rエ mod5

A: As 5 is an odd number, by fermat's theorem, we have             x5-1 = 1 (mod 5)           => x4…

Q: Solve the congruence3x−7 = 2 (mod 16). Your solution should be positive and reduced modulo16.

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Q: (a) Find all solutions r to the congruence 341x = 16 mod 912

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Solve the congruence: 341x + 19 = 291 (mod 9).

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Q: Find an integer A so that: A79 = 7 (mod 277) Please solve step by step thanks!

A: Given an equation. Let's solve for A.

Q: 6. Find all incongruent solutions to each congruence. Show your steps. (a) 135x = 108 (mod 612) (b)…

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Q: If possible, solve the following linear congruences. (a) 42x = 1014 (mod 91) (b) 42x = 1015 (mod 91)

A: If possible, we have to solve the following linear congruences.

Q: Find the solution of the following equations: 6x = 1(mod 33), 7x 1(mod 9)

A: If the given congruence equation is:.It is known that if a and m are relatively prime, then the…

Q: Take the last four digits ABCD of your student identification number, and let AB and CD be the…

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Q: 3. Solve the following congruences. † (a) 10x = 5 (mod 21) (b) 10x = 5 (mod 15) † (c) 10x = 4 (mod…

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Q: k from problem 2 and the method used in the example at the end of solve the congruence: 7x³ = 6…

A: Given: Congruence is To Find : Solve the congruence equation

Q: Solve the quadratic congruence x² = 35 (mod 817).

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Q: (b) If the public key for an RSA cryptosystem is (N, e) = (69,5), find the private key d.

A: We follow the standard techniques use in the RSA algorithm. The detailed typeset solution is…

Q: ind all solutions of the linear congruence: 9x = 5 mod (14)

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Q: Solve the congruence x² = 9 (mod 600).

A: Given congruence is x2≡9 mod 600

Q: Solve the system 2.x = 3(mod 5) 3r 2(mod 7) I = 2(mod 6)

A: As per our guidelines we supposed to solve the very first question when multiple questions are…

Q: Solve the congruences: 52x + 4 = 8(mod 22) 17x = 19(mod 100) 3x = 9(mod 12)

A: