(4) Elgamal public key cryptosystem (encryption):Start with the prime p = 17 and the primitive root g = 3.Alice sends Bob the public key A = 5.Bob wants to send the message m = 13 to Alice.Bob chooses the random element k = 2.Using the Elgamal public key cryptosystem, compute the pair of numbers(C₁, C₂) that Bob sends to Alice.Note: Do not work out how Alice computes the plaintext message m fromthe ciphertext (C₁, C₂).

The prime p = 17 and the primitive root g = 3Alice sends Bob the public key A = 5Bob wants to send…

Answered: (4) Elgamal public key cryptosystem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the method of undetermined coefficients to determine the form of a particular solution for the given equation. y'"' + 10y" – 11y=xe* + 4x What is the form of the particular solution with undetermined coefficients? Yp(x) = ] (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)
(RSA public key cryptosystem) Bob chooses the secret primes p = 5 and q = 11. Bob chooses the encryption exponent e = 3. Bob publishes N = 55 and e = 3. If Bob receivers the ciphertext c = 24 from Alice, what is the plaintext m that Bob obtains by deciphering c?
Let p and q be prime numbers.(1) If p is not equal to q, how many generators does Zpq have?(2) If p = q, how many generators does Zp2 have
(4) Elgamal public key cryptosystem (encryption): Start with the prime p = 29 and the primitive root g = 2. Alice sends Bob the public key A = 3. Bob wants to send the message m₁ = 15 to Alice. Bob chooses the random element k = 5. Using the Elgamal public key cryptosystem, compute the pair of numbers (C₁, C₂) that Bob sends to Alice.
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(3) Diffie-Hellman key exchange: Start with the prime p = 17 and the primitive root g = 3. (a) Alice chooses the secret key a = 4. Compute the public key A = gº (mod p) Alice sends A to Bob. (b) Bob chooses the secret key b = 3. Compute the public key B = gb (mod p) Bob sends B to Alice. (c) Use Diffie-Hellman key exchange to compute the secret key that Alice and Bob share.
a. Given p=23, q=7, and e=5, generate the public key (n,e) and the private key (n,d) using RSA Key generation algorithm. b. Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=7 to send to Bob. Show the ciphertext. c. Given Bob's public key of (85, 7) and private key of (85, 55), show how Bob can decrypt the ciphertext y=8 received from Alice. Show the plaintext. d. Using the fast exponentiation method (page 182), determine 535 mod 47
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4) Elgamal public key cryptosystem (encryption): Start with the prime p = 13 and the primitive root g = 2. Alice sends Bob the public key A = 3. Bob wants to send the message m = 10 to Alice. Bob chooses the random element k = 3. Using the Elgamal public key cryptosystem, compute the pair of numbers (C1, C2) that Bob sends to Alice. Note: Do not work out how Alice computes the plaintext message m from the ciphertext (C₁, C2).
Many online portals now use 2-Factor Authentication. After you login with your username and password, a code is sent to your phone and you have to enter this code. Assume this code is six digits long. What is the likelihood that this code will consist of at least one repeated digit? (zero is a valid digit, meaning an authentication code could consist of all zeroes. Here are examples of authentication codes with repeated digits – 000000, 154443, 112339, 556688). Please show how you would do this in excel, thank you!

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