(5) Elgamal public key cryptosystem (decryption):Start with the prime p = 17 and the primitive root g = 3.Alice sends Bob the public key A = 5.Bob encrypts the message m and sends the pair of numbers (8,2) to Alice.Alice's secret key is a = 5.Using Elgamal public key decryption, Alice computes the plaintext messagem from the ciphertext (8, 2). What is the number m that Alice obtains?

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Answered: (5) 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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[Algebraic Cryptography] How do you solve this? Second picture is for context
d out of 57 = 3 (18) + 3 g question QR + 5 ךסד Encryption of the message 'NO' by Caesar's cipher is yet ered ked out of Flag question vestion 4 -1 ot yet nswered Given that A = 3 -5 The value of 12 23 is 4 Marked out of 050 -2 7 Flag question
Suppose (n, d) = (55, 3) is the private key of an RSA cryptosystem. If the received ciphertext is C = 49 what is the corresponding plaintext? O 3 4 10 14
(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?
(b) A computer room has 36 computers, numbered from 0 to 35. Assign a computer to each of the following students by the hashing function h(k)= k mod 36 where k is the class number of the student. Solve the problem when a collision occurs (In case of collisions, the computer number will usually be assigned to the next available storage location). (i) Student number of Jerry: 138 (ii) Student number of Ray: 36 (iii) Student number of Ivy: 34 (iv) Student number of Lucy: 66 (v) Student number of Ivan: 124
Having chosen primes p and q, and suitable integers d and e, what is the public-key of our RSA cipher in this case? Select one: a. (φ(pq), e) b. (pq, e) c. (d. e) d. (p. q) Clear my choice
1.3. For this exercise, use the simple substitution table given in Table 1.11. (a) Encrypt the plaintext message The gold is hidden in the garden. (b) Make a decryption table, that is, make a table in which the ciphertext alphabet is in order from A to Z and the plaintext alphabet is mixed up. (c) Use your decryption table from (b) to decrypt the following message. IBXLX JVXIZ SLLDE VAQLL DEVAU QLB
Apply the affine cipher formula C=(5P + 2) mod 26 to encript "LASER PRINTER". JGNSA DUNTXNA JSNAS DNUTXAN JGSAN DNUTXAN JGSAN DUNXANT
(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.
1. (a) Use Fermat's Little Theorem to calculate: (i) 123578946 (mod 47) (ii) 58¹17 (mod 59) (iii) 56 +5060 +500600 + 50006000 (mod 7) (b) Messages are to be encoded using the RSA method, and the primes chosen are p = 11 and q = 13, so that n = pq = 143. The encryption exponent is e = 17. Thus, the public key is (143, 17). (i) Show that the decryption exponent d (the private key) is 113. (ii) Use the repeated squaring algorithm to find the encrypted form c of the message m = 44.
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
The ciphertext 75 was obtained using the RSA algorithm with n = 437 and e = 3. You know the plaintext is either 8 or 9. Determine which it is without factoring n.

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