Problem 4. The plaintext P has been encrypted with RSA n = 65, e = 29...
o-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-5x13-65 and e-5. I. Describe the key pair generation procedure for Bob to generate his private key kor- d. With the above given parameters, use EEA to calculate d 2. Describe RSA encryption procedure that Alice uses to encrypt her plaintext message x to its above given parameters, what will be y? ciphertext y before sending the message to Bob. Suppose Alice's message x-...
Decrypt the ciphertext 1369 1436 0119 0385 0434 1580 0690 that was encrypted by the RSA algorithm using with key (n, e) = (2419, 211). (Hint: The decoding exponent is d = 11. Note that it may be necessary to fill out a plaintext block by adding zeros on the left).
3. (RSA) Consider N-pq where p- 3 and q 5. (a) Calculate the value of N p. N 15 (b) Let c 3 be the encoding number. Verify that c satisfies the require- ments of an encoding number (c) Find the decoding number d. [Hint: cd Imod(p 1)(q 1).] 3dI mod 2 (d) Consider the single character message 'b' (not including the quotes) Using its ASCII code it becomes the numerical plaintext message " 98 Calculate the encrypted message ba...
(d) Decrypt the ciphertext message LEWLYPLUJL PZ H NYLHA ALHJOLY that was encrypted with the shift cipher f(p) (p+7) mod 26. [10 points] (e) [Extra Credit - 5 points] Encrypt the message "BA" using the RSA cryptosystem with key (ne) = (35,5), where n = p . q 5-7 and ged(e, (p-1) 1)) (5, 24) 1. 6. [5 points each (a) Is 2 a primitive root of 11? (b) Find the discrete logarithm of 3 modulo 11 to the base...
Question 29 1 pts In an application of the RSA cryptosystem, Bob selects positive integers p, q, e, and d, where p and a are prime. He publishes public key (e, N), where N =p'q. the number d is the decryption key. 0 = (p-1)(q-1). Select all the statements that are correct. Ifm is not equal to por q, then (m) mod N=m It must be the case that d'e mod 0 - 1 If mis not equal to por...
p=3, q=7
Suppose that Bob wants to create an example of an RSA public-key cryptosystem by using the two primes p ??? and q ???. He chooses public encryption key e He was further supposed to compute the private decryption key d such that ed 1 mod A(pq)). However, he confuses A and and computes instead d' such that ed' =1 (mod P(pq)). (i) Prove that d' works as a decryption key, even though it is not necessarily the same...
Computing RSA by hand. Let p = 13, q = 23, e = 17 be your initial parameters. You may use a calculator for this problem, but you should show all intermediate results. Key generation: Compute N and Phi(N). Compute the private key k_p = d = e^-1 mod Phi(N) using the extended Euclidean algorithm. Show all intermediate results. Encryption: Encrypt the message m = 31 by applying the square and multiply algorithm (first, transform the exponent to binary representation)....
Alice has the RSA public key (n, e) = (11413, 251) and private key d = 1651. And Bob also has his own RSA public key (n’, e’) = (20413, 2221) and private key d’ = 6661. Alice wants to send the message 1314 to Bob with both authentication and non-repudiation. Use Maple, calculate what is the ciphertext sent by Alice. And Verify that Bob is able to recover the original plaintext 1314.
(16 pts) In the RSA public key cryptography system (S,N,e,d,E,D), let p = 347, q = 743, and N = 347 · 743 = 247821. (a) (8 pts) Which of the two numbers 4193, 4199 can be an encryption key, and why? If one of them can be an encryption key e, find its corresponding decryption key d. (b) (8 pts) How many possible pairs (e,d) of encryption and decryption keys can be made for the RSA system? (If you...
Crypotography Question 1. A message m was encrypted using the RSA algorithm with n=899 and e=13. The ciphertext is 706. Find the message m. Show all the work from the scratch, including finding 1/e(using the extended Euclidean algorithm) and the resulting modular exponentiation...