5. (6 points + 4 points) Given p-71, 9-97, find o(n). If e - 197, find...
(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...
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...
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...
For the RSA encryption algorithm , do the following (a) Use p=257,q=337(n=pq=86609),b=(p-1)(q-1)=86016. Gcd(E,b)=1, choose E=17, find D, the number which has to be used for decryption, using Extended Euclidean Algorithm (b) One would like to send the simple message represented by 18537. What is the message which will be sent? (c) Decrypt this encrypted message to recover the original message.
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-...
4. Suppose you wish to encrypt the message, M 42 using RSA encryption. Given a public key where p- 23 and q-11 and the relative prime e- 7. Find n, and show all necessary steps to encrypt your message (42). (Hint: check p.411 of the text for information on public key RSA) (5 points)
Problem 4. The plaintext P has been encrypted with RSA n = 65, e = 29 to yield the ciphertext C = 3 = P29 mod 65. Find P using the decryption key d, and prove the congruence class of P that solves this congruence is unique.
Discrete Structures problem Suppose we use p = 7 and q = 5 to generate keys for RSA. a) What is n ? b) What is on)? c) One choice of e is 5. What are the other choices for e? d) Explain how you got your answer for part c. e) For the choice of e = 5 what is d? Show work. f) Using the public key (n, e), what is the message 3 encrypted as? Show work...
Consider the RSA algorithm. Let the two prime numbers, p=11 and q=41. You need to derive appropriate public key (e,n) and private key (d,n). Can we pick e=5? If yes, what will be the corresponding (d,n)? Can we pick e=17? If yes, what will be the corresponding (d,n)? (Calculation Reference is given in appendix) Use e=17, how to encrypt the number 3? You do not need to provide the encrypted value.
Exercise 4: Suppose Bob's set of RSA keys includes p 17, q 23, and e 5. Determine Bob's public and private keys. Show how Alice would encrypt the message M 200, and show Bob's decryption of the message. Exercise 4: Suppose Bob's set of RSA keys includes p 17, q 23, and e 5. Determine Bob's public and private keys. Show how Alice would encrypt the message M 200, and show Bob's decryption of the message.