Bob chooses 7 and 11 as p and q prime numbers. Now he chooses two exponents e to be 13, then d is 37. Note e * d mod 60 = 1 i.e. they are inverse to each other. Now imagine that Alice wants to send the plaintext 5 to Bob. She uses RSA algorithm to encrypt the message (perform encryption). Also, show your work how Bob perform decryption operation in order to extract plaintext.
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Bob chooses 7 and 11 as p and q prime numbers. Now he chooses two exponents...
In a RSA cryptosystem, a participant A uses two prime numbers p = 13 and q = 17 to generate her public and private keys. If the public key of A is 35, then the private key of A is 11. Alice wants to encrypt a message to Bob by using the RSA algorithm and using keys in (A) The plaintext = “HI”. Answer: _______________
Alice has a message M=51 to send to Bob securely using ElGamal encryption algorithm. Bob chooses p= 8167, g=4063, x=71. Alice chooses r=29. Show the encryption and decryption steps.
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...
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-...
5. Consider the RSA encryption scheme, Alice wants to send a message to Bob. Both Alice and Bob have p= 17,9 = 19. Alice has e=31 and Bob has e=29. a. What is the public key pair used in the transmission? 2 marks b. What is the secret key pair used in the transmission? 4 marks c. Encrypt the message m=111. 4 marks d. Decrypt the resulting ciphertext. 4 marks e. What's the security problem between Alice and Bob? How...
2. Alice is a student in CSE20. Having learned about the RSA cryptosystem in class, she decides to set-up her own public key as follows. She chooses the primes p=563 and q = 383, so that the modulus is N = 21 5629. She also chooses the encryption key e-49. She posts the num- bers N = 215629 and e-49 to her website. Bob, who is in love with Alice, desires to send her messages every hour. To do so,...
Suppose that Bob, very concerned with security, selects an encrypting modulus n=pq where p and q are large primes. Suppose he also chooses two encrypting exponents e1 and e2. He asks people sending him messages to “double encrypt” their messages as follows. For each plain text (an element of Zn), he asks them to encrypt it using RSA with modulus n and encrypting exponent e1, and then encrypt the result of that using RSA with modulus n and encrypting exponent...
5. We must assume that keys are not secure forever, and will eventually be discovered; thus keys should be changed periodically. Assume Alioe sets up a RSA cryptosystem and announces N = 3403, e = 11. (a) Encrypt m = 37 using Alice's system (b) At some point. Eve discovers Alice's decryption exponent is d = 1491. Verify this (by decrypting the encrypted value of rn = 37). (c) Alice changes her encryption key to e = 31, Encrypt rn...
Question1: Alice and Bob use the Diffie–Hellman key exchange technique with a common prime q = 1 5 7 and a primitive root a = 5. a. If Alice has a private key XA = 15, find her public key YA. b. If Bob has a private key XB = 27, find his public key YB. c. What is the shared secret key between Alice and Bob? Question2: Alice and Bob use the Diffie-Hellman key exchange technique with a common...
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)....