Question 2:
You are Alice. Bob publishes his ElGamal public key (q, a, ya) = (101, 2, 14). You desire to send the secret message “CALL ME” to Bob. Using the equivalence A = 01, B = 02, and so on up to Z = 26, you encode the message into the number 03 01 12 12 13 05. Regarding each of these two-digit numbers as a plaintext block, compute the message that you will send to Bob using his public key. This requires you to pick a “random” number k; use k = 32.
You are Bob. You get a message from Alice. You like Alice a lot, so you are eager to read the message. Use your secret key (101, 2, 10) to decrypt Alice’s message. Notice that you don’t need to know what value of k Alice used in order to do this.
The public key to encrypt message (101,2,14).
Now we calculate the encrypted message for each plaintext block using k=32.
Encrypted message is pair (c1,c2) for each plaintext.
c1=gkmod p and c2=m*(ga)k mod p
Here g=2, p=101 and ga=14
03 : c1= 232mod 101= 68 and c2= 3* (14)32mod 101 =83 so (68,83)
Using calculation as above:
01 : k=66 (13,87)
12:k=5 (32,89)
12 : k= 45 (41,89)
13:k=17 (75,78)
05: k=67 (26,30)
Now to decrypt the message we have private key 10.
Message decrypted by:
m= c2 * (c1)-xmod p
here x=10 and (c1)-x is basically mod inverse p of (c1)x
Using this message is decrypted as:
(68,83)= mod inverse p of (c1)x =84 ,m=(84*83)mod 101=3
(13,87)= mod inverse p of (c1)x =36 ,m=(36*87)mod 101=1
(52,89)= mod inverse p of (c1)x = 95,m=(95*89)mod 101=12
(41,89)= mod inverse p of (c1)x = 100,m=(100*89)mod 101=12
(75,78)= mod inverse p of (c1)x = 17,m=(17*78)mod 101=13
(26,30)= mod inverse p of (c1)x = 17,m=(17*30)mod 101=5
So message decrypted= 03 01 12 12 13 05
Question 2: You are Alice. Bob publishes his ElGamal public key (q, a, ya) = (101,...
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...
Need help!! please explain — crypto math thank you!! 7. Alice and Bob use the ElGamal public key cryptosystem with p 19, and a 3. Bob chooses the secret x = 4, What is β? Alice sends the ciphertext (2.3). What is the message? 8. The points (3, +5) e on the elliptic curve y2-a3 2. Find another poin with rational coordinates on this curve. 9. For the elliptic curve y2--2 (mod 7), calculate (3,2)(5,5) 0. Let P (,0) be...
Bob publishes his public key (e, N) = (109, 221) Show that if Eve can factor N (N = 13 middot 17), then she can determine Bob's private key d. What is Bob's private key? Now suppose that Eve intercepts the message 97. Use Bob's private key to decrypt the message
Bob wants to send an encrypted message using public key cryptography to Alice. What key does he use for encryption? You need to be explicit whose key it is and what kind of key it is. 1 AB I
The Diffie-Hellman public-key encryption algorithm is an alternative key exchange algorithm that is used by protocols such as IPSec for communicating parties to agree on a shared key. The DH algorithm makes use of a large prime number p and another large number, g that is less than p. Both p and g are made public (so that an attacker would know them). In DH, Alice and Bob each independently choose secret keys, ?? and ??, respectively. Alice then computes...
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-...
Bob uses p = (141, 19) as his public key and S = 21 as his secret key. Is Bob's system correct? Please show all work and explanations. Thank You
5.6 Exercise. Describe an RSA Public Key Code System based on the primes and 17. Encode and decode several messages Of coursc, the fun of being a spy is to break codes. So get on your trench coal, pull out your magnifying glass, and begin to spy. The next exercise asks you to break an RSA code and save the world 5.7 Excrcise. You are a secret agent. An evil spy with shallow mumber thery skills uses the RSA Public...
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,...
Write code for RSA encryption package rsa; import java.util.ArrayList; import java.util.Random; import java.util.Scanner; public class RSA { private BigInteger phi; private BigInteger e; private BigInteger d; private BigInteger num; public static void main(String[] args) { Scanner keyboard = new Scanner(System.in); System.out.println("Enter the message you would like to encode, using any ASCII characters: "); String input = keyboard.nextLine(); int[] ASCIIvalues = new int[input.length()]; for (int i = 0; i < input.length(); i++) { ASCIIvalues[i] = input.charAt(i); } String ASCIInumbers...