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 prime
q = 2 3 and a primitive root a = 5 .
a. If Bob has a public key YB = 1 0 , what is Bob’s private key
YB?
b. If Alice has a public key YA = 8 , what is the shared key K with
Bob?
c. Show that 5 is a primitive root of 23.
Question3 : In the Diffie–Hellman protocol, each participant
selects a secret number x and sends
the other participant ax
mod q for some public number a. What would happen if the
participants sent each other xa for some public number a instead?
Give at least one
method Alice and Bob could use to agree on a key. Can Eve break
your system with-
out finding the secret numbers? Can Eve find the secret
numbers?
Question4: This problem illustrates the point that the
Diffie–Hellman protocol is not secure
without the step where you take the modulus; i.e. the “Indiscrete
Log Problem” is
not a hard problem! You are Eve and have captured Alice and Bob and
imprisoned
them. You overhear the following dialog.
Bob: Oh, let’s not bother with the prime in the Diffie–Hellman
protocol, it will
make things easier.
Alice: Okay, but we still need a base a to raise things to. How
about a = 3?
Bob: All right, then my result is 27.
Alice: And mine is 243.
What is Bob’s private key XB and Alice’s private key XA? What is
their secret com-
bined key?
Question5: Section 10.1 describes a man-in-the-middle attack on the
Diffie–Hellman key
exchange protocol in which the adversary generates two
public–private key pairs for
the attack. Could the same attack be accomplished with one pair?
Explain.
Question6: Is (5, 12) a point on the elliptic curve y2
= x 3 + 4 x - 1 over real numbers?
Question7 : This problem performs elliptic curve
encryption/decryption using the scheme out-
lined in Section 10.4. The cryptosystem parameters are E11(1, 7)
and G = (3, 2). B’s
private key is nB = 7.
a. Find B’s public key PB.
b. A wishes to encrypt the message Pm = (10, 7) and chooses the
random value
k = 5. Determine the ciphertext Cm.
c. Show the calculation by which B recovers Pm from Cm.
Question8: The following is a first attempt at an elliptic curve
signature scheme. We have a global
elliptic curve, prime p, and “generator” G. Alice picks a private
signing key XA and
forms the public verifying key YA = XAG. To sign a message M:
■ Alice picks a value k.
■ Alice sends Bob M, k, and the signature S = M - kXAG.
■ Bob verifies that M = S + kYA.
a. Show that this scheme works. That is, show that the verification
process produces
an equality if the signature is valid.
b. Show that the scheme is unacceptable by describing a simple
technique for forging
a user’s signature on an arbitrary message.
(Don’t forget to show your work briefly.)
As per Chegg policy for multiple questions we have to do only first question unless specified by the user.
Thank you!
Question1: Alice and Bob use the Diffie–Hellman key exchange technique with a common prime q =...
5. Diffie-Hellman key exchange. Alice and Bob use Diffie-Hellman key exchange protocol to communicate in secret. They publicly announce a prime number p = 23 and a primitive root r = 5 under modulus 23, Alice picks a secret key a-6 and in turn receive the key ß-19 from Bob (a.) (2 points) What is the key that Alice sends to Bob? b) (2 points) What is the shared secret key?
Diffie-Hellman Key Exchange: Alice and Bob wants to agree on a key. First, both agree on p = 23 and g = 5 which is public. Alice chooses her secret key xA = 8 and Bob xB = 14. (a) What will be the shared secret key? (b) DH Key exchange is vulnerable to the following attack. Adversary sits between Alice and Bob, intercepting all messages. Alice and Bob thinks they talk to each other while in fact both talking...
users A and B use the Diffie-Hellman key exchange technique with a common prime p=107 and a primitive root g=5. If user A has private key 112 and publick key 3 and user B has private key 146 and publick key 19 Find the following Ans If user C just joined the group and his private key is 6. what is the security key between A and C? what is the security key between B and C?
In a Diffie-Hellman Key Exchange, Martha and John have chosen prime value q = 19 and primitive root a = 10. If Martha's secret key is 4 and John's secret key is 6, determine the following three values: The value Martha sends to John. The value John send to Martha The shared key they exchanged.
Find Alice and Bob’s secret number in Diffie-Hellman key exchange if g=5, p=103, A = 102, B = 94.
Answer all of it asap Discrete mathematics Problem 10 (10 pts) Alice and Bob would like to exchange a key using the Diffie-Hellman protocol that uses the following public information: the cyclic group Zio, and 5 as its base element. Alice: If she chooses 3 as her private key, which element does she send to Bob. Bob: If he chooses 4 as his private key, which element does he send to Alice Key-Exchanged: What is their Private Key exchanged. Problem...
The Diffie-Hellman key exchange is vulnerable to the following type of attack. An opponent Carol intercepts Alice’s public value and sends her own public value to Bob. When Bob transmits his public value, Carol substitutes it with her own and sends it to Alice. After this exchange, Carol simply decrypts any messages sent out by Alice or Bob, and then reads and possibly modifies them before re-encrypting with the appropriate key and transmitting them to the other party. Choose all...
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...
The Diffie-Hellman key exchange is vulnerable to the following type of attack. An opponent Carol intercepts Alice’s public value and sends her own public value to Bob. When Bob transmits his public value, Carol substitutes it with her own and sends it to Alice. After this exchange, Carol simply decrypts any messages sent out by Alice or Bob, and then reads and possibly modifies them before re-encrypting with the appropriate key and transmitting them to the other party. Choose all...
In this question, you need to compute the key computed using the Diffie Hellman key exchanged process. Suppose the prime is 31 and the primitive root is 3. Find the public keys when the two parties choose 7 and 9 as their private keys. Next find the shared Key computed by both parties. HINT: Once you know how to the formula works, it is very easy to simply use Excel to look for the public keys and to calculate K....