Question: (2) This exercise is about the DiieHellman exchange protocol. Alice and Bob agrees to use the public prime p = 1051 and the public primitive

(2) This exercise is about the DiieHellman exchange protocol. Alice and Bob agrees to use the public prime p = 1051 and the public primitive root or = 7. Alice also chooses a secret random number 1? = 113. And Bob chooses a secret random number 1!; = 53. (3.} Describe what information Alice and Bob send each other. Justify your a11 swer. {b} Determine the shared secret that each obtains. {c} Suppose that Eve witnesses this entire exchange, the information that Alice sent to Bob. the information that Bob sent to Alice, and the public informa tion ofthis exchange. That is. Eve has p = 1051. (1 = 7, or\" (mod 1051) = 7113 (mod 1051). and (15' (mod 1(151] = 753 (mod 1(151}. Eve cannot compute dis crete logarithms directly, but she is able to compute modular exponentiation with positive exponents only. Describe hovr she can obtain Alice's and Bobs shared secret, namely or"?! (mod 10:31}; this involves solving the necessaryr equations that Eve should solve. Note: In this Whole question, you may use sagemath to compute the intermediate modular exponentiations that you will encounter

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

011401 1 ALVVJL'JUL U (2) This exercise is about the DifeHellrnan exchange protocol. Alice and Bob agrees to use the public prime p : 1051 and the public primitive root (1 : 7. Alice also chooses a...

Diffie-Hellman exchange protocol. Alice and Bob agrees to use the public prime p = 1051 and the public primitive root a = 7. Alice also chooses a secret random number r= 113. And Bob chooses a secret...

The purpose of Diffie-Hellman key exchange algorithm is to enable two users to exchange a key securely that can be used for subsequent encryption of message.For example, if Alice and Bob agree on a...

using python Problem 5: Diffie-Hellman a. Write a function DH(p,A,y) for Bob that takes as input a prime p, Alice's public key A and Bob's private key y and returns their common secret key S. b. Test...

1. Alice and Bob agree to use the prime p = 1373 and the primitive root g = 2 for communications using the ElGamal public key cryptosystem. (a) Alice chooses a = 947 as her private key. What is the...

Alice and Bob wish to use the Diffie - Hellman key exchange. They agree to use the prime 3 7 and base g = 5 . Bob's private keys is k B = 5 . Alice sends her public key A = 1 6 to Bob. ( a ) Is g...

The basic problem of cryptography is the following: Alice and Bob want to communicate over a public channel such that an eavesdropper cannot understand their communication. For that reason, they...

1. Alice and Bob want to establish a common key pair using the Diffie-Hellman key exchange protocol and then use it in to send each other messages using a symmetric cipher. They agree by email on a...

Describe the steps that Alice and Bob follow when they use the Diffie-Hellman key exchange protocol to generate a shared key. Assume that they use the prime p = 23 and take a = 5, which is a...

Discuss the three dimensions of channel structure that should be considered in developing alternative channel structures.

Josit Ltd. initiated a one-person pension plan in January 2005 that promises the employee a pension on retirement according to the following formula: pension benefit = 2.5% of final salary per year...

The business is a separate entity, so the activities of a business must be kept separate from any other financial activities of its business owners

At the beginning of 2024, Glasson Academy reported a balance in common stock of $166,000 and a balance in retained earnings of $66,000. During the year, the company issued additional shares of stock...