Question

You and I want to communicate using RSA. I have found a “large” prime for us...

You and I want to communicate using RSA. I have found a “large” prime for us to use, n=33 (3*11).

a) Calculate the totient and come up with the smallest possible private key that will work. Justify that this private key is good (point out what has to be true).

b) Calculate the associated public key. Start at least by writing down what has to be true for a value to be the public key.

c) What are your public and private key pairs?

Homework Answers

Answer #1

-----------------------------------------------------------------------------------

It is given that n = 33

Since, n = pq

p = 3, q = 11

-------------------------------------------

a)

Totient

We have to find the smallest possible private key d such that

where

Lets us find all possible values of e, such that 1 < e < 20 and for each e we will find corresponding d, then we will finally select d, e such that d is smallest

With  1 < e < 20, and gcd(e, 20) = 1 ,

The possible values for e are 3, 7, 9, 11, 13, 17, 19

We find d such that (de) mod 20 = 1

When e = 3, d = 7, since, 21 mod 20 = 1

When e = 7, d = 3, since, 21 mod 20 = 1

When e = 9, d = 9, since, 81 mod 20 = 1

When e = 11, d = 11, since, 121 mod 20 = 1

When e = 13, d = 17, since, 221 mod 20 = 1

When e = 17, d = 13, since, 221 mod 20 = 1

When e = 19, d = 19, since, 361 mod 20 = 1

Clearly when d = 3 is the smallest possible value for private key,

and e = 7 is the corresponding public key

-------------------------------------------

b)

When d = 3

Associated public key => e = 7

Public key e must satisfy

and   

When d = 3, e = 7, (de) mod 20 = 1

gcd(7, 20) = 1

-------------------------------------------

c)

Public key pair => (e, n) = (7, 33)

Private key pair => (d, n) = (3, 33)

----------------------------------------------

I hope this helps you,

Please rate this answer if it helped you,

Thanks for the opportunity

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Good afternoon interns, As you all know, you are all vying for the 15 openings to...
Good afternoon interns, As you all know, you are all vying for the 15 openings to be offered at the end of the internship. Another chance has come up for you to show us that you deserve one of those positions here at Firmament Financials Inc. New clients, Mr. and Mrs. Perez are planning on starting a family and would like to start saving for their child’s college education. The want to know what they can afford when their child...
This laboratory assignment involves implementing a data structure called a map. A map associates objects called...
This laboratory assignment involves implementing a data structure called a map. A map associates objects called keys with other objects called values. It is implemented as a Java class that uses arrays internally. 1. Theory. A map is a set of key-value pairs. Each key is said to be associated with its corresponding value, so there is at most one pair in the set with a given key. You can perform the following operations on maps. You can test if...
Part III – Something's Not Right “It’s good to have you home, honey. I missed you....
Part III – Something's Not Right “It’s good to have you home, honey. I missed you. How was the flight?” Stacey had come to the airport to pick Frank up and she leaned over to kiss him as he climbed into the car with his luggage. “How were the meetings? You look tired,” she added. “The past week was intense and I am exhausted. I thought I would manage some R & R during the trip, but no such luck....
Kirby walked into Nancy’s office and said, “I need to talk to you.” He then closed...
Kirby walked into Nancy’s office and said, “I need to talk to you.” He then closed the door and said, “I didn’t appreciate it when you challenged my new production scheduling plan in the meeting. If you had real concerns, why didn’t you wait to talk to me in private? It’s embarrassing to have someone trash my ideas and I don’t want it to happen again.” Nancy, taken by surprise by Kirby’s response replied, “Well, I’m sorry if I embarrassed...
Task In your accounting career you will be required to analyse current accounting issues and communicate...
Task In your accounting career you will be required to analyse current accounting issues and communicate your theoretical understanding to your professional colleagues and your clients. For this assignment assume that you are the senior accountant working for a major firm. Question 1 - 9 marks (1,500 words) The CEO has forwarded to you an interesting article and requires you to provide her with a deeper theoretical understanding of the issues discussed so that she can fully engage in the...
In narrative essay format, I want you to address a business/organization case study using multiple concepts...
In narrative essay format, I want you to address a business/organization case study using multiple concepts from class. The case question and case text begin on page 5 of this document. You need to demonstrate their best understanding of management and organizational behavior theory, and the application of those ideas to improve the understanding of various issues. You need to clearly identify at least 3 distinct, substantive issues. For each issue you need to 1), identify evidence from the case...
1. You have gotten your dream job, which comes with the benefit of a 401(k) plan....
1. You have gotten your dream job, which comes with the benefit of a 401(k) plan. You are trying to figure out how to make your investments. While the stock market has been very strong lately, you are afraid it is overdue for a correction. On the other hand, you also want to continue gaining if the stock market keep climbing. You have done a fair bit of analysis and come up with the following payoff table, for the gain...
Hi. I want to get feedback on this question. What should i add or remove or...
Hi. I want to get feedback on this question. What should i add or remove or any correction. Boulded written is question and regulat writing is answer. Please guide. Thank you. BACKGROUND Apply audit risk and materiality concepts to address the following circumstances regarding Able & Baker LLP’s audits of the financial statements of Foster Engineering, Inc. 1. Able & Baker LLP auditors are beginning their audit of Foster’s 2017 financial statements. Because of changes in the market and increased...
The assignment summary sheets will be submitted week 14 with Test 3. You are to personally...
The assignment summary sheets will be submitted week 14 with Test 3. You are to personally experience the power and satisfaction of developing these skills firsthand and to reflect and write about this experience. Over the years, many students have shared amazingly rewarding experiences as they worked on these skills. The assignment will be evaluated and be weighted as 5% of your final mark (together, they are worth 20% of your mark for Test 3, which is worth 25% of...
Read This before You Ever Debate "Capitalism" Again Paul Mueller (Links to an external site.)Links to...
Read This before You Ever Debate "Capitalism" Again Paul Mueller (Links to an external site.)Links to an external site. June 30, 2017 Capitalism is a divisive and misunderstood term—exceeded in its misapprehension only, perhaps, by socialism. While support for socialism has had a resurgence owing to the last election, capitalism still hangs under the dark cloud of notoriety given to it by the coiner of the term, Karl Marx. Writing in the heat and filth of Britain’s industrial revolution, Marx...