# Let a M be a finite set of messages, and let S(M) denote the set of all permutations of M (all…

Let a M be a finite set of messages, and let S(M) denote the set of all permutations of M (all bijective functions f : M ? M). We’ll assume that if given a description of s ? S(M), both s and s -1 are efficiently computable. Suppose P ? S(M) is such that ?x, y ? M, ?s ? P such that s(x) = y.

(a) Show that |P| = |M|. (This is easy, but makes sure you’ve parsed the definition.)

(b) Show that if |P| = |M|, then the following encryption scheme is perfectly secure, provided you only use it once: 1 Key generation: select a random s ? P; Encryption: m 7? s(m) Decryption: c 7? s -1 (c)

(c) Show that the above is false if |M| < |P| < 2|M|.

(d) Observe that for any finite group G and any g ? G, the map x 7? gx is a permutation of G. By viewing G itself as a set of permutations of G in this way, show that the above property is satisfied (with M = P = G). (e) The traditional xor one time pad is a special case of the above. What is the finite group in this case?

Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with Online Academic Experts
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Nursing
The writer was timely and proficient. I had to ask for a revision, but I got it back quickly with no other issues. Would use this essay writing service again
Customer 452441, November 14th, 2021
English 101
great summery in terms of the time given. it lacks a bit of clarity but otherwise perfect.
Customer 452747, June 9th, 2021
Awesome job, Thank you
Customer 453201, June 12th, 2022
Nursing
Usually, references need to be within the past 5 years. Thank you :)
Customer 452547, July 16th, 2021
Psychology
thank you!
Customer 452947, October 21st, 2021
Education
N/A
Customer 453057, May 23rd, 2022
Psychology
quick and before due date/time.
Customer 453027, January 29th, 2022
Management
Thank you!!! I received my order in record timing.
Customer 452551, February 9th, 2021
Social Work and Human Services
Great work I would love to continue working with this writer thought out the 11 week course.
Customer 452667, May 30th, 2021
Social Sciences
Very fast report with excellent information on the topic. Thank you for your speedy service in such a short time.
Customer 453213, June 15th, 2022
First of all, the writer made sure that he completely understood my assignment and all the guidelines before he began writing. My paper was finished very fast and well before the specified deadline. I thought it was written excellently. He definitely completely grasped the topic. Overall, he is a great writer and I couldn't have asked for better.
Customer 452441, November 29th, 2021
English 101
IThank you
Customer 452631, April 6th, 2021
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend