Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
The goal of this exercise is to work thru the RSA system in a simple case: We will use primes p = 71, q = 61 and form 71 · 61 = 4331. n = [This is typical of the RSA system which chooses two large primes at random generally, and multiplies them to find n. The public will known but p and q will be kept private.]

The goal of this exercise is to work thru the RSA system in a simple case: We will use primes p = 71, q = 61 and form 71 · 61 = 4331. n = [This is typical of the RSA system which chooses two large primes at random generally, and multiplies them to find n. The public will known but p and q will be kept private.]

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
See similar textbooks
icon
Related questions
Question
The goal of this exercise is to work thru the RSA system in a simple case: We will use primes p = 71, q = 61 and form 71 ·61 = 4331. n = [This is typical of the RSA system which chooses two large primes at random generally, and multiplies them to find n. The public will know n but p and q will be kept private.] Now we choose our public key e = 13. This will work since gcd(13, (p – 1)(q – 1)) = gcd(13, 4200) = 1. [In general as long as we choose an 'e' with gcd(e, (p-1) (q-1))=1, the system will work.] Next we encode letters of the alphabet numerically say via the usual: (A=0,B=1,C=2,D=3,E=4,F=5,G=6,H=7,l=8, J=9,K=10,L=11,M=12,N=13,0=14,P=15,Q316,R=17, S=18,T=19,U=20,V=21,W=22,X=23,Y=24,Z=25.) We will practice the RSA encryption on the single integer 15. (which is the numerical representation for the letter "P"). In the language of the book, M=15 is our original message. The coded integer is formed via c = Me mod n. Thus we need to calculate 1513 mod 4331. This is not as hard as it seems and you might consider using fast modular multiplication. The canonical representative of 1513 mod 4331 is
Transcribed Image Text:The goal of this exercise is to work thru the RSA system in a simple case: We will use primes p = 71, q = 61 and form 71 ·61 = 4331. n = [This is typical of the RSA system which chooses two large primes at random generally, and multiplies them to find n. The public will know n but p and q will be kept private.] Now we choose our public key e = 13. This will work since gcd(13, (p – 1)(q – 1)) = gcd(13, 4200) = 1. [In general as long as we choose an 'e' with gcd(e, (p-1) (q-1))=1, the system will work.] Next we encode letters of the alphabet numerically say via the usual: (A=0,B=1,C=2,D=3,E=4,F=5,G=6,H=7,l=8, J=9,K=10,L=11,M=12,N=13,0=14,P=15,Q316,R=17, S=18,T=19,U=20,V=21,W=22,X=23,Y=24,Z=25.) We will practice the RSA encryption on the single integer 15. (which is the numerical representation for the letter "P"). In the language of the book, M=15 is our original message. The coded integer is formed via c = Me mod n. Thus we need to calculate 1513 mod 4331. This is not as hard as it seems and you might consider using fast modular multiplication. The canonical representative of 1513 mod 4331 is
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS