Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Prior to the discovery of any specific public-key schemes, such as RSA, an existence proof was developed whose purpose was to demonstrate that public-key encryption is possible in theory. Consider the functions f₁(x₁)=z₁; f₂(x2, y2)=Zz; f(x3, Y3) = Z3

Prior to the discovery of any specific public-key schemes, such as RSA, an existence proof was developed whose purpose was to demonstrate that public-key encryption is possible in theory. Consider the functions f₁(x₁)=z₁; f₂(x2, y2)=Zz; f(x3, Y3) = Z3

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
8. Prior to the discovery of any specific public-key schemes, such as RSA, an existence proof was developed whose purpose was to demonstrate that public-key encryption is possible in theory. Consider the functions f₁(x₁) = Z₁; f₂(x2, y2) = Z2; f(x3, y3) = Z3 where all values are integers with Function can be represented by a vector M1 of length N, in which the kth entry is the value of Similarly, and can be represented by matrices M2 and M3. The intent is to represent the encryption/decryption process by table lookups for tables with very large values of N. Such tables would be impractically huge but could, in principle, be constructed. The scheme works as follows: Construct M1 with a random permutation of all integers between 1 and N; that is, each integer appears exactly once in M1. Construct M2 so that each row contains a random permutation of the first N integers. Finally, fill in M3 to satisfy the following condition: fi(fe(fi(k),p),k) = p for all k, p with 1 ≤k, p≤N In words, 1. M1 takes an input k and produces an output x. 2. M2 takes inputs x and p giving output z. 3. M3 takes inputs z and k and produces p. The three tables, once constructed, are made public. (a) It should be clear that it is possible to construct M3 to satisfy the preceding condition. As an example, fill in M3 for the following simple case: 5 4 M1 = 2 3 5 2 3 4 4 2 5 3 2 314 2 5 3 4 1 M2 1 13 4 5 25 (c) Argue that this is a secure scheme. M3 = Convention: The ith element of M1 corresponds to "ki" The ith row of M2 corresponds to "x = i" the jth column of M2 corresponds to "p=j" The ith row of M3 corresponds to "z=i" the jth column of M3 corresponds to "k=j". [6 marks] (b) Describe the use of this set of tables to perform encryption and decryption between two users. [3 marks] [3 marks]
Transcribed Image Text:8. Prior to the discovery of any specific public-key schemes, such as RSA, an existence proof was developed whose purpose was to demonstrate that public-key encryption is possible in theory. Consider the functions f₁(x₁) = Z₁; f₂(x2, y2) = Z2; f(x3, y3) = Z3 where all values are integers with Function can be represented by a vector M1 of length N, in which the kth entry is the value of Similarly, and can be represented by matrices M2 and M3. The intent is to represent the encryption/decryption process by table lookups for tables with very large values of N. Such tables would be impractically huge but could, in principle, be constructed. The scheme works as follows: Construct M1 with a random permutation of all integers between 1 and N; that is, each integer appears exactly once in M1. Construct M2 so that each row contains a random permutation of the first N integers. Finally, fill in M3 to satisfy the following condition: fi(fe(fi(k),p),k) = p for all k, p with 1 ≤k, p≤N In words, 1. M1 takes an input k and produces an output x. 2. M2 takes inputs x and p giving output z. 3. M3 takes inputs z and k and produces p. The three tables, once constructed, are made public. (a) It should be clear that it is possible to construct M3 to satisfy the preceding condition. As an example, fill in M3 for the following simple case: 5 4 M1 = 2 3 5 2 3 4 4 2 5 3 2 314 2 5 3 4 1 M2 1 13 4 5 25 (c) Argue that this is a secure scheme. M3 = Convention: The ith element of M1 corresponds to "ki" The ith row of M2 corresponds to "x = i" the jth column of M2 corresponds to "p=j" The ith row of M3 corresponds to "z=i" the jth column of M3 corresponds to "k=j". [6 marks] (b) Describe the use of this set of tables to perform encryption and decryption between two users. [3 marks] [3 marks]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

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