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A Classical Introduction to Cryptography Exercise BookPrehistory of Cryptography

A Classical Introduction to Cryptography Exercise Book: Prehistory of Cryptography Chapter 1 Exercises Exercise 1 Mappings, etc. The goal of this exercise is to remind the notions of function, injection, surjection, bijection, permutation, and transposition. If any of those notions is not clear to you, keep reading! Consider the two sets X = {xl,xz,. . . , x,) and Y = {yl, y2,. . . , ym), and a function f : X - y. As f is a function, it assigns to each element of X a single element of y. 1 If n < m, can f be a function? What about the case where n > m? 2 Consider the case where n = 3 and m = 4. Which of the following diagrams represent a function? Explain why (or why not). 3 A function f is said to be 1 - 1 (one to one), or injective, if each element of y is the image of at most one element of X, i.e., for all Xl,X2 E X, f (~1) = f (~2) * 21 = 22. 2 EXERCISE BOOK Which of the following diagrams represent an injective function? 4 A function f is said to be surjective if each element of y is the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Classical Introduction to Cryptography Exercise BookPrehistory of Cryptography

Springer Journals — Jan 1, 2006
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Publisher
Springer US
Copyright
© Springer Science+Business Media, Inc. 2006
ISBN
978-0-387-27934-3
Pages
1 –15
DOI
10.1007/0-387-28835-X_1
Publisher site
See Chapter on Publisher Site

Abstract

Chapter 1 Exercises Exercise 1 Mappings, etc. The goal of this exercise is to remind the notions of function, injection, surjection, bijection, permutation, and transposition. If any of those notions is not clear to you, keep reading! Consider the two sets X = {xl,xz,. . . , x,) and Y = {yl, y2,. . . , ym), and a function f : X - y. As f is a function, it assigns to each element of X a single element of y. 1 If n < m, can f be a function? What about the case where n > m? 2 Consider the case where n = 3 and m = 4. Which of the following diagrams represent a function? Explain why (or why not). 3 A function f is said to be 1 - 1 (one to one), or injective, if each element of y is the image of at most one element of X, i.e., for all Xl,X2 E X, f (~1) = f (~2) * 21 = 22. 2 EXERCISE BOOK Which of the following diagrams represent an injective function? 4 A function f is said to be surjective if each element of y is the

Published: Jan 1, 2006

Keywords: Block Cipher; Data Encryption Standard; MONDAY Morning; Modular Addition; Perfect Secrecy

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