If an encryption function er is identical to the decryption function dr, then the key K is said to be an involutory key. (a) Let K = (a, b) be a key in an affine cipher over Z/nZ. Show that K is an involutory key if and only if a- = a (mod n) and b(a+1) = 0 (mod n). (b) Suppose that you have an alphabet with 50 letters. How many possible affine ciphers are there? (c) Find all involutory keys in the affine cipher over Z/50Z.

If an encryption function er is identical to the decryption function dr, then the key K is said to be an involutory key. (a) Let K = (a, b) be a key in an affine cipher over Z/nZ. Show that K is an involutory key if and only if a- = a (mod n) and b(a+1) = 0 (mod n). (b) Suppose that you have an alphabet with 50 letters. How many possible affine ciphers are there? (c) Find all involutory keys in the affine cipher over Z/50Z.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

(6)
dr, then the key K is said to be an involutory key.
(a) Let K = (a, b) be a key in an affine cipher over Z/nZ. Show that K is an
involutory key if and only if a-l = a (mod n) and b(a+1) = 0 (mod n).
(b) Suppose that you have an alphabet with 50 letters. How many possible
affine ciphers are there?
(c) Find all involutory keys in the affine cipher over Z/50Z.
If an encryption function ek is identical to the decryption function

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