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Back to Rings and Encryption

Exercise 5

Avg difficulty 3.0

Let N=8N=8, p=3p=3, and q=64q=64. Let Bob’s public key be

h(x)=24x7+15x6+50x5+48x4+40x3+46x2+14x+19.h(x)=24x^{7}+15x^{6}+50x^{5}+48x^{4}+40x^{3}+46x^{2}+14x+19.

Alice wants to transmit the character ‘U’ to Bob. Suppose Alice encodes ‘U’ using the ASCII conversion table (1.1) and obtains an ‘encoding fuzz’ polynomial of x−1x-1. What is the encrypted message?

Kan, A Complete Introduction to Abstract Algebra, Rings, Rings and Encryption, Exercise 5

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Adapted from A Complete Introduction to Abstract Algebra © 2022–2026 Kan Onn Kit. Licensed under CC BY-SA 4.0. Source: A Complete Introduction to Abstract Algebra. Imported at revision a559e8b.