(a) Suppose Alice and Bob use the simple encryption scheme in which c = (m + k) mod N and m = (c – k) mod N. Suppose that Eve knows that N = 4657. Suppose that she also manages to learn that the message m corresponding to c = 1322 is 3411. Can she infer the value for k? What is k?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.8: Introduction To Cryptography (optional)
Problem 6E
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Discrete Math Problem on Cryptography

Exercise 3.8.6: Deducing the key from a single (plaintext, ciphertext) pair.
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(a) Suppose Alice and Bob use the simple encryption scheme in which c = (m + k) mod N and m = (c – k) mod N. Suppose that Eve
knows that N = 4657. Suppose that she also manages to learn that the message m corresponding to c = 1322 is 3411. Can she
infer the value for k? What is k?
Feedback?
Transcribed Image Text:Exercise 3.8.6: Deducing the key from a single (plaintext, ciphertext) pair. About (a) Suppose Alice and Bob use the simple encryption scheme in which c = (m + k) mod N and m = (c – k) mod N. Suppose that Eve knows that N = 4657. Suppose that she also manages to learn that the message m corresponding to c = 1322 is 3411. Can she infer the value for k? What is k? Feedback?
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