Consider the affine cipher with key k = (k1, k2) whose encryption and decryption functions are given by (1.11) on page 43. Alice and Bob decide to use the prime p = 601 for their affine cipher. The value of p is public knowledge, and Eve intercepts the ciphertexts c1 = 324 and c2 = 381 and also manages to find out that the corresponding plaintexts are m1 = 387 and m2 = 491. Determine the private key and

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

Consider the affine cipher with key k = (k1, k2) whose encryption and decryption functions are given by (1.11) on page 43.

Alice and Bob decide to use the prime p = 601 for their affine cipher. The value of p is public knowledge, and Eve intercepts the ciphertexts c1 = 324 and c2 = 381 and also manages to find out that the corresponding plaintexts are m1 = 387 and m2 = 491. Determine the private key and then use it to encrypt the message m3 = 173.

Sect. 1.1. Another variant, called an affine cipher, is a combination of the shift
cipher and the multiplication cipher. The key for an affine cipher consists of
two integers k = (k₁, k2) and encryption and decryption are defined by
ek(m) = k₁ · m + k₂
dk (c) = k₁. (c-k₂)
·
where k is the inverse of k₁ modulo p.
(mod p),
(mod p),
(1.11)
Transcribed Image Text:Sect. 1.1. Another variant, called an affine cipher, is a combination of the shift cipher and the multiplication cipher. The key for an affine cipher consists of two integers k = (k₁, k2) and encryption and decryption are defined by ek(m) = k₁ · m + k₂ dk (c) = k₁. (c-k₂) · where k is the inverse of k₁ modulo p. (mod p), (mod p), (1.11)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,