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

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

See similar textbooks

Related questions

Q: 7. Using the Affine Cipher E11,4(x) = 11x + 4 (mod 26), encipher 'GAUSS'. Show your work.

A: Using the Affine Cipher,E11,4(x) = 11x+ 4 (mod 26),encipher 'GAUSS'.

Q: If a = 282 and b = 34 then find the followving: 1) Find gcd(a, b) "use Euclidean algorithm" 2) Write…

A: Euclidean algorithm is one of the easiest way of finding gcd of two numbers. According to Euclidean…

Q: 7. Use the algorithm introduced in section 2.2 to find the inverse, if it exists, of the following…

A: Given :A=-2-31-3-31-2-41

Q: 6.3. Alice's public key for a knapsack cryptosystem is M = (5186, 2779, 5955, 2307, 6599, 6771,…

A: We can solve this question by hand and by computer.I will provide you both method to solve this…

Q: Starting with any rectangle, we can create a new and larger rectangle by attaching a square to the…

A: A sequence of the form a, a+d, a+2d, . . . , a+(n-1)d, a+nd, . . . is called an arithmetic sequence.…

Q: Use the Euclidean Algorithm with back-substitution tofind thegcd(a, b)and then writegcd(a, b)…

Q: The affine cipher E is given by E(x) ≡ 15x − 7 (mod 26). The conversion table for letters and…

A: E(x) = 15x - 7 (mod 26) Therefore, the decryption is given by D(y) = 7•(y+7) (mod 26)

Q: Exercise 9.2.26. Given that 3 4 (;). A = and b = 2 3 (a) Use the encryption function f(p) = Ap + b…

Q: 1. A long-winded, encrypted transmission has been intercepted. Frequency analysis of the entire…

A: As per our guidelines we are supposed answer only one question and rest can be reposted

Q: How would you decrypt the Vigen`ere cipher used to encrypt "pineapple"? In general, if your friend…

Q: Consider the following LP: min 5x1 + 4x2 s.t. x1 + x2 ≥ 1 2x1 − x2 ≥ 1 3x2 ≤ 2 x1, x2 ≥ 0. a. Write…

A: Consider the following LP: min 5x1 + 4x2 s.t. x1 + x2 ≥ 1 2x1 − x2 ≥ 1 3x2 ≤ 2 x1, x2 ≥ 0. a. Write…

Q: Find the general solution to the system of congruences: x ≡ 3 (mod 7), x ≡ 4 (mod 13).

A: We have to find a general solution to the system of congruences:x ≡ 3 (mod 7),x ≡ 4 (mod 13).

Q: 1.1. Build a cipher wheel as illustrated in Figure 1.1, but with an inner wheel that rotates, and…

A: To complete the tasks using the cipher wheel, follow these steps:Step 1: Prepare the Cipher…

Q: 7. Encrypt the message MERRY CHRISTMAS PEOPLE using blocks of five letters and the transposition…

A: Understand that we need to encrypt the message "MERRY CHRISTMAS PEOPLE" using the transposition…

Q: Establish the following Fibonacci identity: Un+8 = Un (mod 3)

A: Given that un is a Fibonacci sequence, we are asked to prove the following Fibonacci identity:…

Q: Express the Vigen`ere cipher as a cryptosystem.

Q: 3. For the numbers 360 and 70, use the Euclidean Algorithm (augmented or otherwise) to find the…

Q: Encrypt the message AT TEN HEAD NORTH TO TRENCHES using a tabular transposition cipher with rows of…

Q: 5. Find the plaintext message if the ciphertext produced by exponential encryption (§8.3) with key…

Q: Decrypt the message "XMJQYJWNSUQFHJ" which was encrypted with a Caesar cipher with a shift of 5 (A…

A: To decode code "XMJQYJWNSUQFHJ" using Caesar cipher with a shift of 5.

Q: The ciphertext 5859 was obtained from the using n=11413 and e=7467. RSA algorit Station…

A: The ciphertext 5859 was obtained from the RSA algorithm using n = 11413 and e = 7467. Usingthe…

Q: In a public key cryptosystem using the RSA algorithm, a user uses two prime numbers 11 and 17. He…

Q: 13. Suppose a message is encrypted using the RSA system with n = 53*61 and e = 19. Suppose the…

A: It is given that, a message is encrypted using the RSA system with n = 53*61 and e = 19. Suppose…

Q: In this problem, you will "crack" an RSA cryptosystem. What is the secret decoding number d for the…

A: Given: Public key n,e=5352381469067,4240501142039 To find: Secret decoding number for the RSA…

Q: Use the extended euclidean algorithm to find a solution to the following modulo constraints. • x ≡…

Q: Suppose that we CNC₂, where uw = v with u € C₁ and v € C. Give an example of a code-sequence which…

A: Error-correcting codes are an essential part of modern communication systems, ensuring reliable…

Q: age produce Assume that a person has ElGamal public key (2633, 3, 1138) and private key k = 965. If…

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)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Determine the private key

VIEW

Step 2: Use private key to encrypt the message

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Cc.33.
Answer number 5
This question is about Perfect Codes in Coding Theory: You may use that a perfect code of length 13 and distance 3 exists over GF(3). A soccer betting form contains a list of 13 matches. Next to each listed match there are three fill-in boxes which correspond to the following three possible guesses: “first team wins”, “second team wins” or “tied match”. The bettor checks one box for each match. Describe a strategy for filling out the smallest number of forms so that at least one of the forms contains at least 12 correct guesses. How many forms need to be filled out under this strategy?
a. Given p=23, q=7, and e=5, generate the public key (n,e) and the private key (n,d) using RSA Key generation algorithm. b. Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=7 to send to Bob. Show the ciphertext. c. Given Bob's public key of (85, 7) and private key of (85, 55), show how Bob can decrypt the ciphertext y=8 received from Alice. Show the plaintext. d. Using the fast exponentiation method (page 182), determine 535 mod 47
The ciphertext 75 was obtained using the RSA algorithm with n = 437 and e = 3. You know the plaintext is either 8 or 9. Determine which it is without factoring n.
(a) Use the Euclidean algorithm to find gcd(131,326). (b) Use the above to find a solution to 131x+326y=gcd(131,326) (c) Does 131 have an inverse modulo 326? If so, find a value in {0,1,2,3,…,325} that is an inverse. If not, explain why not?
Problem 6. In class, we learned a simple symmetric shift cipher (a.k.a. Caesar cipher). The secret key K is an integer in {0, 1,..., 25}. As always, we map each alphabet letter .,Z} to an integer {0, 1,...,25}. The encryption and description are defined x = {A, B, by ... Enc(x, k) = (x + k) mod 26, Dec(x, k) = (x - k) mod 26. (a) As a warm-up, encrypt "CSCI IS COOL" using a Caesar cipher with k='F'. (b) Here's the ciphertext generated by the shift cipher. Find the corresponding plaintext (please explain the approach/strategy you used to find the key). IWXHFJTHIXDCXHTPHN