密码学代写 | Math 435 Introduction to Cryptography

这个作业是回答密码学相关的问题
Math 435
Introduction to Cryptography
Homework 1
Due Sunday, June 21, 2020
1. The ciphertext SEOYKJOEJ has been generated with a shift cipher. Determine the key
and the plaintext.
2. Show that the encryption key of a cryptosystem is always injective. In other words, if
ek(x) = ek(y), then x = y. [Hint: try decrypting.]
3. Use the affine cipher ek(x) = 3x + 1 to encipher the plaintext BADGERS. What is the
decrypting function dk(x)?
4. Find the affine cipher (if it exists) that encrypts the plaintext BC into the ciphertext
AD. If no such affine cipher exists, show why it does not exist.
5. Suppose you encrypt using an affine cipher, then encrypt the encryption using another
affine cipher. Is there any advantage to doing this, rather than using a single affine
cipher? Why or why not? [Hint: for example, if f(x) = 3x + 1 and g(x) = 5x + 2,
what does f(g(x)) look like?]
6. Use the Euclidean algorithm to compute 7−1
in Z60 or explain why no such value exists.
7. The ciphertext CRWWZ was encrypted with an affine cipher. We know that the plantext
starts with HA. Decrypt the message.
8. Using MAMA as the key for a Vigen´ere cipher, encrypt BE COOL. What is the minimum
block-length of this cipher?
9. The ciphertext YIFZMA was encrypted by a Hill cipher with matrix
9 2
13 3
. Find
the plaintext.
10. How many keys are there for each of the following ciphers?
(a) Shift ciphers
(b) Affine ciphers
(c) General substitution ciphers
(d) Vigen´ere ciphers where the keyword has length 3