Problem #1 Given below is a well-known cryptosystem called affine Caesar cipher, as well as some ciphertext generated using the affine Caesar cipher. P = C = Z 26 = {0, 1, 2, ..., 25}; K = {(a, b) Z26 Z26 | gcd(a, 26) = 1} y = E([a,b], x) = (ax + b) mod 26, x = D([a,b], y) = a-1 (y – b) mod 26, where x P, y C. Ciphertext sample: VPWOMFUWOFMYMHUNWBBWGCRVVPSFVPUTHUJWMC OMFUOVSVWOVWGSRSFSREOWOQMHKOBMHVPWOUFG HETVWMFOEOVUYVMMZCVGSFEMCCOUEMCHKFMQRU NIUMBRWFUSHSRIUZHSVMBWFNVPUOUGHUVKUEVM MVPUFEMCQWRRPSJUVHCREGHSGKUNVPUOEOVUY For this problem, please do the following: (a) provide an analysis detailing its strength/weakness; (b) attempt to uncover the plaintext associated with the ciphertext; (c) attempt to determine the secret key (a, b) used.
Problem #1
Given below is a well-known cryptosystem called affine Caesar cipher, as well as some
ciphertext generated using the affine Caesar cipher.
P = C = Z 26 = {0, 1, 2, ..., 25};
K = {(a, b) Z26 Z26 | gcd(a, 26) = 1}
y = E([a,b], x) = (ax + b) mod 26,
x = D([a,b], y) = a-1 (y – b) mod 26,
where x P, y C.
Ciphertext sample:
VPWOMFUWOFMYMHUNWBBWGCRVVPSFVPUTHUJWMC
OMFUOVSVWOVWGSRSFSREOWOQMHKOBMHVPWOUFG
HETVWMFOEOVUYVMMZCVGSFEMCCOUEMCHKFMQRU
NIUMBRWFUSHSRIUZHSVMBWFNVPUOUGHUVKUEVM
MVPUFEMCQWRRPSJUVHCREGHSGKUNVPUOEOVUY
For this problem, please do the following:
(a) provide an analysis detailing its strength/weakness;
(b) attempt to uncover the plaintext associated with the ciphertext;
(c) attempt to determine the secret key (a, b) used.
One of the earliest and most basic encryption techniques is the Caesar Cipher. It is merely a sort of substitution cipher in which each letter of a given text is substituted with a letter that is located a certain number of positions farther down the alphabet. As an illustration, if there was a shift of 1, A would be replaced by B, B by C, and so on. Julius Caesar, who reportedly employed it to communicate with his officials, is said to be the inspiration for the method's moniker.
Therefore, in order to cipher a given text, we require an integer value, or "shift," that represents the number of positions down which each letter in the text has been moved.
Modular arithmetic can be used to express the encryption by first converting the letters' letters into numbers, where A = 0, B = 1,..., Z = 25.
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