COT5937Lec1 - In particular the following rules were...

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Cryptography Lecture One Overview We first talked about the shift cipher and then split up into three groups. Each group would have a message for another using the shift cipher. The group the message was intended for would know the key. Once each group decrypted the message intended for them, we switched messages to see who could decrypt the messages NOT intended for them first. The group that one used the technique of trying to match common two and three letter words to that with the cipher text in order to find the correct key. One group “made” a little chart that you could slide over any number of letters to aid the trying different possible keys. Yet another group attempted frequency analysis in order to find out the correct key. After the exercise, we went over the formal definition of a cryptosystem given on page one of the text. Next, some mod rules had to be developed for future use. By definition, we have a b (mod n) n | (a – b).
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Unformatted text preview: In particular, the following rules were examined: 1) if a ≡ b (mod n) and c ≡ d (mod n) then (a+c) ≡ (b+d) (mod n) 2) if a ≡ b (mod n) and c ≡ d (mod n) then ac ≡ bd (mod n) 3) if a ≡ b (mod n) then f(a) ≡ f(b) (mod n), where f is a polynomial with integer coefficients, and a and b are integers as well. Also, we discussed the difference between (mod n) and mod n. Whenever we do NOT use the parentheses, the result must lie in between 0 and n-1. The other mathematical background covered was Euclid’s algorithm and a proof of why it works. Then we used the algorithm to show that if the gcd(a,b) = c, then there exists integers x and y such that ax + by = c. After looking at the shift cipher, we took a look at the Affine cipher. Before the end of class we determined that in order for the Affine cipher to work, the secret key a would have to be relatively prime with the number of letters in the alphabet; in our case, 26....
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This document was uploaded on 07/14/2011.

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