Unformatted text preview: In particular, the following rules were examined: 1) if a â‰¡ b (mod n) and c â‰¡ d (mod n) then (a+c) â‰¡ (b+d) (mod n) 2) if a â‰¡ b (mod n) and c â‰¡ d (mod n) then ac â‰¡ bd (mod n) 3) if a â‰¡ b (mod n) then f(a) â‰¡ 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 Euclidâ€™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.
- Summer '09