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Unformatted text preview: cipher involves a key (α,β) and maps the plaintext x to
the ciphertext y via
y = αx + β (mod 26 ) Example: y= 9x+2 (mod 26)
Decryption solves for x. This would normally be simple algebra
1
x = (y − β) (mod 26 )
α
What does (1/α) mean?
It is the inverse of α (mod 26)… ok, so what does that mean? Inverses (mod n)
Inverses
When you think of a number (a1) in normal algebra, you think of division.
What is really going on is that you are finding another number b such that
ab=1.
So, when we write a1 (mod n) we really mean the number b such that
ab=1 (mod n).
How do we find this b?
– We will see a fast way to do it for large n later… for now, just make a
table!
– Example, suppose a=7, n=26
7*1 = 7 mod 26 7*4 = 28 = 2 mod 26 7*2 = 14 mod 26 7*5 = 9 mod 26
7*3 = 21 mod 26 7*6 = 16 mod 26 … and so on…
Until you find a number b such that 7b=1 mod 26. (b= 15)
Final Comment: You only have inverses when gcd(a,n) = 1 More on the Affine Cipher
More
We need gcd(α,26)=1 in order to have an invertible function
(see...
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This note was uploaded on 01/07/2013 for the course 332 519 taught by Professor Wadetrappe during the Fall '12 term at Rutgers.
 Fall '12
 WadeTrappe

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