This would normally be simple algebra 1 x y mod 26

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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 (a-1) 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 a-1 (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.

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