canek_varblockencr

canek_varblockencr - Mathemagical Encryption 1 Mathemagical...

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Mathemagical Encryption 1 Mathemagical Encryption: Variable Block Length Encryption Canek Acosta University of Florida
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Mathemagical Encryption 2 Abstract Over the course of the past semester I have been learning card tricks. It did not take long for me to come across what are referred to as “self-working” tricks. Many of these are based on mathematics and led me to envision a variable block length encryption scheme. I have chosen to pursue this as my term project because I had noticed there are almost no textbook examples of variable block length encryption, as well as the fact that it was an exciting application for the concepts I had learned practicing magic and in this class.
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Mathemagical Encryption 3 Mathemagical Encryption: Variable Block Length Encryption Throughout the course, we have discussed block and stream ciphers. Block ciphers took a fixed amount of bits, bytes, or characters and rearranged them either by transposition, substitution, or a combination of the two. Stream ciphers,which worked with data as it came in, still eventually broke them into fixed quantities to in order to encrypt and decrypt the data. Today variable block size, means to most, the compatibility of an algorithm with various block sizes. I , however, propose a system of encryption with what I'll call true variability . What I mean by this is that each and every block you work with can be a completely different block size without causing any issues whatsoever in the encryption scheme. First, we will introduce the mathematics behind the encryption scheme. Mathematical Background Down Under Deal The Down Under Deal, otherwise known as the Australian Shuffle, is a component of various magic tricks. If dealt in a particular manner, each pile of cards can effectively be reduced to one predictable card. The Down Under Deal is done exactly how it sounds. You take the top card of a pile and discard it or place it down on the table. Then you take the next card and place it under the pile. This is repeated until one card remains. The card remaining is mathematically predictable. It will be 2(z mod 2^x) where x = max(x| 2^x <= z) and z is the size of the pile you are working with. That is, it is twice the the difference between the pile of cards and the closest power of two. By Induction we can show that this process can be done for any z. Using this method, we can use variable blocks(analagous to the piles) to hide valuable data amongst garbage or misleading data. Simply place the valuable data at the predictable
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Mathemagical Encryption 4 location for the individual in charge of decryption to extract. Proof: By Induction Base Case : z =3. Dicard 1, place 2 at bottom, 3 is discarded and we are left with 2. Induction Hypothesis
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This note was uploaded on 01/17/2012 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.

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canek_varblockencr - Mathemagical Encryption 1 Mathemagical...

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