Braid Cryptography

# Braid Cryptography - Akshaya Annavajhala Math 363 Professor...

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Akshaya Annavajhala 4/26/08 Math 363 Professor Langer j 3 b (Braid Cryptography) Group Members: Stephen Fleming, Jason Messer, and Mike Szabo. It is the year 2001, and Alice is a White House Secretary with a Classified clearance. Each day, she handles about 20 messages unsuitable for KGB eyes. Most of these messages are not very important, although, on average, she needs to send President Bob about four sensitive messages that the KGB would love to get its hands on. Therefore, Vladimir Putin has sent over Oscar, the KGB rezident for Washington, D.C., to find out the most treasured secrets in the U.S.A. Luckily for Alice and Bob, there are no knot theorists in the Kremlin, so their messages are easily broken. Thus, they know of Oscar’s presence and mission. Therefore, Alice and Bob agree on encrypting all of their messages. They hire the services of a prominent mathematician, Professor Langer, who advises that they use the Braid Cryptography Scheme to ensure near- infallible security in their communications. Being the President, Bob likes to appear intelligent, so he asks Professor Langer to explain the reasoning behind this new scheme. Always willing to teach, the Professor explains: “Any cryptographic scheme requires a one-way method of transforming a message. That is, without additional information, it is difficult to reverse the transformation. In many modern cryptographic methods, this is done with arithmetic or bit operations, such as the multiplication of large factors or the ‘bitwise exclusive or’ operator. This bit operator compares two bit streams and produces another one, whose bit in a certain position is 0 if both of the original streams are

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the same in that spot, and 1 if they are different. Neither of these functions allows for easy reversal, with the factoring of a sufficiently large number produced by the multiplication of primes eluding even the most high-tech computers today. To develop the Braid Cryptographic Scheme, many problems involving braids were analyzed, in order to develop the most secure encryption possible. “The most difficult problem encountered with braid theory was the generalized conjugate
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Braid Cryptography - Akshaya Annavajhala Math 363 Professor...

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