
Western Kentucky University Contractor/Vendor Key Agreement Form 2011-2025 free printable template
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Imagine two people who have never met could do an amazing trick Alice and Lobar allowed to communicate over a line which is tapped so any message they pas swill be intercepted by Eve who is always listening the trick is to agree on secret numerical key without Eve also obtaining a copy how is this possible first let×39’s explore how this trick misdone using colors so how could a Lebanon agree on a secret color without evening it out the trick is based on two facts one it's easy to mix two colors together to make a third color and to give it a mixed color it's hard to reverse it in order to find the exact original colors this is the basis for block easy in one direction hard in the reverse direction this is known as a one-way function now the solution works as follows first they publicly agree on a starting color say yellow next Alice and Bob both randomly select private colors and mix them into the public yellow in order to disguise their private color now Alice keeps her private color and sends her mixture to Bob and Bob keeps his private color and sends his mixture to Alice now the heart of the trick Alice and Bob add their private colors to the other person×39’s mixture and arrive at a shared secret color notice how Eve is unable to determine this color since she needs one of the private colors to do so and that is the trick now to do this with numbers wended a numerical procedure which is easy in one direction and hard in the reverse direction this brings us to modular arithmetic which is known as clock arithmetic for example to find 42 mod 12we take a rope of length 46 units and wrap it around a clock of 12 units chichis called the modulus and wherever the rope ends is the solution, so we say 42mod 12 is congruent to 10 easy now to make this work we need a prime modulus such as 17 instead of 12 then we find the primitive root of 17 which is number that has no factors in common in this case 3, and it has this important property that when raised to different exponents the solution distributes uniformly around the clock 3 is known Ashe generator so if we raise 3 to any exponent X the solution is equally likely to be any integer between 0 & 17now the reverse procedure is hard say given 12 find the exponent 3 needs to braised 2 this is called the discrete logarithm problem, and now we have our one wave function easy to perform but hard to reverse given 12 you would have to resort to trial and error in order to find the matching exponent how hard is this well with small numbers it×39’s easy but if we use a prime modulus which is hundreds of digits long it starts to get seriously hard even if you had access tall the computational power on earth it could take thousands of years or more to find the answer, so the strength of anyway function is based on the time needed to reverse it now this is our solution first Alice and Bob publicly agree on a prime modulus and a generator for example 17 and 3 then Alice selects private random number say 54 and...
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