This is called theĭiscrete logarithm problem. Say, given 12, find the exponent three needs to be raised to.
If we raise three to any exponent x, then the solution is equally likely to be any integer between zero and 17.
Has this important property that when raised to different exponents, the solution distributes We use a prime modulus, such as 17, then we findĪ primitive root of 17, in this case three, which So we say 46 mod 12 isĬongruent to 10, easy. For example, to find 46 mod 12, we could take a rope of length 46 units and rap it around a clock of 12 units, which is called the modulus, and where the rope ends is the solution. This brings us to modular arithmetic, also known as clock arithmetic. PS: I interpreted the "how" as 'you can do the math, but you can't understand how it works to transfer messages'Ī numerical procedure, which is easy in one directionĪnd hard in the other. This is why modular arithmetic works in the exchange system.ĭoes that help? Or did you not understand the math itself? You can easily find the answer to a modular equation, but if you know the answer to a modular equation, you can't find the numbers that were used in the equation. In math, if you add two numbers, and Eve knows one of them (the public key), she can easily subtract it from the bigger number (private and public mix) and get the number that Bob and Alice want to keep secret. What you need is something like the colors shown in the last video: Colors are easy to mix, but not so easy to take apart. Since Eve is always watching, she will see Alice and Bob exchange key numbers to their One Time Pad encryptions, and she will be able to make a copy and decode all your messages. Basically, the problem with your ordinary One Time Pad is that it's difficult to secretly transfer a key.
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