Read Online Nine Algorithms That Changed the Future: The Ingenious Ideas That Drive Today's Computers by John MacCormick, Chris Bishop - Free Book Online Page A
Authors: John MacCormick, Chris Bishop
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together: you just say something like “mix one pot of ‘sky blue' with six pots of ‘eggshell' and five pots of ‘aquamarine'.” But there are hundreds or thousands of colors of every conceivable shade, so it's impossible to work out which exact colors went into a mixture just by looking at it. And it's impossible to work out which colors went into a mixture by trial and error, because there are just too many colors to try.
Now, the rules of the game are going to change just a little bit. Each of you is going to have a corner of the room curtained off for privacy, as a place where you store your paint collection and where you can go to secretly mix paints without the others seeing. But the rules about communication are just the same as before: any communication between you, Arnold, and Eve must be out in the open. You can't invite Arnold into your private mixing area! Another rule regulates how you can share mixtures of paint. You can give a batch of paint to one of the other people in the room, but only by placing that batch on the ground in the middle of the room and waiting for someone else to pick it up. This means that you can never be sure who is going to pick up your batch of paint. The best way is to make enough for everybody, and leave several separate batches in the middle of the room. That way anyone who wants one of your batches can get it. This rule is really just an extension of the fact that all communication must be public: if you give a certain mixture to Arnold without giving it to Eve too, you have had some kind of “private” communication with Arnold, which is against the rules.
Remember that this paint-mixing game is meant to explain how to establish a shared secret. At this point you may well be wondering what on earth mixing paints has got to do with cryptography, but don't worry. You are about to learn an amazing trick that is actually used by computers to establish shared secrets in a public place like the internet!
First, we need to know the objective of the game. The objective is for you and Arnold to each produce the same mixture of paint, without telling Eve how to produce it. If you achieve this, we'll say that you and Arnold have established a “shared secret mixture.” You are allowed to have as much public conversation as you like, and you are also allowed to carry pots of paint back and forth between the middle of the room and your private mixing area.
Now we begin our journey into the ingenious ideas behind public key cryptography. Our paint-mixing trick will be broken down into four steps.
Step 1. You and Arnold each choose a “private color.”
Your private color is not the same thing as the shared secret mixture that you will eventually produce, but it will be one of the ingredients in the shared secret mixture. You can choose any color you want as your private color, but you have to remember it. Obviously, your private color will almost certainly be different from Arnold's, since there are so many colors to choose from. As an example, let's say your private color is lavender and Arnold's is crimson.
Step 2. One of you publicly announces the ingredients of a new, different color that we'll call the “public color.”
Again, you can choose anything you like. Let's say you announce that the public color is daisy-yellow. Note that there is only one public color (not two separate ones for you and Arnold), and, of course, Eve knows what the public color is because you announce it publicly.
Step 3. You and Arnold each create a mixture by combining one pot of the public color with one pot of your private color. This produces your “public-private mixture.”
Obviously, Arnold's public-private mixture will be different from yours, because his private color is different from yours. If we stick with the above example, then your public-private mixture will contain one pot each of lavender and daisy-yellow, whereas Arnold's public-private mixture consists of crimson and
Now, the rules of the game are going to change just a little bit. Each of you is going to have a corner of the room curtained off for privacy, as a place where you store your paint collection and where you can go to secretly mix paints without the others seeing. But the rules about communication are just the same as before: any communication between you, Arnold, and Eve must be out in the open. You can't invite Arnold into your private mixing area! Another rule regulates how you can share mixtures of paint. You can give a batch of paint to one of the other people in the room, but only by placing that batch on the ground in the middle of the room and waiting for someone else to pick it up. This means that you can never be sure who is going to pick up your batch of paint. The best way is to make enough for everybody, and leave several separate batches in the middle of the room. That way anyone who wants one of your batches can get it. This rule is really just an extension of the fact that all communication must be public: if you give a certain mixture to Arnold without giving it to Eve too, you have had some kind of “private” communication with Arnold, which is against the rules.
Remember that this paint-mixing game is meant to explain how to establish a shared secret. At this point you may well be wondering what on earth mixing paints has got to do with cryptography, but don't worry. You are about to learn an amazing trick that is actually used by computers to establish shared secrets in a public place like the internet!
First, we need to know the objective of the game. The objective is for you and Arnold to each produce the same mixture of paint, without telling Eve how to produce it. If you achieve this, we'll say that you and Arnold have established a “shared secret mixture.” You are allowed to have as much public conversation as you like, and you are also allowed to carry pots of paint back and forth between the middle of the room and your private mixing area.
Now we begin our journey into the ingenious ideas behind public key cryptography. Our paint-mixing trick will be broken down into four steps.
Step 1. You and Arnold each choose a “private color.”
Your private color is not the same thing as the shared secret mixture that you will eventually produce, but it will be one of the ingredients in the shared secret mixture. You can choose any color you want as your private color, but you have to remember it. Obviously, your private color will almost certainly be different from Arnold's, since there are so many colors to choose from. As an example, let's say your private color is lavender and Arnold's is crimson.
Step 2. One of you publicly announces the ingredients of a new, different color that we'll call the “public color.”
Again, you can choose anything you like. Let's say you announce that the public color is daisy-yellow. Note that there is only one public color (not two separate ones for you and Arnold), and, of course, Eve knows what the public color is because you announce it publicly.
Step 3. You and Arnold each create a mixture by combining one pot of the public color with one pot of your private color. This produces your “public-private mixture.”
Obviously, Arnold's public-private mixture will be different from yours, because his private color is different from yours. If we stick with the above example, then your public-private mixture will contain one pot each of lavender and daisy-yellow, whereas Arnold's public-private mixture consists of crimson and
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