So What Have Prime Numbers and Galois Fields To Do With Your Privacy?

Remember at school they told you that 17 divided by 5 doesn’t go? Then they told you that there’s a remainder from the division, and that the answer is 3 remainder 2.

In this operation, we might be only interested that the result of the division is 3 (an integer division), and that there’s a remainder of 2. In cryptography, though, we would throw away the 3, and concentrate on the 2. For this we define the operation as a modulus (or mod). And so 17 (mod 5) is 2. If you are into Python, this is 17 % 5.

In cryptography, we are basically not interested in all those negative numbers, and those decimal point values, as we only deal with positive integers (Z).

And something magical happens when we use prime numbers for our mod operations, and where we can constrain the numbers that we use, but still our math operations still work. This is called Finite Fields (Zp), and they protect your privacy like nothing else.

Prime numbers and you

Prime numbers are protecting your identity virtually every time that you connect to a Web site. With symmetric key methods, such as AES and 3DES, we often use a scrambling function with the key added, and where we take blocks of input data and then swap rows and columns. This is then fed…