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I could understand the integer arithmetic example they gave and I think you are pointing out how this is flawed security-wise (its use lies in explaining the me
by barking 8y ago
I could understand the integer arithmetic example they gave and I think you are pointing out how this is flawed security-wise (its use lies in explaining the method). This flaw is addressed by using finite field arithmetic but I did't understand that part too well.
- blattimwind 8y agoThe modulo reduction used in finite fields essentially "scrambles" the structure of many objects.
- mehrdadn 8y agoFinite field arithmetic is basically what you would get if you were to reduce the integers to a set of finite size, but keep the arithmetic rules similar to what they were before. Using an infinite set like the integers is a bad idea because you can't have a uniform distribution over all the integers, and hence some members will be more likely than others, which leaks information. The special case of finite-field arithmetic we usually care about is GF(p), which is when the integers start at 0 and wrap around at p, where p is a prime number. We care about this because when p is prime, then we can ensure numbers are uniformly random in the range 0..p-1, which is something we need in order to guarantee information-theoretic security.