6 ms·

I'm not a mathematician but here is my ELI5 understanding of it based on linked wikipedia article. If you know the coordinates of any 2 points on a line you ca

I'm not a mathematician but here is my ELI5 understanding of it based on linked wikipedia article. If you know the coordinates of any 2 points on a line you can recover the equation for that line. The same is true for 3 points on a quadratic curve and 4 points on cubic curve, etc. So if our secret is the number c we can put it in the equation for, say, a quadratic: ax^2 + bx + c = 0 We can then give any number of people the coordinates for different single points on this curve. None of these people know the equation but if any 3 of them share their coordinates they can work out the equation and thus the value of c.

mehrdadn 8y ago
Just remember the caveat with the ELI5 explanation is that if I tell you the first two points on a parabola are (0,0) and (1,0) you will figure that the third point is more likely to be around (2,0) than, say, (2,2^30).
- 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 ago
    The modulo reduction used in finite fields essentially "scrambles" the structure of many objects.
  - mehrdadn 8y ago
    Finite 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.
bradleyjg 8y ago
If you take it one step further and show how it still works modulo p, the algorithm serves as a great introduction to how and why finite fields are used in cryptography.
Fnoord 8y ago
A good ELI5 analogy is the Pythagoras' theorem [1]. Its taught here (NL) at school at around age 12, so its not quite ELI5 but closest I can think of. [1] https://en.wikipedia.org/wiki/Pythagorean_theorem https://en.wikipedia.org/wiki/Pythagorean_theorem

mehrdadn 8y ago

Just remember the caveat with the ELI5 explanation is that if I tell you the first two points on a parabola are (0,0) and (1,0) you will figure that the third point is more likely to be around (2,0) than, say, (2,2^30).

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 ago
  The modulo reduction used in finite fields essentially "scrambles" the structure of many objects.
- mehrdadn 8y ago
  Finite 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.

bradleyjg 8y ago

If you take it one step further and show how it still works modulo p, the algorithm serves as a great introduction to how and why finite fields are used in cryptography.

Fnoord 8y ago

A good ELI5 analogy is the Pythagoras' theorem [1]. Its taught here (NL) at school at around age 12, so its not quite ELI5 but closest I can think of. [1] https://en.wikipedia.org/wiki/Pythagorean_theorem https://en.wikipedia.org/wiki/Pythagorean_theorem