rot13maxi on Nostr: The first term of the polynomial is the x^0 coefficient, which is also the ...
The first term of the polynomial is the x^0 coefficient, which is also the y-intercept :-)
For example, say your secret is the number 5 and you want to have a 2/3 split. You randomly generate a polynomial. Lets say its y = 5 + 3x. Then you make three shares where each share is a point (x,y) so if you want to use 1,2,3 for the x coordinates youd have (1,8), (2,11), (3,14). If you take two of those points, maybe the 1 and 3 points and interpolate a line through them, it’ll intercept the y axis at 5, which is what you get if you set x to 0 in y=5+3x.
As jesse said, this generalizes upwards: for a t-of-n split, you pick a polynomial of degree t-1, and then you pick n points on the curve.
The DKG used in frost is kind of that in reverse: everyone makes their own polynomial and then passes around coefficients to pick a secret that none of them know.
For example, say your secret is the number 5 and you want to have a 2/3 split. You randomly generate a polynomial. Lets say its y = 5 + 3x. Then you make three shares where each share is a point (x,y) so if you want to use 1,2,3 for the x coordinates youd have (1,8), (2,11), (3,14). If you take two of those points, maybe the 1 and 3 points and interpolate a line through them, it’ll intercept the y axis at 5, which is what you get if you set x to 0 in y=5+3x.
As jesse said, this generalizes upwards: for a t-of-n split, you pick a polynomial of degree t-1, and then you pick n points on the curve.
The DKG used in frost is kind of that in reverse: everyone makes their own polynomial and then passes around coefficients to pick a secret that none of them know.