Comment by Tepix
9 hours ago
Instead of going from two lines to curves, parabolas etc, couldn't you also add another dimension instead?
9 hours ago
Instead of going from two lines to curves, parabolas etc, couldn't you also add another dimension instead?
Probably, but the nice thing about polynomials is the secret is the value when x is 0. What is the point on the hyper geometry where I look up the secret?
Yes?
If I use 3 shares and require all three to recover, then I think I could let the 3 points define a plane. Then the plane would intersect the axis at a unique point.
If I want 4 or more shares, I can make them by just generating more points on that same plane. Then I think any three of those should recover the secret. So it seems like that would all work about the same as with the polynomials? Then I can go to still more dimensions when I want to require more shares to reveal the secret.
Two points make a line in any number of dimensions.
Yes, but without a specific plane to intersect with, that still doesn't define a third point, if you want to check intersection with an axis, you'd need a third point in tridimensional space, for example.
Think GP is suggesting an N-dimensional plane in K>N dimensions.