Category: Group theory

Sharing secrets with polynomials

This post will present a couple ways to share secrets using polynomials. We have a group of n people who want to share a secret between them so that k of them will have to cooperate in order to unlock the secret. For example, maybe a committee of n = 5 wants to require the cooperation of […]

Addition on Curve1174

I’ve written about elliptic curve and alluded to the fact that there’s a special kind of addition for points on the curve. But I haven’t gone into details because it’s more complicated than I wanted to get into. However, there’s a special case where the details are not complicated, the so called Edwards curves. I’ll look […]

Groups of order 2019

How many groups have 2019 elements? What are these groups? 2019 is a semiprime, i.e. the product of two primes, 3 and 673. For every semiprime s, there are either one or two distinct groups of order s. As explained here, if s = pq with p > q, all groups of order s are isomorphic if q is not a factor of p-1. […]