Editing Secret sharing (section)

===Shamir's scheme===
{{main|Shamir's secret sharing}}

In this scheme, any ''t'' out of ''n'' shares may be used to recover the secret.  The system relies on the idea that one can construct a unique [[polynomial]] of degree {{nowrap|''t'' − 1}}, such that each of the ''t'' points lies on the polynomial.  It takes two points to define a straight line, three points to fully define a quadratic, four points to define a cubic curve, and so on. That is, it takes ''t'' points to define a polynomial of degree {{nowrap|''t'' − 1}}.   The method is to create a polynomial of degree {{nowrap|''t'' − 1}} with the secret as the first coefficient and the remaining coefficients picked at random.  Next find ''n'' points on the curve and give one to each of the players.  When at least ''t'' out of the ''n'' players reveal their points, there is sufficient information to fit a {{nowrap|(''t'' − 1)}}th degree polynomial to them, the first coefficient being the secret.