Secret sharing schemes and noncommutative polynomial interpolation

Abstract

Secret sharing schemes and polynomial interpolation - their link is by now historic. This thesis uses and develops noncommutative models of interpolation and subsequently extends the original Shamir scheme of 1979 in several instances.

Using first left-oriented quaternion polynomials, also present are two novel schemes which use free quaternion polynomials.

The schemes exhibited, though making no use of the numerous advancements of secret sharing schemes, may be themselves conceivably advanced in much the same way that the Shamir scheme has. Thus the groundwork for schemes with noncommutative polynomials is founded.