Applications of Algebraic Curves to Cryptography

107 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.Secondly, we use algebraic functions with two poles to obtain efficient secret sharing schemes. We present a method to find the lower bounds for the minimum distance of geometric codes. We apply this to the two-point codes on a Hermitian function field. The lower bounds turn out to be sharp and they meet the formulas by Homma and Kim for the actual minimum distance of the Hermitian two-point codes with a shorter proof and fewer cases for the formulas. Moreover, our approach gives an efficient error correcting algorithm to decode up to half the actual minimum distance.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD