A New Approach to Construct (K, N) Threshold Secret Sharing Schemes Based on Finite Field Extension

Abstract

With increase in use of internet there is need to keep passwords, secret keys, important information secret. One way to do this is encryption. But it also need key which should be kept secure. Sometimes key is secure. But what will happens if the key is lost, forgotten etc. This problem can be solved using secret sharing. Instead of sharing whole secret, it is divided into pieces and distributed to finite set of pieces and some subset of pieces called access structure of scheme, which can recover secret. Here we propose a new way to construct threshold secret sharing schemes based on finite field extension using Blakley's secret sharing as a base. It is useful in many cryptographic applications and security. Because of finite fields the size of numbers stays within a specified range, doesn't matter how many operations we apply on number.