(A) modified ElGamal ECC using a knapsack scheme

Abstract

In this thesis, we propose a modified ElGamal elliptic curve cryptosystem using a knapsack scheme. We will use an elliptic curve defined over $F_{p^n}$. And we will encrypt or decrypt a message using the knapsack scheme. To use the knapsack scheme, a sender must share a sequence with a receiver. We share the sequence with a similar method to ElGamal ECC. Also, we will consider possible attacks and the complexity for the ElGamal ECC and the proposed cryptosystem. Finally, we will compare the proposed cryptosystem with the ElGamal ECC in the terms of security and efficiency.