Abstract
Problem statement: In this research, we incorporate the polynomial interpolation method in the discrete logarithm problem based cryptosystem which is the elliptic curve cryptosystem. Approach: In this study, the polynomial interpolation method to be focused is the Lagrange polynomial interpolation which is the simplest polynomial interpolation method. This method will be incorporated in the encryption algorithm of the elliptic curve ElGamal cryptosystem. Results: The scheme modifies the elliptic curve ElGamal cryptosystem by adding few steps in the encryption algorithm. Two polynomials are constructed based on the encrypted points using Lagrange polynomial interpolation and encrypted for the second time using the proposed encryption method. We believe it is safe from the theoretical side as it still relies on the discrete logarithm problem of the elliptic curve. Conclusion/Recommendations: The modified scheme is expected to be more secure than the existing scheme as it offers double encryption techniques. On top of the existing encryption algorithm, we managed to encrypt one more time using the polynomial interpolation method. We also have provided detail examples based on the described algorithm.
Highlights
Whitfield Diffie and Martin Hellman had introduced the Diffie-Hellman key exchange scheme to the cryptography world which later planted the seeds for the development of public key cryptosystem (Diffie and Hellman, 1976)
We are going to turn our attention to elliptic curve cryptosystem which is the elliptic curve discrete logarithm based public key cryptosystem
elliptic curve cryptosystem (ECC) was based on discrete logarithm problem by using a group of points on an elliptic curve defined over finite field and its running times is fully exponential
Summary
Whitfield Diffie and Martin Hellman had introduced the Diffie-Hellman key exchange scheme to the cryptography world which later planted the seeds for the development of public key cryptosystem (Diffie and Hellman, 1976). In this scheme, two keys namely public key and secret key are used where public key is made public for encryption steps whereas secret key is kept secretly for decryption steps and it is computationally infeasible. ECC was based on discrete logarithm problem by using a group of points on an elliptic curve defined over finite field and its running times is fully exponential.
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