Research Article Open Access

Polynomial Interpolation in the Elliptic Curve Cryptosystem

Liew Khang Jie and Hailiza Kamarulhaili

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.

Journal of Mathematics and Statistics
Volume 7 No. 4, 2011, 326-331

DOI: https://doi.org/10.3844/jmssp.2011.326.331

Submitted On: 16 August 2011 Published On: 28 October 2011

How to Cite: Jie, L. K. & Kamarulhaili, H. (2011). Polynomial Interpolation in the Elliptic Curve Cryptosystem. Journal of Mathematics and Statistics, 7(4), 326-331. https://doi.org/10.3844/jmssp.2011.326.331

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Keywords

  • Lagrange polynomial interpolation
  • discrete logarithm problem
  • elliptic curve
  • cryptosystem
  • polynomial interpolation
  • curve cryptosystem
  • public key cryptosystem
  • finite field
  • advanced cryptography