Scalar Multiplication via Elliptic Net using Generalized Equivalent Sequences
Norliana Muslim1, Mohamad Rushdan Md. Said2
1Norliana Muslim*, Department of Engineering, Faculty of Engineering and Life Sciences, University Selangor, Bestari Jaya, Malaysia.
2Mohamad Rushdan Md. Said, Institute for Mathematical Research, University Putra , Selangor, Malaysia.
Manuscript received on September 23, 2019. | Revised Manuscript received on October 15, 2019. | Manuscript published on October 30, 2019. | PP: 4418-4424 | Volume-9 Issue-1, October 2019 | Retrieval Number: A2007109119/2019©BEIESP | DOI: 10.35940/ijeat.A2007.109119
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Chord and tangent is a classical method to calculate the elliptic curve scalar multiplication. Alternatively, the scalar multiplication can be calculated by dividing polynomials over certain finite fields and the first elliptic net scalar multiplication was implemented on a short Weierstrass curve. The net was originated from non-linear recurrence sequences, namely as elliptic divisibility sequence. It is well known that the linear recurrence sequences have been applied in the cryptosystem as a cipher in the encryption and decryption process. From the perspective of cryptographic application, the elliptic divisibility sequence is used generally for integer factorization, solving elliptic curve discrete logarithm problem and computation of pairing or scalar multiplication. But there is a lack of contribution of these non-linear recurrence sequences in scalar multiplication. Therefore, this paper aims to discuss a generalization of the equivalent sequence of elliptic divisibility for computing scalar multiplication. The experimental results of scalar multiplication via the net and its coding in computer programming are presented. The future direction of scalar multiplication via the elliptic net is also discussed.
Keywords: Elliptic curve, Division polynomials, Scalar multiplication.