Arithmetic of Koblitz Curve Secp256k1 Used in Bitcoin Cryptocurrency Based on One Variable Polynomial Division

5 Pages Posted: 26 Apr 2019

See all articles by Santoshi Pote

Santoshi Pote

Ramrao Adik Institute of Technology, Students

Virendra Sule

Indian Institute of Technology (IIT), Bombay

B.K. Lande

Mukesh Patel School of Technology Management and Engineering

Date Written: April 8, 2019

Abstract

Bitcoin uses a specific Koblitz curve secp256k1 is a type of elliptic curve defined by the Standards for Efficient Cryptography Group (SECG). This paper develops an approach for arithmetic (point addition and doubling) on secp256k1 Koblitz curve over finite fields using one variable polynomial based on Euclidean division. This approach succeeds in computing these operations due to a striking observation about computing the gcd of two polynomials one which represents the elliptic curve as its roots and the other representing the lines which intersect or are tangent to the curve. The resulting algorithm is tested on realistic secp256k1 Koblitz curve and is shown to be scalable to perform the computations.

Keywords: koblitz curve, finite field, polynomial division

Suggested Citation

Pote, Santoshi and Sule, Virendra and Lande, B.K., Arithmetic of Koblitz Curve Secp256k1 Used in Bitcoin Cryptocurrency Based on One Variable Polynomial Division (April 8, 2019). 2nd International Conference on Advances in Science & Technology (ICAST) 2019 on 8th, 9th April 2019 by K J Somaiya Institute of Engineering & Information Technology, Mumbai, India, Available at SSRN: https://ssrn.com/abstract=3367674 or http://dx.doi.org/10.2139/ssrn.3367674

Santoshi Pote (Contact Author)

Ramrao Adik Institute of Technology, Students ( email )

India

Virendra Sule

Indian Institute of Technology (IIT), Bombay ( email )

Powai
IIT Bombay, Powai
Mumbai, Maharashtra 400076
India

B.K. Lande

Mukesh Patel School of Technology Management and Engineering ( email )

Mumbai
India

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