Arithmetic of Koblitz Curve Secp256k1 Used in Bitcoin Cryptocurrency Based on One Variable Polynomial Division
5 Pages Posted: 26 Apr 2019
Date Written: April 8, 2019
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
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