No abstract

Elliptic curve cryptography is one of the most efficient public-key cryptosystems compared to the Rivest-Shamir-Addleman scheme. One of the methods to compute elliptic curve scalar multiplication is division polynomials which utilize the non-linear recurrence relation also known as the elliptic net. Previous studies were related to elliptic curve scalar multiplication via elliptic net which implemented the use of C++, GP/PARI or Java programming. This study aims to implement the Python programming in the SageMath compiler for computing elliptic net scalar multiplication based on the National Institute of Standards and Technology curve of the type P-192. The implementation could be seen at three main processes which are the scalar decomposition, the blocks of elliptic net generation namely the initial and final blocks, as well as scalar multiplication computation. The base point and prime field of the short Weierstrass curve with a large scalar are the parameters used in the process. The results showed that the implemented programming was easier while working with a large prime number field, vulnerable to errors and can be easily verified. The implemented programming can also be used to compute scalar multiplication on other standardizations of elliptic curve cryptography such as Brainpool 384-bit prime field or NUMS 256-bit prime field curves.