Effective Implementations of Scalar Multiplications in Elliptic Curve Cryptography

Digitization is the term used to describe the current global technological migration from traditional to computational with the aid of IOT. Although the amount of data handled for daily applications is rapidly growing, security issues continue to be a top priority. The elliptic curve cryptography algorithm (ECC) is used in many security protocols for basic security features including digital signatures, authentication, and confidentiality. This technique helps shield data from side channel assaults. Scalar multiplication, which demands more time complexity and involves inverse operations, is essential to the execution of ECC. Here, we present a novel approach to efficiently implement scalar multiplication using the Residue Number System (RNS) with the Sum of Residues (SOR) parallel implementation in order to lower the time complexity of scalar multiplications by converting high-order curve points to low-order ones that have fewer inverse functions. Using point addition and doubling, this new approach is applied to two standard curves: the Edward curve (ED25519) and the Kobilitz curve (SECP256K1). The results demonstrate how well the RNS-based scalar multiplication implements the use of ECC.