A Large Scalar Multiplication Algorithm using Modified Pell Numbers for Key Generation

Abstract

Cryptographic algorithms consist of two parts, a key and an algorithm, to encrypt and decrypt data. The key is an essential part that works with the algorithm. The security of encryption schemes depends on the key size (key length) and the longer the key, the better the security it provides. Applying an elliptic curve has for key agreement provides a high-performance architecture and high security. The main process for calculating key points in Elliptic Curve Cryptography (ECC) is called scalar multiplication, which relates to point addition and point doubling. An efficient algorithm, proposed as the Large Scalar Multiplication Algorithm using Modified Pell Numbers (LSMA-MPN), was introduced to speed up the calculation of points on elliptic curves during large scalar multiplications. This system also reduced computation time by applying Modified Pell numbers in a 22 matrix representation. The experimental results showed that computation time was reduced by approximately 67% in comparison with the computation time required by a general algorithm.