Elliptic Curve Cryptography: A Mathematical Approach

Abstract: Mathematics consider as Heart of Cryptography, which is a science of securing communication and data. Mathematics underpins the algorithms used to encrypt and decrypt data. For example, public-key cryptography relies on mathematical problems like factoring large numbers RSA (Rivest, Shamir, and Adleman) or solving discrete logarithms (Elliptic Curve Cryptography). Mathematical procedures generate secure keys used in encryption. The strength of these keys is often based on complex mathematical problems that are computationally difficult to solve. Cryptography often requires random numbers for key generation and other processes. Mathematical methods ensure that these random numbers are truly unpredictable and secure. In essence, mathematics is the foundation that makes modern cryptography both robust and reliable, ensuring secure communications in the digital age.