Mathematics · Group Theory

To understand the application of Elliptic Curve Groups in cryptography, one must trace the algebraic hierarchy up to its security implementation. Arrange the following mathematical and cryptographic steps in the correct progressive sequence, starting from the most basic structural conditions to the final security mechanism. A. The inclusion of an identity element to transition the structure into a Monoid. B. The establishment of closure and associativity conditions to form a Semigroup. C. The application of the computational difficulty of the Discrete Logarithm Problem within finite groups for security. D. The addition of inverse conditions to formally complete the structure as a Group. Choose the correct answer from the options given below: