The theoretical framework establishes that public-key cryptography relies on computational number theory to solve symmetric key exchange over insecure channels via asymmetric protocols based on finite abelian groups. Security is derived from the intractability of computationally hard problems, specifically the Discrete Logarithm Problem and the Computational Diffie-Hellman Problem within cyclic groups such as $\mathbb{Z}_n^*$ or elliptic curve point sets. The discipline bridges abstract algebra concepts like group axioms (closure, associativity, identity, inverse) and subgroup orders with algorithmic complexity analysis to define cryptographic strength boundaries independent of specific implementation methods.
The theoretical framework establishes that public-key cryptography relies on computational number theory to solve symmetric key exchange over insecure channels via asymmetric protocols based on finit…