Cryptography is the academic discipline concerned with the design, analysis, and implementation of methods for securing information and communications through the use of mathematical algorithms. This field investigates the construction and analysis of protocols and schemes aimed at achieving security properties such as confidentiality, integrity, authentication, and non-repudiation in the presence of adversaries. Key characteristics involve reliance on computational complexity theory, rigorous mathematical proofs of security, and the development and composition of cryptographic primitives and protocols, which are fundamental for securing modern digital systems and transactions.