Axiomatic Emergence AA; The Physical Origin of Cryptography

This paper starts from two fundamental principles—Information Conservation(A1) and Finite-Step Computability (A2)—to systematically derive the core concepts and protocol systems of modern cryptography. Research shows that fundamental cryptographic building blocks such as encryption, hashing, digital signatures, and security protocols are not ad hoc tools designed to counter specificthreats but are mathematical structures that inevitably arise from the universalneed to ensure controlled and verifiable transmission of information in untrustedenvironments, subject to the fundamental principles of information processing. Weprove that the boundary between computational feasibility (A2) and computational infeasibility naturally defines the foundation of cryptographic security; whilethe recoverability of information among authorized parties and its concealmentfrom unauthorized parties (as a specific form of A1) strictly constrain the mathematical properties that cryptographic transformations must satisfy. This paperfurther proposes experimental validation of the emerged cryptographic frameworkthrough side-channel attack experiments, solving competitions for computationallyhard problems, and formal verification of security protocols, thereby establishing afalsifiable bridge between the formal theory of cryptography and the physical realityof computation.