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 con
cepts and protocol systems of modern cryptography. Research shows that fun
damental cryptographic building blocks such as encryption, hashing, digital sig
natures, and security protocols are not ad hoc tools designed to counter specific
threats but are mathematical structures that inevitably arise from the universal
need to ensure controlled and verifiable transmission of information in untrusted
environments, subject to the fundamental principles of information processing. We
prove that the boundary between computational feasibility (A2) and computa
tional infeasibility naturally defines the foundation of cryptographic security; while
the recoverability of information among authorized parties and its concealment
from unauthorized parties (as a specific form of A1) strictly constrain the math
ematical properties that cryptographic transformations must satisfy. This paper
further proposes experimental validation of the emerged cryptographic framework
through side-channel attack experiments, solving competitions for computationally
hard problems, and formal verification of security protocols, thereby establishing a
falsifiable bridge between the formal theory of cryptography and the physical reality
of computation.