A formal proof is a proof expressed in a precise language that a computer can check step by step, such as a proof assistant or theorem prover. Unlike a natural-language argument, it removes ambiguity by encoding theorems, assumptions, and inference rules in machine-readable form.
In cyber security, formal proofs matter because they can verify critical properties of software and protocols, such as whether an authentication flow resists forgery or whether a cryptographic algorithm is used correctly. Defenders use them to reduce design flaws in high-trust code, while attackers may target the build, dependency, or toolchain that produces the proof artifact. A formal proof is strongest when paired with independent review, reproducible builds, and clear provenance, because the proof only certifies what was actually encoded.