Proof-Theoretic Cryptography: A New Paradigm from the Cut-Elimination Theorem

Traditional cryptography faces the challenge that digital resources can be copied infinitely and usage traces cannot be verified, relying solely on trust or centralized records. We propose a verifiable consumption mechanism based on proof net cut elimination, introducing a new security dimension—consumption auditability—which solves the fundamental problem of “how to publicly verify that a digital resource has been consumed.” Potential applications include double-spending prevention for e-tickets, non-repudiable self-destructing messages, one-time authorization tokens, and fair voting. In particular, for big data security, this mechanism can provide one-time tokens for data usage rights, enabling non-repudiable auditing of data flow and copy‑proof data assets, thereby offering a cryptographically verifiable, trust‑free new approach to data ownership and usage metering.