History-Recoverability Post-Quantum Security (HR-PQS)

Abstract

This paper introduces History-Recoverability Post-Quantum Security (HR-PQS), a lightweight theoretical framework for post-quantum security based on the principle of unrecoverable history. Rather than treating the quantum threat as merely a problem of replacing vulnerable cryptographic algorithms, HR-PQS reformulates post-quantum security as a question of whether future quantum-capable adversaries can reconstruct meaningful past histories from stored ciphertexts, keys, logs, backups, certificates, metadata, and operational residues. The central claim is that post-quantum cryptography is necessary but not sufficient. Even when quantum-resistant algorithms are deployed, long-lived information may remain vulnerable through archived ciphertexts, residual key material, metadata leakage, certificate chains, traffic patterns, and backup recovery paths. HR-PQS therefore shifts the security objective from simple decryption failure to semantic history-unrecoverability. The framework unifies existing security practices such as post-quantum cryptography, perfect forward secrecy, ratcheting, secure key erasure, re-encryption, envelope encryption, metadata hiding, and cryptographic agility under a single operational principle: history pruning. In this view, key rotation is not merely a lifecycle procedure, but a mechanism for cutting future reconstruction paths from past encrypted histories. Mathematically, HR-PQS models a future quantum adversary as a relational observer with access to quantum computation, classical computation, internal information, stored ciphertexts, backups, and metadata. Security is defined through a history-recoverability functional combining mutual information leakage, semantic recovery advantage, collapse risk, and operational cost. The paper further introduces a semantic recovery game and a history-recoverability distance for measuring whether an adversary can reconstruct useful domain-specific features of past information, such as financial transaction graphs, medical diagnosis patterns, communication networks, or enterprise activity timelines. The theory is inspired by TrinityLabo's Recoverable Reality Principle and Relational Recoverable Reality Principle, but reverses their role for cryptographic security: in physical theory, good compression should remain recoverable; in security theory, attacker-side reconstruction must remain impossible. HR-PQS is not proposed as a new cryptographic primitive or replacement protocol. Instead, it is a lightweight upper-level theory for organizing existing and emerging post-quantum security practices around the deeper requirement of protecting the past from future reconstruction. In short: not merely quantum-resistant encryption, but unrecoverable history.