Observer-Quotient Security: Composable Leakage Bounds for Hidden State Continuations

2026-07-03

AI Summary

This work addresses the challenge of uniformly modeling information leakage arising from persistent hidden states in interactive cryptographic systems by proposing a security framework grounded in observer quotient spaces. It introduces session-tagged observer-indexed experiments, adaptive schedulers, and ideal quotient functionalities to explicitly couple hidden-state persistence with observer capabilities, thereby establishing composable leakage bounds and reducing security to indistinguishability between real and ideal worlds. The paper innovatively formulates additive sequential flaws, product total-variation parallel bounds, and an adaptive observer encapsulation mechanism. Leveraging non-uniform simulators, observability kernel identification, and control-theoretic tools—such as dissipativity and input-to-state stability (ISS) residual bounds—it achieves advantage reduction. The framework’s efficacy is validated through leakage auditing and linear time-invariant (LTI) observer design in settings including IND-CPA encryption, deterministic encryption, and timing, cache, power, and electromagnetic side channels.

Abstract

Observer-quotient security studies interactive cryptographic systems whose security depends on what an admissible observer can distinguish across transcripts, leakage traces, and hidden implementation continuations. The paper defines observer-indexed experiments with session identifiers, adaptive schedulers, oracle forwarding, simulators, ideal quotient functionalities, and nonuniform environments, and proves a real/ideal emulation theorem in which sequential morphism defects add, parallel defects obey a product-TV bound, and adaptive observer choice is absorbed by an explicit wrapper construction. The resulting advantage bound is indexed by $δ_{\mathrm{obs},t}$, $δ_{K,t}$, $δ_{\mathrm{post},t}$, $δ_{\mathrm{sim},t}$, $η_t$, and the residual floor $ρ_T(\mathbb E Z_T)$. The framework is instantiated for IND-CPA encryption with timing leakage, deterministic encryption with entropy ledgers, and finite-state side-channel refinement under transcript, timing, cache, power, EM, and profiled observers. The optimization/control component identifies hidden continuations with observability kernels, treats sensor redesign as quotient refinement, and converts dissipativity, PL-type rates, and ISS residual bounds into concrete reductions in distinguishing advantage. Ancillary code and synthetic data reproduce the finite-state leakage audit and LTI observer-design benchmark.

Problem

• observer-quotient security
• hidden state continuations
• composable leakage bounds
• side-channel observers
• interactive cryptographic systems

Innovation

• observer-quotient security
• composable leakage bounds
• hidden state continuations
• real/ideal emulation
• side-channel refinement