n parties over a complete synchronous or semi-synchronous network continuously compute a public Mealy FSM on periodically supplied secret-shared inputs. Parties do not know their compromise history and maintain secret shares of FSM state and output.

1. assumption

   Cryptographic and hardware setup

   assumed

   Every party has a true random number generator and tamper-resistant access to its private key and the configuration authority's public key; parties can authenticate fresh public keys, derive pairwise secure channels, and establish secure broadcast.

   Parties, network, key setup, hardware, inputs, and clocks
2. assumption

   Stabilizing time base

   inherited component

   A self-stabilizing Byzantine clock-synchronization protocol supplies logical global pulses and common round numbers in the semi-synchronous setting; this clock is an assumed underlying service, not constructed in the announcement.

   Parties, network, key setup, hardware, inputs, and clocks · Clock, key, VSS, state-validation, transition, and output pipeline
3. threat model

   Temporary total mixed compromise

   defined

   A computationally bounded adversary may passively or actively corrupt any number of parties, including all n for a finite interval, but watchdog-driven recovery prevents indefinite control of every party and the adversary cannot immediately recapture a just-recovered party.

   Mixed mobile adversary and recovery assumptions

Each transition round refreshes communication keys, verifiably reshapes the state shares, securely checks that they encode a legitimate state, and evaluates public transition and output circuits using an existing MPC protocol.

1. protocol

   Fresh channel establishment

   composed from primitives

   Parties generate fresh key pairs from local true randomness, use Byzantine agreement to agree on each public key, and derive fresh pairwise symmetric keys before processing the next FSM transition.

   Clock, key, VSS, state-validation, transition, and output pipeline
2. algorithm

   State validation and reset

   specified

   VSS supplies redundant state shares and an MPC evaluates an error-detection circuit such as Berlekamp-Welch to test polynomial degree and membership in the legal-state set. Invalid state is replaced by shares of public default state S0.

   Clock, key, VSS, state-validation, transition, and output pipeline · Secure self-stabilizing FSM Algorithm 1
3. algorithm

   Private transition and output evaluation

   specified

   On a valid state, MPC applies transition circuit T to the current state and new input and output circuit O to produce secret-shared next state and output; after reset, the same circuits run from S0.

   Secure self-stabilizing FSM Algorithm 1

The brief states conditional recovery rather than uninterrupted security: during total compromise all secrets may be exposed, and protection resumes only after the required party threshold and supporting services recover.

1. claim

   Consistency and security convergence

   construction claim

   Once fewer than roughly one third of participants are Byzantine in the illustrated setting, state checking and secure transition evaluation are claimed to restore consistent state, correct computation, and confidentiality.

   Secure self-stabilization problem and claimed direction · Secure self-stabilizing FSM Algorithm 1
2. claim

   Loss of stale adversarial state knowledge

   graph conditional

   With unknown fresh inputs, a complete FSM transition graph makes every state possible to the adversary after the first post-convergence transition; an expander transition graph is stated to erase state knowledge after logarithmically many transitions.

   Post-convergence secrecy recovery under transition-graph conditions

The announcement defines the setting, composes known cryptographic and stabilization components, and supplies Algorithm 1 and recovery intuition. It does not present a formal ideal functionality, simulator, theorem statement, full proof, implementation, or experiment.

1. evidence

   Mechanism-level support

   mechanism inspected

   Fresh randomness severs old channel-key exposure, error-correcting state checks remove malformed Byzantine shares, the default state restores legality, and post-recovery secret inputs drive the FSM away from previously known state.

   Clock, key, VSS, state-validation, transition, and output pipeline · Post-convergence secrecy recovery under transition-graph conditions

Recovery depends on trustworthy local reset, TRNGs, secure hardware keys, clock stabilization, Byzantine agreement, VSS, and an MPC whose threshold has recovered. The protocol does not protect secrets already learned during total compromise or guarantee correct outputs before convergence.

1. limitation

   Formal and systems obligations

   unresolved in brief

   The three-page source does not analyze composability among all assumed services, recovery timing, adaptive re-corruption rates, output handling during unsafe rounds, implementation overhead, or failures of the hardware watchdog and configuration authority.

   Parties, network, key setup, hardware, inputs, and clocks · Secure self-stabilizing FSM Algorithm 1