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Computational Obfuscations and Random Oracles for Derandomizing Asynchronous Consensus

James Aspnes, Shlomi Dolev, Amit Hendin

TL;DR

The paper tackles asynchronous consensus under the FLP impossibility by proposing a two-stage derandomization that combines post-quantum time-lock-based program obfuscation with a post-quantum random oracle. A threshold conciliator is derandomized via obfuscation of a threshold function, while an adopt-commit framework and oracle-based recovery drive agreement in a bounded-adversary setting. Key contributions include preprocessing/execution schemes for a threshold-encoding function, a security-argument sketch for obfuscation hardness, and a multi-round consensus protocol that leverages both threshold and oracle conciliators. The work demonstrates how cryptographic obfuscation and random oracles can be integrated into distributed consensus to overcome classical impossibility results, with practical considerations for implementation and tuning. Overall, it provides a concrete theoretical pathway to derandomize asynchronous consensus under computational assumptions using post-quantum primitives and structured cryptographic obfuscation.

Abstract

A method for converting an asynchronous randomized consensus to a deterministic asynchronous consensus is presented. The method uses program computation obfuscation and a random oracle, assuming a computationally bounded scheduler, to overcome the impossibility result of Fischer, Lynch, and Paterson. Two stages are combined, in the first, a new form of computational program obfuscation implemented by post-quantum cryptographic hash functions is introduced, employing time lock puzzles to imply a computational gap between the consensus participants and the (imaginary adversarial) scheduler. In the second stage, a random oracle is implemented by using a post-quantum cryptographic hash function that allows each process to harvest pseudo-randomization from the (cleartext) program and a (consensus) round (variable) and, in turn, implies the completion of the consensus in the presence of a computationally bounded scheduler.

Computational Obfuscations and Random Oracles for Derandomizing Asynchronous Consensus

TL;DR

The paper tackles asynchronous consensus under the FLP impossibility by proposing a two-stage derandomization that combines post-quantum time-lock-based program obfuscation with a post-quantum random oracle. A threshold conciliator is derandomized via obfuscation of a threshold function, while an adopt-commit framework and oracle-based recovery drive agreement in a bounded-adversary setting. Key contributions include preprocessing/execution schemes for a threshold-encoding function, a security-argument sketch for obfuscation hardness, and a multi-round consensus protocol that leverages both threshold and oracle conciliators. The work demonstrates how cryptographic obfuscation and random oracles can be integrated into distributed consensus to overcome classical impossibility results, with practical considerations for implementation and tuning. Overall, it provides a concrete theoretical pathway to derandomize asynchronous consensus under computational assumptions using post-quantum primitives and structured cryptographic obfuscation.

Abstract

A method for converting an asynchronous randomized consensus to a deterministic asynchronous consensus is presented. The method uses program computation obfuscation and a random oracle, assuming a computationally bounded scheduler, to overcome the impossibility result of Fischer, Lynch, and Paterson. Two stages are combined, in the first, a new form of computational program obfuscation implemented by post-quantum cryptographic hash functions is introduced, employing time lock puzzles to imply a computational gap between the consensus participants and the (imaginary adversarial) scheduler. In the second stage, a random oracle is implemented by using a post-quantum cryptographic hash function that allows each process to harvest pseudo-randomization from the (cleartext) program and a (consensus) round (variable) and, in turn, implies the completion of the consensus in the presence of a computationally bounded scheduler.

Paper Structure

This paper contains 13 sections, 10 theorems, 3 equations, 4 algorithms.

Table of Contents

  1. Introduction
  2. Overview.
  3. The system
  4. The consensus task
  5. Bound on the cost of finding a bad execution
  6. Hidden threshold conciliator
  7. Computational obfuscation for threshold encoding
  8. Preprocessing Algorithm.
  9. Execution of the Obfuscated Program.
  10. Security Arguments Sketch.
  11. From conciliators to consensus
  12. Possible implementations of random oracles
  13. Concluding remarks

Key Result

Theorem 4.1

Given inputs $P_1,\dots,P_n$ representing processes in a shared-memory system where, in all executions, (a) each process $p_i$ outputs a decision value within $s$ steps, and (b) each process $p_i$ uses a total of at most $t$ time to compute its transitions, there is an adversary program that compute

Theorems & Definitions (18)

  • Theorem 4.1
  • Lemma 4.2
  • proof
  • Lemma 4.3
  • proof
  • Lemma 4.4
  • proof
  • Lemma 4.5
  • proof
  • Lemma 4.6
  • ...and 8 more