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SeCritMass: Threshold Secret Petitions

Florian Breuer

TL;DR

The paper tackles the coordination problem of collective action under fear of retaliation by proposing an $n$-threshold secret petition framework that keeps signers anonymous until a critical mass is reached. It details an ElGamal-based construction (SeCritMass) with distributed key fragments, verifiable secret sharing, and secure multi-party computation to compute per-signature uniqueness hashes, enabling decryption only after $n$ signatures. The contribution includes a comprehensive design with entities, parameters, key generation, cyphersignatures, trigger/expiration mechanics, and variants for multiple thresholds and real-world applications like sexual harassment reporting and internal organizational complaints. It also discusses security considerations, attack scenarios, and practical governance requirements to preserve coercion resistance and signer privacy while enabling credible collective action.

Abstract

We introduce the notion of an $n$-threshold secret petition, in which users add encrypted signatures to a petition, and the signatures are decrypted if and only if at least $n$ signatures have been gathered. This solves the coordination problem in which users wish to sign a petition or commit to a cause, but do not want to be identified as having signed it before enough others have signed it too. We present an implementation of such a petition based on the ElGamal cryptosystem. Applications include reporting misconduct in situations were complainants hesitate to come forward alone, such as in allegations of sexual harassment or police brutality.

SeCritMass: Threshold Secret Petitions

TL;DR

The paper tackles the coordination problem of collective action under fear of retaliation by proposing an -threshold secret petition framework that keeps signers anonymous until a critical mass is reached. It details an ElGamal-based construction (SeCritMass) with distributed key fragments, verifiable secret sharing, and secure multi-party computation to compute per-signature uniqueness hashes, enabling decryption only after signatures. The contribution includes a comprehensive design with entities, parameters, key generation, cyphersignatures, trigger/expiration mechanics, and variants for multiple thresholds and real-world applications like sexual harassment reporting and internal organizational complaints. It also discusses security considerations, attack scenarios, and practical governance requirements to preserve coercion resistance and signer privacy while enabling credible collective action.

Abstract

We introduce the notion of an -threshold secret petition, in which users add encrypted signatures to a petition, and the signatures are decrypted if and only if at least signatures have been gathered. This solves the coordination problem in which users wish to sign a petition or commit to a cause, but do not want to be identified as having signed it before enough others have signed it too. We present an implementation of such a petition based on the ElGamal cryptosystem. Applications include reporting misconduct in situations were complainants hesitate to come forward alone, such as in allegations of sexual harassment or police brutality.
Paper Structure (16 sections, 3 equations, 1 figure)

This paper contains 16 sections, 3 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Formalization
  3. Requirements
  4. SeCritMass scheme details
  5. Entities
  6. Parameters.
  7. Key generation
  8. Signatures.
  9. Trigger.
  10. Expiration.
  11. Validators vs. key rabbits
  12. Applications and variants
  13. Multiple thresholds
  14. Sexual harassment reporting
  15. Complaints within an organization
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Signature process with $k=3$ key rabbits and $v=1$ validator.