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Zero-Knowledge Proof-of-Identity: Sybil-Resistant, Anonymous Authentication on Permissionless Blockchains and Incentive Compatible, Strictly Dominant Cryptocurrencies

David Cerezo Sánchez

TL;DR

The proposed solution effectively limits the number of mining nodes a single individual would be able to run while keeping membership open to everyone, circumventing the impossibility of full decentralization and the blockchain scalability trilemma when instantiated on a blockchain with a consensus protocol based on the cryptographic random selection of nodes.

Abstract

Zero-Knowledge Proof-of-Identity from trusted public certificates (e.g., national identity cards and/or ePassports; eSIM) is introduced here to permissionless blockchains in order to remove the inefficiencies of Sybil-resistant mechanisms such as Proof-of-Work (i.e., high energy and environmental costs) and Proof-of-Stake (i.e., capital hoarding and lower transaction volume). The proposed solution effectively limits the number of mining nodes a single individual would be able to run while keeping membership open to everyone, circumventing the impossibility of full decentralization and the blockchain scalability trilemma when instantiated on a blockchain with a consensus protocol based on the cryptographic random selection of nodes. Resistance to collusion is also considered. Solving one of the most pressing problems in blockchains, a zk-PoI cryptocurrency is proved to have the following advantageous properties: - an incentive-compatible protocol for the issuing of cryptocurrency rewards based on a unique Nash equilibrium - strict domination of mining over all other PoW/PoS cryptocurrencies, thus the zk-PoI cryptocurrency becoming the preferred choice by miners is proved to be a Nash equilibrium and the Evolutionarily Stable Strategy - PoW/PoS cryptocurrencies are condemned to pay the Price of Crypto-Anarchy, redeemed by the optimal efficiency of zk-PoI as it implements the social optimum - the circulation of a zk-PoI cryptocurrency Pareto dominates other PoW/PoS cryptocurrencies - the network effects arising from the social networks inherent to national identity cards and ePassports dominate PoW/PoS cryptocurrencies - the lower costs of its infrastructure imply the existence of a unique equilibrium where it dominates other forms of payment

Zero-Knowledge Proof-of-Identity: Sybil-Resistant, Anonymous Authentication on Permissionless Blockchains and Incentive Compatible, Strictly Dominant Cryptocurrencies

TL;DR

The proposed solution effectively limits the number of mining nodes a single individual would be able to run while keeping membership open to everyone, circumventing the impossibility of full decentralization and the blockchain scalability trilemma when instantiated on a blockchain with a consensus protocol based on the cryptographic random selection of nodes.

Abstract

Zero-Knowledge Proof-of-Identity from trusted public certificates (e.g., national identity cards and/or ePassports; eSIM) is introduced here to permissionless blockchains in order to remove the inefficiencies of Sybil-resistant mechanisms such as Proof-of-Work (i.e., high energy and environmental costs) and Proof-of-Stake (i.e., capital hoarding and lower transaction volume). The proposed solution effectively limits the number of mining nodes a single individual would be able to run while keeping membership open to everyone, circumventing the impossibility of full decentralization and the blockchain scalability trilemma when instantiated on a blockchain with a consensus protocol based on the cryptographic random selection of nodes. Resistance to collusion is also considered. Solving one of the most pressing problems in blockchains, a zk-PoI cryptocurrency is proved to have the following advantageous properties: - an incentive-compatible protocol for the issuing of cryptocurrency rewards based on a unique Nash equilibrium - strict domination of mining over all other PoW/PoS cryptocurrencies, thus the zk-PoI cryptocurrency becoming the preferred choice by miners is proved to be a Nash equilibrium and the Evolutionarily Stable Strategy - PoW/PoS cryptocurrencies are condemned to pay the Price of Crypto-Anarchy, redeemed by the optimal efficiency of zk-PoI as it implements the social optimum - the circulation of a zk-PoI cryptocurrency Pareto dominates other PoW/PoS cryptocurrencies - the network effects arising from the social networks inherent to national identity cards and ePassports dominate PoW/PoS cryptocurrencies - the lower costs of its infrastructure imply the existence of a unique equilibrium where it dominates other forms of payment

Paper Structure

This paper contains 55 sections, 10 theorems, 69 equations, 5 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Literature
  4. Proof-of-Personhood Considered Harmful (and Illegal)
  5. Building Blocks
  6. Consensus based on the Cryptographic Random Selection of Transaction Processing Nodes
  7. X.509 Public Key Infrastructure
  8. Electronic Passports
  9. Verifiable Computation
  10. Verifiable Validation of X.509 Certificates as Anonymous Credentials
  11. Cryptographic Accumulators
  12. Remote Attestation
  13. Authentication Protocols
  14. Authentication Protocols using Zero-Knowledge
  15. Security Goals
  16. ...and 40 more sections

Key Result

Theorem 4

For any initial state, a system satisfying GR-$m$, ND-$m$, NS-$\delta$, and ED-$\left(\epsilon,\delta\right)$ converges in probability to $\left(m,\epsilon,\delta\right)$-decentralization. impossibleDecentralization

Figures (5)

  • Figure 4.1: Simplified overview of mutual attestation.
  • Figure 4.2: Legend: (1) National identity card is a mandatory smartcard; (2) National identity card is a voluntary smartcard; (3) No national identity card, but cryptographic identification is possible using an ePassport, driving license and/or health card; (4) Non-digital identity card.
  • Figure 4.3: Availability of biometric passports. Source (ICAO, 2019)
  • Figure 4.4: Mobile App using Non-Zero-Knowledge Authentication
  • Figure :

Theorems & Definitions (40)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 4
  • Theorem 5
  • Conjecture 6
  • Theorem 7
  • proof
  • Definition 8
  • Example 9
  • ...and 30 more