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

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