Zero-Knowledge Proofs in Identity Management — Cryptography, Key Management, Post-Quantum, Sovereign AI, and Post-Cloud Architecture (Mf+So)

Abstract

This paper presents a comprehensive analysis of zero-knowledge proof (ZKP) systems and their application to privacy-preserving identity management within the MF+SO sovereign identity vault. Zero-knowledge proofs, introduced by Goldwasser, Micali, and Rackoff (1985), enable a prover to convince a verifier of the truth of a statement without revealing any information beyond the statement's validity. We examine three families of ZKP systems in the context of MF+SO's identity assertions: zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge), zk-STARKs (Zero-Knowledge Scalable Transparent Arguments of Knowledge), and Bulletproofs. For each family, we analyze the setup assumptions (trusted setup vs. transparent), proof size, verification complexity, prover computation, and post-quantum security. The paper identifies three canonical use cases within MF+SO: (1) age verification without date of birth disclosure, where the user proves that their age exceeds a threshold without revealing their exact birth date; (2) credential possession proof, where the user proves they hold a valid credential for a resource without revealing which credential among a set they hold; and (3) membership in an allowlist without position disclosure, where the user proves their identifier appears in a list without revealing their position in the list. We present benchmark data for each use case using the Groth16 zk-SNARK (prover time: 1.2 seconds, proof size: 192 bytes, verification: 2.3 ms) and the STARK-based approach using the Winterfell library (prover time: 4.8 seconds, proof size: 48 KB, verification: 8.1 ms). The implementation complexity analysis demonstrates that zk-SNARKs require trusted setup ceremonies but provide the most compact proofs, while zk-STARKs eliminate the trusted setup requirement at the cost of larger proofs. The paper concludes with an analysis of the protocol integration requirements, including circuit compilation for the MF+SO identity predicate lang... Part of The Anticloud research corpus by Lois-Kleinner Alpasan (ORCID: 0009-0009-2233-6107). This work explores cryptography, key management in the context of sovereign AI infrastructure, post-cloud computing architectures, and transparent, blackbox-free systems.