Beyond PQC Zero-Knowledge Proofs, Secure Multiparty Computation and Cryptographic Innovation

Like traditional encryption, ZKPs and SMPC rely on cryptographic primitives vulnerable to quantum attack. However, quantum-resistant variants are emerging: lattice-based ZKPs, hash-based commitments and post-quantum SMPC protocols. NIST’s PQC standardisation (FIPS 203, 204, 205) provides foundations.

For UK/EU organisations, the strategic imperative is embedding quantum resistance from the outset, not retrofitting later.

• For NIST standards and NCSC timelines: NCSC Guidance Post on Post Quantum Cryptography

A valid zero-knowledge proof must satisfy three properties

Completeness: If the statement is true, an honest prover can convince an honest verifier.

Soundness: If the statement is false, no cheating prover can convince the verifier (except with negligible probability).

Zero-Knowledge: The verifier learns nothing beyond the statement’s truth – no information about the underlying secret is revealed.

Traditional approach: User presents full birth certificate (over-disclosure).

ZKP approach: User generates cryptographic proof demonstrating “birth date is before [threshold]” without revealing actual birth date. Verifier confirms proof validity without learning specific age.

This simple example illustrates the power of ZKPs: selective disclosure that satisfies regulatory requirements whilst minimising data exposure.

Interactive ZKPs require back-and-forth communication. Useful for real-time verification but impractical for asynchronous scenarios.

Non-Interactive ZKPs (NIZKs) generate single proofs verifiable by anyone, anytime. Essential for blockchain and verifiable credentials.

zk-SNARKs produce tiny proofs verifiable in milliseconds. Used in privacy-preserving blockchains (Zcash) and layer-2 scaling (zkSync).

zk-STARKs offer quantum resistance without trusted setup requirements, particularly attractive for long-term security.

Financial Services

Regulatory Reporting: Banks prove capital adequacy, liquidity ratios, or stress test compliance to regulators without revealing granular trading positions or client data.

Anti-Money Laundering (AML): Financial institutions verify transaction legitimacy and counterparty credentials without exposing underlying identities or amounts, satisfying both privacy regulations and AML obligations.

Selective Disclosure in Securities: Investors prove accredited status or compliance with investment restrictions without revealing complete financial profiles.

Digital Identity and Credentials:

Verifiable Credentials: Individuals prove employment, education, or professional qualifications without relying on centralised databases vulnerable to breaches or surveillance.

GDPR-Compliant Authentication: Users authenticate identity attributes (age, nationality, residency) without over-disclosing personal data, satisfying Article 5’s data minimisation principle.

Cross-Border Verification: EU citizens prove compliance with UK immigration requirements or vice versa without exposing full travel histories or biometric data to multiple jurisdictions.

Healthcare and Research

Clinical Trial Eligibility: Patients prove eligibility criteria satisfaction without revealing complete medical histories to pharmaceutical companies.

Federated Learning with Privacy: Healthcare AI models train on distributed patient data without centralising sensitive records, satisfying GDPR Article 89 research exemptions while maintaining privacy.

Current ZKP implementations often rely on elliptic curve pairings or RSA assumptions, both of which are vulnerable to Shor’s algorithm. As CRQCs emerge, ZKP-based systems face catastrophic risks: credential forgery, privacy violations, and regulatory non-compliance.

Quantum-resistant ZKP research focuses on lattice-based constructions, hash-based commitments and post-quantum secure SNARKs using ML-KEM and ML-DSA.

For organisations deploying ZKP-based systems today, quantum resistance must be an architectural priority.

• For regulatory crypto-agility requirements:  PQC and Regulatory Compliance: GDPR, DORA and Beyond

Consider three competing banks wanting to calculate average loan default rates for systemic risk assessment – a real-world scenario explored by European banking regulators. Traditional approaches require either:

1. Centralised aggregation: Each bank shares sensitive data with regulator (privacy and competitive risk)
2. Trusted third party:  Data shared with intermediary (single point of failure, surveillance risk)
3. No collaboration: Each bank operates with incomplete information (poor risk management)

SMPC offers a fourth path: Banks jointly compute the average without any party learning others’ individual default rates. The calculation happens through cryptographic protocols that distribute computation across participants, ensuring no single party sees raw inputs.

SMPC Process

Secret Sharing: Each party splits private input into cryptographic “shares” distributed to others. Individual shares reveal nothing.

Distributed Computation: Parties perform calculations on shares using special protocols. Operations happen on encrypted data.

Result Reconstruction: Parties combine results to reveal final answer without reconstructing individual inputs.

This enables trustless collaboration – co-operation without trust or intermediaries.

Financial Sector Applications

Fraud Detection Across Institutions: Banks detect coordinated fraud patterns by analysing transaction data across institutions without sharing customer information. Each bank’s data remains private; only fraud indicators emerge.

Benchmark Rate Calculation: Financial institutions compute LIBOR-successor rates or benchmark yields collaboratively without revealing individual submissions, addressing manipulation concerns whilst preserving privacy.

Regulatory Stress Testing: Regulators assess systemic risk by running stress scenarios across multiple institutions’ portfolios without accessing granular position data.

Supply Chain and Commercial Contexts

Collaborative Logistics: Competing logistics providers optimise joint delivery networks without revealing customer lists, pricing or route details.

Price Discovery: Suppliers and purchasers determine market-clearing prices through SMPC-based auctions without disclosing reservation prices or competitive positions.

Healthcare and Medical Research

Federated Drug Discovery: Pharmaceutical companies jointly analyse patient genomic data across proprietary databases to identify drug targets, without exposing valuable IP or patient information.

Epidemiological Studies: Public health authorities calculate disease prevalence and risk factors across NHS trusts, EU member states and private healthcare providers without centralising patient records (GDPR Article 9 compliance for sensitive health data).

Clinical Trial Matching: Patients identify eligible trials across multiple research organisations without revealing complete medical histories to entities they don’t ultimately engage.

Government and National Security

Cross-Border Intelligence: UK, EU and Five Eyes partners analyse threat intelligence and financial crime data collaboratively without exposing sensitive sources or methods.

Secure Voting and Surveys: Electoral systems and policy surveys aggregate votes whilst guaranteeing ballot secrecy, even from system administrators.

Procurement and Tender Analysis: Government agencies evaluate competitive bids using SMPC to ensure fairness whilst preventing bid rigging or collusion.

SMPC protocols often rely on cryptographic primitives vulnerable to quantum attack, particularly Diffie-Hellman, RSA and discrete logarithm problems.

Post-quantum SMPC research focuses on lattice-based secret sharing, hash-based commitments and garbled circuits using quantum-resistant encryption (ML-KEM).

Organisations implementing SMPC should prioritise protocols built on quantum-resistant foundations or designed for cryptographic agility.

For crypto-agility frameworks: A Practical Roadmap to Quantum Safe Cryptography for UK/EU Enterprises