PARI is a recent SNARK based on equifficient polynomial commitments, giving an exceptionally compact proof of just 1280 bits over the BLS12-381 curve, which is the smallest among all the known SNARKs in the literature. However, PARI does not achieve the zero-knowledge property; despite being very efficient, it is therefore less suitable for applications requiring witness privacy. In this work, we propose a zero-knowledge extension of PARI making it ideal for privacy-centric applications yet keeping the proof size compact. We prove perfect completeness, perfect zero-knowledge in the random-oracle model with challenge space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>𝔽</mml:mi> <mml:mi>⧵</mml:mi> <mml:mi>K</mml:mi> </mml:mrow> </mml:math> , and knowledge soundness in the algebraic group model with random oracles under the SDH assumption.
Zero-knowledge proofs (ZKPs) are a fundamental building block in cryptography, enabling powerful privacy-preserving and verifiable computations. In the post-quantum era, hash-based ZKPs have emerged as a promising direction due to their conjectured resistance to quantum attacks, along with their simplicity and efficiency. In this work, we introduce SmallWood, a hash-based polynomial commitment scheme (PCS) and zero-knowledge argument system optimized for relatively small instances. Building on the recent degree-enforcing commitment scheme (DECS) from the Threshold-Computation-in-the-Head (TCitH) framework, we refine its formalization and combine it with techniques from Brakedown. This results in a new hash-based PCS that is particularly efficient for polynomials of relatively small degree –typically up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> – outperforming existing approaches in this range. Leveraging this new PCS, we design a hash-based zero-knowledge argument system that outperforms the state-of-the-art in terms of proof sizes for witness sizes ranging from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Additionally, we present exact zero-knowledge arguments for lattice-based problems using SmallWood, demonstrating highly competitive performance: our scheme yields proof sizes under 25 KB across a wide range of lattice parameters, including Kyber and Dilithium instances.
This paper assesses the adequacy of technology-neutral privacy frameworks in addressing quantum threats to zero-knowledge proofs (ZKPs) and other privacy-enhancing technologies (PETs) in global data protection regimes. Challenging assumptions that cryptographic innovation inherently bolsters privacy rights, the analysis demonstrates how post-quantum migration, absent binding regulatory duties, risks entrenching a ‘quantum divide’ in access and liability. Grounded in legal frameworks and actual deployments, including Zcash’s classical Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (ZK-SNARKs) and NantHealth Inc.’s quantum-aware homomorphic encryption systems, the paper contends that access to PETs is becoming ever more determined by institutional capability and geopolitical factors, as illustrated by comparative case studies. This research evaluates the efficacy of statutes such as the European Union’s (EU) General Data Protection Regulation (GDPR) (Article 32), the California Consumer Privacy Act (CCPA) (§ 1798.150), and the Health Insurance Portability and Accountability Act (HIPAA) (45 C.F.R. § 164.308) in imposing liability for quantum vulnerable systems, using the cases to illustrate gaps in mandating equitable post-quantum migration. The conclusion reflects upon legal gaps enabling unequal protections, advocating reforms including mandatory quantum risk assessments. This article is also included in The Business & Management Collection which can be accessed at https://hstalks.com/business/.