Lantern Achieves Short, Post-Quantum Zero-Knowledge Proofs via Polynomial Product Systems ∞ Research

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Briefing

The core problem is the impracticality of existing post-quantum Zero-Knowledge Proofs (ZKPs), which suffer from prohibitively large proof sizes and slow performance, thus limiting the viability of quantum-safe confidential transactions and ZK-Rollups. The foundational breakthrough is mathsfLantern, a new lattice-based ZKP protocol that fundamentally re-architects the proof generation process by proving the knowledge of a short vector’s small Euclidean norm using a novel polynomial product proof system. This mechanism avoids the inefficient prior approach of proving smallness for every vector coefficient, resulting in a 2-3X reduction in proof size and enabling the first truly efficient, quantum-safe succinct arguments essential for the future of decentralized, private, and quantum-resilient blockchain architecture.

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Context

The established theoretical limitation is the impending threat of quantum computers, which can break the elliptic curve cryptography underpinning most current ZKP systems (like zk-SNARKs). While lattice-based cryptography offers a quantum-safe alternative, prior lattice-based ZKP protocols were academically recognized as being too inefficient, generating proofs tens of kilobytes in size, which is too large for practical on-chain verification and data-intensive applications. This trade-off between post-quantum security and cryptographic efficiency presented a fundamental barrier to the long-term viability of private and scalable decentralized systems.

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Analysis

mathsfLantern’s core mechanism is a shift in how the crucial lattice-based security requirement ∞ proving a vector has a small Euclidean norm ∞ is satisfied. Previous systems required explicitly proving the smallness of each vector coefficient, which led to high overhead. mathsfLantern innovates by observing that the inner product of a vector with itself can be derived as the constant coefficient of a product of polynomials derived from the vector.

The protocol then leverages a polynomial product proof system to succinctly verify this relationship, effectively proving the small norm of the vector without needing to check every coefficient individually. This is conceptually simpler and mathematically more efficient, resulting in the dramatic reduction in proof size.

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Parameters

Proof Size Reduction ∞ 2-3X smaller than prior works. This is the factor by which mathsfLantern improves upon the proof size of existing lattice-based ZKP protocols.
Proof Size (Basic Statements) ∞ 13KB. This is the absolute size of the resulting proof for basic lattice-related statements, a critical metric for on-chain viability.
Security Basis ∞ Module-SIS and Module-LWE. These are the specific algebraic lattice problems whose hardness guarantees the protocol’s post-quantum security.

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Outlook

This research opens a critical new avenue for practical post-quantum cryptography in the blockchain space. The ability to generate short, quantum-safe proofs in the kilobyte range makes private, scalable, and quantum-resilient ZK-Rollups and confidential asset transfers viable within the next three to five years. The new polynomial product proof technique for inner products is a fundamental building block that can be immediately integrated into other lattice-based primitives, accelerating the industry’s transition to a quantum-secure cryptographic foundation.

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Verdict

The mathsfLantern protocol provides the foundational cryptographic primitive required to make scalable, efficient, and post-quantum secure blockchain architecture a near-term reality.

Lattice-based cryptography, Post-quantum security, Zero-knowledge proofs, Short proof size, Polynomial product proof, Module-SIS hardness, Module-LWE hardness, Quantum-safe primitives, Succinct arguments, Cryptographic efficiency, Privacy-preserving applications, Euclidean norm proof, Approximate range proof, Confidential transactions, ZK-Rollups, PQC standardization Signal Acquired from ∞ ethz.ch