SLAP Achieves Efficient Post-Quantum Polynomial Commitments under Standard Lattice Assumptions ∞ Research

The image showcases a high-tech modular system composed of white and metallic units, connected centrally by intricate mechanisms and multiple conduits. Prominent blue solar arrays are attached, providing an energy source to the structure, set against a blurred background suggesting an expansive, possibly orbital, environment

A striking blue crystalline structure, interspersed with clear, rectangular elements, emerges from a wavy, dark blue body of water under a light blue sky. White, foamy masses cling to the base and upper parts of the formation, suggesting dynamic interaction with the water

Briefing

Previous lattice-based polynomial commitments faced limitations with large common reference strings, reliance on non-standard assumptions, or suboptimal tradeoffs between soundness and verification time. SLAP introduces a new lattice-based polynomial commitment scheme featuring polylogarithmic common reference string size, quasi-linear commitment time, polylogarithmic verification time, and negligible soundness error. This scheme achieves security under the standard Module-SIS assumption, significantly advancing the feasibility of building post-quantum secure and scalable verifiable computation systems crucial for future blockchain architectures.

A high-fidelity render showcases a sophisticated, multi-component industrial mechanism, predominantly white with striking metallic blue accents, featuring linear rails and intricate connections. The focus is on a central actuator-like component with detailed surface patterns, suggesting advanced engineering and automated processes

Context

Polynomial commitment schemes are foundational for constructing succinct arguments like zk-SNARKs. However, existing lattice-based constructions encountered significant limitations. Prior schemes either required non-standard cryptographic assumptions such as powerBASIS, resulted in common reference string sizes quadratic in the polynomial’s degree, or compromised on soundness error or verification time, hindering their practical adoption for post-quantum secure verifiable computation.

A sophisticated metallic and luminous blue circuit structure, partially covered in granular white snow, dominates the view. A central, polished silver and blue component resembles a high-performance network node or validator core, radiating intricate, glowing blue circuit board pathways

Analysis

SLAP constructs a novel polynomial commitment scheme utilizing a Merkle tree-like structure, built upon a “toy” 2-to-1 commitment scheme. This recursive approach facilitates succinct verification. The scheme incorporates evaluation protocols inspired by FRI and Bulletproofs, which involve splitting polynomials into components and employing randomness for linear combinations, enabling efficient recursive updates. This approach achieves strong security properties, including negligible soundness and reliance on standard assumptions, alongside efficiency characterized by polylogarithmic common reference string size and verification time, without the drawbacks of previous lattice-based methods.

A translucent, textured casing encloses an intricate, luminous blue internal structure, featuring a prominent metallic lens. The object rests on a reflective surface, casting a subtle shadow and highlighting its precise, self-contained design

Parameters

Core Concept ∞ Lattice-Based Polynomial Commitments
New System/Protocol ∞ SLAP
Key Authors ∞ Albrecht, M. R. et al.
Security Assumption ∞ Module-SIS
Verification Complexity ∞ Polylogarithmic
Common Reference String Size ∞ Polylogarithmic
Prover Time ∞ Quasi-linear
Soundness Error ∞ Negligible
Primary Application ∞ Post-quantum zk-SNARKs
Conference ∞ EUROCRYPT ’24

A brilliant, square-cut crystal is held within a segmented white ring, suggesting a secure element or core processing unit. This assembly is intricately connected to a vibrant blue, illuminated circuit board, indicative of advanced computational infrastructure

Outlook

This research establishes a robust foundation for post-quantum secure verifiable computation, addressing a critical need for long-term cryptographic security. Future work will likely focus on improving the concrete efficiency of SLAP, as current proof sizes remain substantial. The methodology could unlock new designs for post-quantum secure zk-SNARKs and other cryptographic primitives, paving the way for decentralized applications resilient against quantum attacks within the next 3-5 years. This also opens avenues for exploring more efficient trapdoor sampling techniques and optimized repetitions in lattice-based constructions.

A vivid blue, reflective X-shaped crystalline structure is enveloped by an intricate, porous light-grey matrix. The surface of the grey structure exhibits a granular, bubbly texture where it meets the blue core

Verdict

SLAP represents a foundational advancement in post-quantum cryptography, providing a robust, efficient, and standard-assumption-based polynomial commitment scheme essential for future secure and scalable decentralized systems.

Signal Acquired from ∞ gfenzi.io