What is the Context of Module SIS Problem?

The Module SIS problem is a significant area of research in post-quantum cryptography, directly impacting the long-term security of digital assets against quantum threats. Cryptographers continually analyze its hardness and develop new schemes whose security relies upon it. News in this specialized domain often covers advancements in lattice cryptography, including new proofs of security or potential vulnerabilities related to the Module SIS problem. Its relevance to blockchain technology lies in future-proofing cryptographic foundations.

Module SIS Problem

Definition

The Module SIS (Short Integer Solution) problem is a mathematical problem foundational to the security of many lattice-based cryptographic schemes. It involves finding a short, non-zero integer vector that satisfies a given system of linear equations over a module. The hardness of solving this problem on average is a key assumption for the security of cryptographic primitives designed to be resistant to quantum computer attacks. It is a generalization of the standard SIS problem.

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∞Small Field Arithmetic

∞Sumcheck Protocol

∞Post-Quantum Cryptography

Lattice-Based Folding Achieves Post-Quantum Recursive Succinct Proof Systems

This lattice-based folding scheme enables the first efficient, post-quantum secure recursive SNARKs, securing future scalable blockchain state against quantum threat.

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∞Folding Schemes

∞IVC PCD

∞CCS Relations

Lattice-Based Folding Achieves Post-Quantum Recursive Zero-Knowledge Proofs

First lattice-based folding scheme secures recursive SNARKs against quantum attack by replacing discrete logarithm commitments with Module SIS.

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∞Post-Quantum Cryptography

∞Cryptographic Hardness Assumption

∞Lattice-Based Cryptography

Lattice Polynomial Commitments Achieve Quantum-Safe, Transparent, Succinct Proofs

A new lattice-based polynomial commitment, secured by the SIS problem, delivers post-quantum SNARKs with smaller proofs and no trusted setup.

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∞Zero-Knowledge Proofs

∞Verifier Efficiency

∞Cryptographic Primitive

Lattice Polynomial Commitments Achieve Post-Quantum Transparent SNARKs

This research delivers the first efficient lattice-based polynomial commitment scheme, securing succinct arguments against quantum adversaries without a trusted setup.

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∞Low-Norm Witnesses

∞Post-Quantum Security

∞Module SIS Problem

Lattice Folding Secures Recursive Zero-Knowledge Proofs against Quantum Threats

LatticeFold replaces discrete log commitments with lattice cryptography, enabling the first post-quantum folding scheme for quantum-safe recursive ZK-SNARKs.

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∞Scalable Verification

∞Polynomial Commitment Scheme

∞Lattice Assumptions

Lattice Polynomial Commitments Achieve Post-Quantum SNARKs without Trusted Setup

A new lattice-based polynomial commitment scheme secures zero-knowledge systems against quantum adversaries while eliminating the need for a trusted setup ceremony.

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∞Folding Schemes

∞Succinct Proof Systems

∞Low-Norm Witnesses

Lattice-Based Folding Achieves Post-Quantum Recursive SNARK Efficiency

The first lattice-based folding protocol enables recursive SNARKs to achieve post-quantum security while matching the performance of pre-quantum schemes.