Short Integer Solution

Definition ∞ The Short Integer Solution (SIS) problem is a fundamental computational problem in lattice-based cryptography, which forms the basis for constructing various cryptographic primitives. It involves finding a non-zero integer vector of small length that, when multiplied by a given matrix, results in a zero vector modulo a certain integer. The presumed difficulty of solving the SIS problem is a cornerstone for the security of many post-quantum cryptographic schemes. This problem is considered hard even for quantum computers.
Context ∞ In discussions surrounding post-quantum cryptography and the security of digital assets, the Short Integer Solution problem is a key concept. News reports about new quantum-resistant signature schemes or encryption methods often refer to the SIS problem or related lattice problems as their underlying security foundation. Understanding the hardness of SIS is essential for evaluating the robustness of cryptographic systems designed to protect blockchain transactions and digital communications from future computational advances.

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→Sublinear Proof Size

→SIS Problem

→Aggregate Signature Scheme

Logarithmic-Size Lattice Signatures Achieve Post-Quantum Blockchain Scalability

This new lattice-based aggregate signature achieves logarithmic size growth, providing post-quantum security while radically compressing blockchain transaction data.

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→Quantum-Safe Security

→Lattice-Based Cryptography

→Efficient Verification

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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→Polynomial Commitments

→Short Integer Solution

→Falsifiable Assumption

Lattice-Based Functional Commitments Secure All Functions with Transparent Post-Quantum Setup

New lattice-based functional commitments secure all functions, enabling post-quantum verifiable computation without a trusted setup.

$A central, lustrous white sphere is enveloped by a fractal, icy blue structure resembling a virus or a complex molecular formation. This crystalline matrix is interwoven with intricate, glowing blue circuitry, evocative of a distributed ledger or a decentralized network. The visual metaphor suggests advanced cryptographic protocols, potentially quantum-resistant algorithms, underpinning blockchain technology. This fusion of organic and digital aesthetics points to the sophisticated, emergent properties within next-generation cryptocurrency ecosystems and their underlying consensus mechanisms.$

→Post-Quantum Cryptography

→SIS Problem

→Cryptographic Migration

Lattice-Based Signatures Secure Blockchain against Quantum Attack Overhead Challenge

Lattice-based cryptography replaces vulnerable ECDSA, securing digital signatures against quantum computers while managing significant data overhead.

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→Quantum Resistance

→Key Size Reduction

→Adaptive Chosen Message

Lattice Cryptography Secures Blockchain Transactions with Smaller Keys

Researchers designed a novel lattice-based signature scheme, using SampleMat and trapdoor-less signing, to reduce post-quantum transaction size, securing blockchains against future quantum attacks.

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→Proof System Efficiency

→Module Homomorphic

→Evaluation Proof

Lattice-Based Polynomial Commitments Achieve Post-Quantum Succinctness and Sublinear Verification

Greyhound is the first concretely efficient lattice-based polynomial commitment scheme, enabling post-quantum secure zero-knowledge proofs with sublinear verifier time.