Lattice-Based Cryptography

Definition ∞ Lattice-based cryptography is a field of study in computer science and mathematics that utilizes mathematical structures known as lattices for cryptographic operations. These systems are considered resistant to attacks from both classical and quantum computers, making them a promising candidate for post-quantum cryptography. The security of these schemes relies on the computational difficulty of solving certain lattice problems. This area is fundamental to securing future digital communications.
Context ∞ Lattice-based cryptography is frequently mentioned in discussions concerning the long-term security of blockchain networks and digital assets against potential future threats, particularly from quantum computing. Research and development efforts are focused on creating practical and efficient lattice-based encryption and signature schemes suitable for widespread adoption. The potential for these cryptographic primitives to safeguard sensitive data and transactions in the coming decades is a key driver of interest.

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→Long Term Security

→Distributed Storage

→Lattice-Based Cryptography

Quantum Shares Enable Publicly Verifiable Cryptographic Data Deletion

This new quantum-secure primitive introduces publicly verifiable deletion to secret sharing, neutralizing the threat of long-term data breach by cryptographically destroying shares on demand.

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→Formal Security Model

→Cryptographic Proof

→Randomness Generation

Quantum-Secure Hybrid VRF Model Ensures Post-Quantum Decentralized Randomness

This new hybrid VRF uses Ring-LWE encryption off-chain and NTRU signatures on-chain, securing decentralized randomness against quantum threats.

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→Cryptographic Hardness Assumption

→Succinct Non-Interactive Arguments

→Modular Blockchain Architecture

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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→Protocol Design

→Selective Disclosure

→Proof Simulation

Blockchain Designated Verifier Proofs Ensure Non-Transferable Privacy on Public Ledgers

The Blockchain Designated Verifier Proof (BDVP) uses a verifier-held trapdoor to simulate fake proofs, restoring non-transferable privacy to ZKPs on public chains.

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→Nonlinear Functions

→Cryptographic Primitive

→Stateless Updates

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.

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→Zero-Knowledge Proofs

→Verifiable Credentials

→Cryptographic Primitives

Lattice ZKPs Match CRHF Proof Size for Post-Quantum Security

Researchers achieved lattice-based ZKPs with proof sizes comparable to hash-based systems, enabling practical, post-quantum private computation.

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→Non-Interactive Argument

→Succinct Proofs

→Communication Complexity

Ring Learning with Rounding Unlocks Efficient Post-Quantum Zero-Knowledge

A new ZKP of Knowledge based on the Ring Learning with Rounding assumption delivers post-quantum security with drastically reduced proof size and verification latency.

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→Lattice-Based Cryptography

→Designated Verifier Model

→Vector Encryption Scheme

Lattice-Based SNARKs Achieve Practical Post-Quantum Proof Size Reduction

A new lattice-based zkSNARK construction reduces post-quantum proof size by $10.3times$, collapsing the massive overhead that hindered quantum-secure verifiable computation.

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→Quantum Resistance

→CCS Relations

→Ajtai Commitment Scheme

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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→Polynomial Product Proof

→Succinct Arguments

→Approximate Range Proof

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

Lantern is a post-quantum ZKP protocol that uses polynomial product proofs to prove vector norms, making proofs 2-3X smaller for scalable, quantum-safe privacy.