Cryptographic Assumptions

Definition ∞ Cryptographic assumptions are unproven mathematical statements that form the foundation for the security of cryptographic systems. These suppositions assert that certain computational problems are practically unsolvable within a reasonable timeframe, even with powerful computing resources. The reliability of encryption, digital signatures, and secure protocols rests upon the enduring difficulty of these underlying mathematical challenges.
Context ∞ News regarding the security of digital assets or blockchain protocols often references cryptographic assumptions, particularly when discussing advancements in quantum computing or new attack vectors. Any challenge to these fundamental beliefs could destabilize current security models, prompting urgent research into post-quantum cryptography. The ongoing validity of these assumptions remains central to the long-term security claims of many digital systems.

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→Threshold Signatures

→Vector Commitments

→Cryptographic Assumptions

Near-Optimal Communication Byzantine Broadcast under Message Adversary Model

A new Byzantine Reliable Broadcast algorithm leverages erasure codes to achieve near-optimal $O(|m| + nkappa)$ communication complexity, securing asynchronous systems against message-dropping adversaries.

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→Iterated Search Problems

→Average Case Hardness

→Distributed Systems Security

Permissionless Consensus Secured in the Standard Model via Complexity Theory

Foundational security for decentralized systems is achieved by grounding Proof-of-Work in fine-grained complexity, moving beyond idealized models.

A transparent, faceted cube housing intricate blue circuitry, resembling a quantum computing core, is centrally positioned against a blurred background of metallic and dark blue components, possibly representing distributed ledger technology nodes or hardware wallets. This visual metaphor explores the convergence of quantum cryptography with blockchain infrastructure, suggesting advanced cryptographic primitives for enhanced digital asset security and decentralized network integrity. The composition hints at next-generation cryptographic solutions for securing blockchain transactions and preventing quantum decryption threats.

→Elliptic Curve Pairings

→Hash-Based ZKPs

→Quasi-Linear Proving

Lattice-Based Zero-Knowledge Proofs Secure Computation against Quantum Threat

The research introduces quantum-resistant zero-knowledge proof systems leveraging hard lattice problems, ensuring long-term privacy and verifiability for decentralized architectures.

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→Lattice Cryptography

→Cryptographic Hardness

→Zero-Knowledge SNARKs

Lattice-Based Arguments Achieve Succinct Post-Quantum Verification Using Homomorphic Commitments

This work delivers the first lattice-based argument with polylogarithmic verification time, resolving the trade-off between post-quantum security and SNARK succinctness.

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→Financial Coordination Mechanisms

→Bandwidth Complexity

→Encrypted Mempools

Threshold Encryption Secures Transaction Ordering Fairness and Mitigates Extractable Value

Threshold encryption decouples transaction submission from execution, forcing validator collusion to extract MEV, thereby enforcing order fairness.

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→Cryptographic Assumptions

→Hyperelliptic Curves

→Post-Quantum Security

Affine One-Wayness Establishes Post-Quantum Verifiable Temporal Ordering for Distributed Systems

Affine One-Wayness is a new post-quantum cryptographic primitive that enforces provable, clock-independent event ordering, enabling Byzantine-resistant distributed synchronization.

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→Proof System Vulnerability

→GKR Protocol

→Cryptographic Attacks

Fiat-Shamir Transformation Vulnerable to Practical Attacks, Impacting Blockchain Security

Researchers expose a critical flaw in Fiat-Shamir, enabling false proofs in widely used systems and demanding re-evaluation of blockchain security foundations.

A crystalline structure composed of interconnected white spheres encased in a transparent shell, set against a blurred background of blue, intricate machinery. This visually represents the foundational atomic elements of blockchain technology, such as cryptographic hashes and distributed ledger immutability. The central cluster signifies a block's data payload, with surrounding spheres potentially symbolizing nodes in a consensus mechanism. The overall aesthetic evokes the complex, secure, and interconnected nature of decentralized finance DeFi protocols and the underlying digital asset infrastructure.

→Public Verifiability

→Multi-Server Cryptography

→Result Integrity

Publicly Verifiable PIR: Private Queries with Public Result Integrity

This research introduces Publicly Verifiable Private Information Retrieval, enabling transparent, auditable private data queries in decentralized systems.