What is the Context of Cryptographic Assumptions?

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.

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.

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∞Proof of Work Scheme

∞Permissionless Consensus

∞Cryptographic Assumptions

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.

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∞Quantum Resistance

∞Algebraic Geometry

∞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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∞Verifiable Computation

∞Post-Quantum Security

∞Short Proofs

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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∞Computational Overhead

∞Transaction Ordering Fairness

∞Bandwidth Complexity

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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∞Hyperelliptic Curves

∞Temporal Verification

∞Logarithmic Scaling

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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∞Protocol Design

∞Cryptographic Attacks

∞Zero-Knowledge Security

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.

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∞Private Information Retrieval

∞Function Secret Sharing

∞Predicate Queries

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.