What is the Context of Cryptographic Assumption?

The security of virtually all digital assets and blockchain networks relies on underlying cryptographic assumptions. News sometimes addresses the emergence of new computational methods or theoretical breakthroughs that could challenge these assumptions, particularly concerning quantum computing. Research into post-quantum cryptography directly addresses the need for new assumptions to maintain long-term security. This area is critical for future digital resilience.

Cryptographic Assumption

Definition

A cryptographic assumption is a fundamental premise about the computational difficulty of solving certain mathematical problems, forming the basis for the security of cryptographic systems. These assumptions assert that specific operations are computationally infeasible for any adversary, even with advanced resources. The reliability of digital security, including blockchain integrity, rests upon the continued validity of these assumptions. It is a bedrock of digital trust.

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∞Constant Size Proofs

∞Cryptographic Assumption

∞Polynomial Commitment

Transparent Constant-Size Zero-Knowledge Proofs Eliminate Trusted Setup

This breakthrough cryptographic primitive, based on Groups of Unknown Order, yields a truly succinct zk-SNARK without a trusted setup, unlocking scalable, trustless computation.

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∞Sequential Computation

∞Fair Transaction Ordering

∞Foundational Security

Verifiable Delay Functions Fail Random Oracle Model Security

Foundational VDF security is disproven in the Random Oracle Model, forcing all future randomness and fair ordering protocols to rely on stronger, structured assumptions.

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∞Standard Assumptions

∞Secret Key Shares

∞Cryptographic Primitives

Adaptively Secure BLS Threshold Signatures from Standard Cryptographic Assumptions

A new threshold signature scheme achieves adaptive security with standard assumptions, fundamentally hardening distributed trust primitives for decentralized systems.

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∞Cryptographic Assumption

∞Information-Theoretic Security

∞Computational Hardness

New Zero-Knowledge Model Circumvents Impossibility for Perfect Soundness

By introducing a security definition based on logical independence, this breakthrough achieves non-interactive, transparent zero-knowledge proofs with perfect soundness, eliminating the need for trusted setups.