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An Introduction to Zero-Knowledge Proofs and zk-SNARKs
This post introduces zero-knowledge proofs and explains how zk-SNARKs allow a prover to convince a verifier that a computation is correct without revealing private inputs. It develops the full path from arithmetic circuits to R1CS and QAPs with concrete examples, then shows how elliptic curves, bilinear pairings, and Groth16 turn these algebraic ideas into practical zero-knowledge proofs.
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The Bitcoin Lightning Network
This post presents a technical but accessible introduction to Lightning, starting from Bitcoin transaction primitives and building upward to channel construction, state updates, watchtowers, revocation, HTLC routing.
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Elliptic Curve Digital Signatures in Bitcoin
In this post, we explain the cryptographic use of elliptic curves by first building the underlying finite abelian group structure, and then deriving ECDSA and Schnorr signatures, as well as the multi-signature (MuSig) scheme, which are currently used in the Bitcoin network.
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Natural Languages as ε-Ambiguity Languages
In this post, we examines the claim that natural languages are ε-ambiguity languages in the sense defined by the probabilistic theories of language and latent-intention inference in (Jiang, 2023). This article surveys linguistic, psycholinguistic, and computational evidence demonstrating that natural languages exhibit precisely this structure.
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A Brief Introduction to Bitcoin
In this post, we provide a concise introduction to the key technologies that underpin the Bitcoin network. This overview highlights several important implementations within Bitcoin and offers readers the foundational knowledge needed to understand how the network operates.