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Foundations: Cryptography

What is a Merkle Proof?A Merkle proof lets you convince someone that a piece of data belongs to a much larger set without sending the whole set

What is a Merkle Proof?A Merkle proof lets you convince someone that a piece of data belongs to a much larger set without sending the whole set. That sounds almost too convenient, but the mechanism is simple: a short chain of hashes ties one leaf to a single root that stands for everything.Mar 21, 202622 min read

What is Poseidon Hash?Poseidon hash matters because ordinary hashes are cheap on CPUs but expensive inside zero-knowledge proofs

What is Poseidon Hash?Poseidon hash matters because ordinary hashes are cheap on CPUs but expensive inside zero-knowledge proofs. Poseidon flips that tradeoff: it is built from finite-field arithmetic so Merkle trees, commitments, and private transactions can be proven with far fewer circuit constraints.Mar 21, 202624 min read

#HASH FUNCTIONS

What is X25519?X25519 is one of the most widely deployed ways to do modern Diffie–Hellman key exchange, but its importance is not just speed

What is X25519?X25519 is one of the most widely deployed ways to do modern Diffie–Hellman key exchange, but its importance is not just speed. It was designed so secure, constant-time implementations are much easier to get right, which is why it appears across TLS 1.3, Noise, WireGuard, and many cryptographic libraries.Mar 21, 202622 min read

What Is Elliptic Curve Cryptography?Elliptic Curve Cryptography lets modern systems get strong public-key security with much smaller keys than older designs

What Is Elliptic Curve Cryptography?Elliptic Curve Cryptography lets modern systems get strong public-key security with much smaller keys than older designs. Its power comes from a simple asymmetry: multiplying a curve point is easy, but reversing that multiplication appears hard — and that gap supports signatures, key exchange, and much of today’s wallet infrastructure.Mar 21, 202627 min read

What is secp256k1?secp256k1 is the elliptic curve behind Bitcoin keys, legacy Ethereum transaction signatures, and many other blockchain systems

What is secp256k1?secp256k1 is the elliptic curve behind Bitcoin keys, legacy Ethereum transaction signatures, and many other blockchain systems. Its importance is easy to underestimate: a short parameter list defines the exact mathematical world in which private keys, public keys, and signatures all have to agree.Mar 21, 202622 min read

What Are KZG Commitments?KZG commitments are a way to commit to an entire polynomial with a single small cryptographic object, then later prove specific values of that polynomial with equally short proofs

What Are KZG Commitments?KZG commitments are a way to commit to an entire polynomial with a single small cryptographic object, then later prove specific values of that polynomial with equally short proofs. That unusual combination of compactness and verifiability is why they matter in modern zero-knowledge systems and blockchain data-availability designs.Mar 21, 202623 min read

What is a Pedersen Commitment?Pedersen commitments solve a delicate problem: how to hide a value completely while still letting others verify arithmetic about it

What is a Pedersen Commitment?Pedersen commitments solve a delicate problem: how to hide a value completely while still letting others verify arithmetic about it. That combination — **perfect hiding** with **additive homomorphism** — is why they sit underneath confidential transactions, range proofs, and many zero-knowledge systems.Mar 21, 202621 min read

What Is a Polynomial Commitment?Polynomial commitments solve a surprisingly specific problem with broad consequences: how do you bind yourself to a whole polynomial now, then later prove just one value of it without revealing everything else? That simple capability sits underneath modern SNARKs, verifiable secret sharing, and blockchain data-availability designs

What Is a Polynomial Commitment?Polynomial commitments solve a surprisingly specific problem with broad consequences: how do you bind yourself to a whole polynomial now, then later prove just one value of it without revealing everything else? That simple capability sits underneath modern SNARKs, verifiable secret sharing, and blockchain data-availability designs.Mar 21, 202624 min read

What is a BLS Signature?BLS signatures matter because they make a strange trade possible: signatures can stay compact even when many participants sign, and those signatures can often be merged into one

What is a BLS Signature?BLS signatures matter because they make a strange trade possible: signatures can stay compact even when many participants sign, and those signatures can often be merged into one. That property is why modern blockchain systems use BLS for validator attestations, multisignatures, and other places where ordinary signatures would create too much bandwidth and verification overhead.Mar 21, 202621 min read

What is Multi-Party Computation (MPC)?Multi-party computation lets several parties compute a result together without handing each other their raw secrets

What is Multi-Party Computation (MPC)?Multi-party computation lets several parties compute a result together without handing each other their raw secrets. It matters because it changes the usual tradeoff between coordination and privacy: you can collaborate on sensitive data, or control a cryptographic key, without any one place becoming the point of total trust or total failure.Mar 21, 202626 min read

#THRESHOLD SYSTEMS

What is a Hash Commitment?A hash commitment lets you publish a short digest now and reveal the underlying value later, in a way that is meant to hide the value at first and lock it in for later verification

What is a Hash Commitment?A hash commitment lets you publish a short digest now and reveal the underlying value later, in a way that is meant to hide the value at first and lock it in for later verification. That simple trick sits underneath coin flipping, auctions, smart-contract commit–reveal flows, and many zero-knowledge systems—but it only works if you understand exactly what the hash is, and is not, buying you.Mar 21, 202626 min read

What is Curve25519?Curve25519 matters because it made strong elliptic-curve cryptography easier to implement safely, not just faster

What is Curve25519?Curve25519 matters because it made strong elliptic-curve cryptography easier to implement safely, not just faster. Its design ties together a carefully chosen curve, a prime field that computers handle efficiently, and formulas that support constant-time key exchange in real protocols like TLS.Mar 21, 202622 min read