Glossary

Short definitions for terms used in this textbook.

Algebra

Abelian group: A group where the operation commutes: $a \star b = b \star a$. See Groups.

Cofactor: The ratio between a full elliptic curve group order and a desired prime subgroup order. See Curves Over Finite Fields.

Elliptic curve: A curve with a group law on its points, often written in short Weierstrass form as $y^2 = x^3 + ax + b$. See Elliptic Curve Group Law.

Field: A number system where addition, subtraction, multiplication, and division by nonzero elements work. See Rings and Fields.

Finite field: A field with finitely many elements, such as $\mathbb{F}_p$. See Finite Fields.

Generator: An element whose repeated operation creates an entire cyclic group or subgroup. See Groups.

Group: A set with one operation satisfying closure, associativity, identity, and inverses. See Groups.

Prime-order subgroup: A subgroup whose number of elements is prime.

Ring: A set with addition and multiplication that distribute correctly. See Rings and Fields.

Scalar multiplication: Repeated addition of a group element, written $kP$ for elliptic curve points.

Subgroup check: A test that verifies a point belongs to the intended subgroup.

Cryptography

BLS signature: A pairing-based digital signature scheme with useful aggregation properties. See BLS Signatures.

BLS12-381: A specific pairing-friendly elliptic curve parameter set used with BLS signatures and other pairing-based protocols. See BLS12-381.

Hash-to-curve: A specified method for mapping bytes to a valid elliptic curve point.

Pairing: A bilinear map $e : G_1 \times G_2 \to G_T$. See Pairings.

Random oracle: An idealized hash-like function that returns consistent but random-looking outputs. See Probability for Cryptography.

Rogue-key attack: An aggregate-signature attack where a malicious public key is chosen to cancel or manipulate another participant's key.

Security parameter: A value controlling the intended hardness of an attack.

VDF: Verifiable delay function; a function that takes sequential time to evaluate but is faster to verify. See Wesolowski VDF.

Chia

Coin: A Chia state object with a parent id, puzzle hash, and amount.

Coin spend: The data needed to spend one coin: coin, puzzle reveal, and solution. See Spend Bundles and BLS.

Farmer: A participant that uses stored plots to find eligible proofs of space. See Consensus Overview.

Harvester: A process that checks plot files for candidate proofs on behalf of a farmer.

Plot: Stored proof-of-space data used during farming. See Chia Proof of Space.

Proof of space: A proof that a participant is storing structured data.

Proof of time: Chia's VDF-based proof that sequential time has passed.

Puzzle reveal: The CLVM program revealed when spending a coin.

Signage point: An intermediate point in a sub-slot where farmers check plot eligibility.

Spend bundle: A group of coin spends plus an aggregate signature. See Spend Bundles and BLS.

Timelord: A process that advances VDFs and publishes proofs of time.

Advanced Terms

Class group (advanced): An unknown-order group built from equivalence classes of binary quadratic forms. See Class Groups.

Frobenius map (advanced): In characteristic $p$, the map $a \mapsto a^p$.

n-Wesolowski (advanced): A segmented Wesolowski-style proof strategy that trades proof size and verification work for proof-generation latency. See n-Wesolowski.