Glossary

Short, plain-language definitions for terms used elsewhere on this site. Each links back to the page where it’s explained in more depth.

Class group

A group derived from an imaginary quadratic field, used as an alternative to an RSA modulus for building a group of unknown order. Its main advantage: the group’s order is genuinely unknown to everyone by construction, from public parameters alone — no trusted setup required. Chia Network uses class groups in production; see Applications.

Discriminant

The parameter that defines a specific class group — roughly analogous to the modulus $N$ in the RSA construction. Chia Network uses a 1024-bit discriminant; see Applications.

Group of unknown order

A mathematical group where nobody involved knows the group’s order (its total number of elements). This property is what makes repeated squaring genuinely sequential — see how it works for why knowing the order would let you skip straight to the answer. Built either from an RSA modulus (needs a trusted setup) or a class group (doesn’t).

Hash-to-prime

A way to deterministically derive a prime number from arbitrary input by hashing the input and searching upward (checking primality at each candidate) until landing on a prime. Used to generate the Wesolowski proof’s $\ell$ from the statement $(x, y, T)$ — see how it works.

Sequentiality

The property that a computation cannot be meaningfully sped up by throwing more parallel hardware at it — the Delay property from what is a VDF. Repeated squaring in a group of unknown order is believed to have this property; there’s no known way to compute $x^{2^T} \bmod N$ in fewer than roughly $T$ sequential steps without knowing the group’s order.

Time-lock puzzle

An earlier, related primitive (Rivest, Shamir, Wagner, 1996) that also uses sequential squaring to force a minimum computation time, but requires a fresh trusted setup for every individual puzzle and has no general mechanism for a third party to publicly verify a solution without redoing the work — the two things a VDF’s proof system solves. See History for the citation and how it relates to VDFs.

Trusted setup

A step in a protocol that requires someone to be trusted to have generated some value honestly and then destroyed the sensitive part of it. For an RSA-modulus-based VDF, this means trusting that whoever generated $N = p \cdot q$ actually forgot $p$ and $q$ — knowing the factorization means knowing the group’s order, which breaks sequentiality entirely. See how it works for why this site’s own demo is explicit that it does not have a real trusted setup.

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Sources: these are standard definitions used consistently across the VDF literature; see History for citations to the original papers that introduced several of these concepts.