> For the complete documentation index, see [llms.txt](https://docs.lacunalabs.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.lacunalabs.io/lacuna-labs/core-concepts.md).

# Core concepts

*The cryptography, in plain terms — with the depth underneath.*

A handful of ideas make private, verifiable money possible. None of them requires a cryptography background to understand.

## Commitments \[The sealed box]

A commitment is a sealed box: it locks in a value and an owner while revealing neither. Publishing it proves the box exists without exposing its contents. Technically it is a hiding, binding hash of a note the value plus the owner's secrets  so identical inputs always produce the same box, yet the box leaks nothing about them.

## Nullifiers \[Spending without revealing]

When you spend, you publish a one-time tag, a nullifier, that marks a box as used without saying which box it was. The contract records every nullifier and rejects repeats, so double-spending is impossible. Because the tag cannot be linked back to its commitment, this protection costs no privacy.

## The anonymity set — privacy in numbers

Privacy here is collective. Rather than naming your box, a spend proves only that it is one of the boxes in the pool. The set it could plausibly be is your anonymity set — and the larger and busier the pool, the stronger everyone's privacy becomes.

## Zero-knowledge proofs

A zero-knowledge proof lets you prove a statement is true without revealing why — like proving you know a password without typing it. Lacuna uses Groth16, which produces tiny proofs, a few hundred bytes, that are fast and cheap to verify on-chain. That efficiency is what makes private transactions practical at scale.

## Poseidon hashing — privacy on a phone

The hardest part of on-device privacy is performance. Poseidon is a hash function purpose-built for zero-knowledge circuits; it sharply reduces the work a proof requires, which is what lets Lacuna generate proofs on a phone rather than a server.

*Fig. 4 — A private transaction in three moves — and what each one does, and does not, make public.*


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