###### tags: 'geometry`

# Geometry Labs YouTube Episode- filming 7 July 2022

Macro episode of the entire series on Techniques for efficient pq finance (what it entails, how it ties in, why it matters- cover the importance of it in the space).

It’s very technical in nature (the material) so I want us to hit home on the benefits of this to your avg blockchain user. I want viewers being able to walk away with some digestable nuggets on why it’s important moving forward

### Overarching Episode on the blog series

We'll start out episode as a refresher for the first 5-10 minutes covering the overview.

**Question for Mitchell:** What high level parts do you want to cover per each? Feel free to inject any notes below or we can just go through each off the cuff tomorrow (note: Strike will have some additional questions later today too he said)

#### Meta
- We have made available free open source reference implementations for Parts 0-3, and will release Part 4 when completed.
- Python libraries available on GitHub and PyPi

#### Part 0: Intro to Lattice Algebra

- Math package that can be used for a variety of cryptography applications
- Automatically uses best practices out-of-the-box (constant time math, number theoretic transform, etc.)
- Allows cryptography developers to focus on the crypto, fast forward past implementing polynomials, etc

#### Part 1: digital signatures

- General concept of one-time digital signatures (lattice OR otherwise) is: message + private key --> signature + verification key
- Use cases: a valid signature for a properly designed + configured scheme confirms both:
- message integrity
- the signer knew the private key

#### Part 2: sig aggregation

- Scaling technique with applications for combining validator signatures, transaciton signatures, or even both together.
- Goal of signature aggregation is to reduce on-chain footprint by storing 1 signature (+ the N verification keys) instead of N keys and N signatures
- Other possible applications like multi-sig wallets, on-chain governance, etc.

#### Part 3: adaptor signatures
- Extension of the digital signatures that provides extended functionality
- Use cases:
- Trustless decentralized cross-chain atomic swaps
- Payment channels (transact off-chain and only settle to the base layer when necessary)

#### Part 4: reducing storage requirments
- Secure fountain architecture (article published, code WIP)
- P2P storage with clever encoding mechanisms
- Reduces local storage requirements with the tradeoff of increased bandwidth
- Works with any blockchain, can be opt-in layer next to existing messaging + storage system.

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### AMA- we'll film this 2nd
We (QRL) have 1-2 dozen ama questions here & we'll gather some more