# 2023 RD targets

## Algberic geometry

### Snark friendly hash functions

* We have many snark frinedly hash functions
* They are all high degree polynomials
* The simplest is
* $x_n = (x_{n-1} + constant_{n} + x_0)^3$
* we do this until n ~= 200
* over a prime feild

* we carea about collisions , finding two $x_0$ where $x_{200}$ is the same
* We also care about preimage resistance. Finding $x_0$ given only x_{200}
* Several sample problems are https://starkware.co/hash-challenge/
* Algebric geometry has many tools for these problems including
* Grobner basis: Which has been tried but we would like to see more attempts
* Homotopy continuation: Which has not been tried and would love to see
* Many more ...

## Lookup arguments

### Better arguments

* A lookup argument is bascially showing that given a polynomial t and b.
* That b contains only values that are in b.
* Make better lookup arguments
* https://eprint.iacr.org/2022/1763

### Lookup focused languages

https://zkresear.ch/t/lookup-singularity/65/6

* Talks about how lookup arguments could be better than polynomial constraints for defining our circuits
* Because it allows for better languages with an easier learning curve.
* And better formal verificaions
* We are intersted in better langauges
* We are intersted in better formal verficiation tools for circuits buitl with just lookup arguments.

## Social graphs

### Social graph proofs

Social graphs are incredibly rich source of information. Humans intuitavely understand socal graphs. Making proofs about social graphs could be very intersting.

Currently we can make proofs about graphs where all the data is public. Ie the connection data between each user is public. We would instead like to be able to make proofs where only the user knows their private data. This introudces a liveness problem. All users need to be online in order for the private sybil rank or eigen trust algorithim to progress. The goal of this project is to find a non interactive version of sybil rand and/or eigen trust, or algorithims with similar properties.

#### non interactive sybil rank like algorithims

#### non interactive eigen trust like algorithims

## Stuff from Mary

* You mentioned that a worry for you was bugs hidden in security proofs and searching for them could be high leverage. Maybe we could include something like that here ?

## Ideas from Brian

## Ideas from Albert

## ideas from Carlos
* A pair of curves designed to speedup IPA with:
* A cycle between them IE. pasta curves
* Good 2-Adacity
* 128-bit security level
* Optimal FFT space (with similar tricks/properties such as Goldilocks)
* A small field as in ~~https://eprint.iacr.org/2020/009 (this is already proven to be impossible by daira~~ Goldilocks.
* AVX2/ASM field implementations for Pasta curves/ Goldilocks/ Pluto-Eris
* Finish the design of Pluto-Eris (Triton curve and pairing).
* GPU implementation of Halo2.
* Dive into an introduction of Baloo as lookup argument for Halo2. Move from the paper to a PoC.
* Halo2 DSL (macro based or new) which facilitates to write queries, assignations etc.. and reduces the complexity and verbosity of the API.

## Ideas from Han

## Ideas from Design team

* Maybe some antorpology / socialogiy ideas could go here ?
* Also psycology research questions
* Also

### Hyper plonk
* Make hyper plonk compeditive with hardware provers
* https://medium.com/@ingonyama/hardware-friendliness-of-hyperplonk-491d8c86605

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