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add nova+cyclefold circuit diagram, add design section

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arnaucube 1 year ago
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src/SUMMARY.md

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- [Decider prove](usage/decider-prove.md)
- [Solidity verifier](usage/solidity-verifier.md)
- [Modularity](usage/modularity.md)
- [Design](design/design.md)
- [Nova+CycleFold circuit](design/novacyclefold-circuit.md)

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src/design/design.md

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# Design
#### Notation
We work on a cycle of curves composed by $E_1$ and $E_2$, where $E_1.F_r = E_2.F_q$ and $E_1.F_q=E_2.F_r$.
We will use $F_r$ to refer to $E_1.F_r=E_2.F_q$, and $F_q$ to refer to $E_1.F_q=E_2.F_r$.
The main circuit constraint field is $F_r$, and $C_{EC}$ circuit constraint field is $F_q$.

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src/design/novacyclefold-circuit.md

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# Nova + CycleFold
[CycleFold](https://eprint.iacr.org/2023/1192.pdf) improves the usage of the cycle of curves proposed in [Nova](https://eprint.iacr.org/2021/370.pdf).
![](../imgs/cyclefold-paper-diagram.jpg)
*CycleFold applied to HyperNova, src: [https://eprint.iacr.org/2023/1192.pdf](https://eprint.iacr.org/2023/1192.pdf)*
<br>
We use a concrete version of the CycleFold approach applied to Nova.
The following image provides a description of the main Nova circuit and CycleFold circuit over a couple of steps, implemented at [nova/circuits.rs](https://github.com/privacy-scaling-explorations/folding-schemes/blob/main/folding-schemes/src/folding/nova/circuits.rs) and [nova/cyclefold.rs](https://github.com/privacy-scaling-explorations/folding-schemes/blob/main/folding-schemes/src/folding/nova/cyclefold.rs).
<a href="../imgs/cyclefold-nova-diagram.png" title="click to expand"><img src="../imgs/cyclefold-nova-diagram.png" /></a>

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