@@ -7,3 +7,5 @@ - [Fold](usage/fold.md)
 	- [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)

@@ -0,0 +1,6 @@
+# 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 $F_q$.

@@ -0,0 +1,14 @@
+# 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>