* Move r1cs and ccs to standalone folders

* Simplify type bounds of SparseMatrixVar

* Implement `EquivalenceGadget` trait for `FpVar` and `NonNativeUintVar`.

Together with the existing `MatrixGadget` and `VectorGadget`, we can now use the same logic for checking R1CS satisfiability of `R1CSVar` both natively and non-natively.

* Simplify trait bounds

* Implement `ArithGadget` for `R1CSMatricesVar` and `CCSMatricesVar`

* `PedersenGadget::commit` now takes slices as input

* Structs for proofs and auxiliary values in protogalaxy

* `u` in LCCCS should be `z[0]`

* `Inputize` trait

* Generic decider circuits

* Verifier should check the commitments in committed instances

* Update the comments according to the new docs

* Fix examples

* Add `DeciderEnabledNIFS::fold_group_elements_native` to wrap code for folding commitments

* Fix incorrect endian

* Format

* Get rid of `unwrap` when possible

* Adding Mova

Co-Authored-By: Togzhan Barakbayeva <45527668+btogzhan2000@users.noreply.github.com>
Co-Authored-By: Ilia Vlasov <5365540+elijahvlasov@users.noreply.github.com>
Co-Authored-By: matthew-a-klein <96837318+matthew-a-klein@users.noreply.github.com>

* Fix CLI

* Updated from main

* Solution to stop the CLI from complaining about deadcode

PR comment

Co-authored-by: arnaucube <root@arnaucube.com>

* Requested changes and update from main

* Refactor NIFSTrait & port Mova impl to it

* refactor NIFSTrait interface to fit Nova variants (Nova,Mova,Ova)

  Refactor NIFSTrait interface to fit Nova variants (Nova,Mova,Ova). The relevant
  change is instead of passing the challenge as input, now it passes the
  transcript and computes the challenges internally (Nova & Ova still compute a
  single challenge, but Mova computes multiple while absorbing at different
  steps).

* port Mova impl to the NIFSTrait

* remove unnecessary wrappers in the nova/zk.rs

* remove Nova NIFS methods that are no longer needed after the refactor

* put together the different NIFS implementations (Nova, Mova, Ova) so
  that they can interchanged at usage.

The idea is that Nova and its variants (Ova & Mova) share most of the
logic for the circuits & IVC & Deciders, so with the abstracted NIFS
interface we will be able to reuse most of the already existing Nova
code for having the Mova & Ova circuits, IVC, and Decider.

* adapt Nova's DeciderEth prepare_calldata & update examples to it

* small update to fix solidity tests

---------

Co-authored-by: Togzhan Barakbayeva <45527668+btogzhan2000@users.noreply.github.com>
Co-authored-by: Ilia Vlasov <5365540+elijahvlasov@users.noreply.github.com>
Co-authored-by: matthew-a-klein <96837318+matthew-a-klein@users.noreply.github.com>
Co-authored-by: arnaucube <root@arnaucube.com>
Co-authored-by: arnaucube <git@arnaucube.com>

* implement HyperNova's DeciderEth

* add remark about Nova's zk layer implementation and the 3 identified use cases

* feat: enable hiding commitments in nova and hypernova

* fix: set blinding values for witness vector

* fix: remove cloning of the cyclefold running instance

* fix: do not re-use blinding values between prove steps

* fix: specify whether the witness should use blinding values using a
const generic

* feat: create a `dummy` method for nova witnesses as well

* chore: clippy - removed unused imports

- Adds the logic to support multi-instances folding in HyperNova's
AugmentedFCircuit & IVC.
- Adds also methods to generate new LCCCS & CCCS instances that don't
depend on the main folding chain, to be folded in in the next step
- Updates CycleFold circuit & methods to work other folding schemes than
  Nova, adapting it to fold multiple points per circuit (instead of
2-to-1 as till now)
- Handle multi-instances folding in the FoldingScheme trait
  interface, which expects 'None' in Nova, and 'Some' in HyperNova &
other multi-folding schemes.

- implement hash of public params for Nova & HyperNova
- abstract pp_hash computation for folding schemes
- add pp_hash to solidity contract generator to verify the decider proof

- implement the IVC `FoldingScheme` trait for HyperNova
- refactor Nova's preprocess logic to make it simplier to use
- add to Decider trait (& Nova's DeciderEth) a preprocess method
- get rid of the `init_nova_ivc_params` and `init_ivc_and_decider_params` methods in `examples` since this is achieved with the `FS::preprocess` & `Decider::preprocess` methods
  - (update the examples code to the simplified interface using
    FS::preprocess & Decider::preprocess)

* circom: add external_inputs

* adapt new external_inputs interface to the FoldingScheme trait and Nova impl

* adapt examples to new FCircuit external_inputs interface

* add state_len & external_inputs_len params to CircomFCircuit

* add examples/circom_full_flow.rs

* merge the params initializer functions, clippy

* circom: move r1cs reading to FCircuit::new instead of each step

* CI/examples: add circom so it can run the circom_full_flow example

* expose params & structs for external usage

* add full_flow example, move examples into 'examples' dir