Feat/Switch Spartan Backend to Use Goldilocks Field (#17)

* Reversable: temporarily remove non-compiling parts

* Remove PCS and add Goldilocks

* Recover intermediate proofs

* Recover intermediate proofs

* Remove elliptic group definition

* Remove remnant ristretto255

* Remove comment blocks

* Correct goldilocks implementation

* Make workflow pass

* Remove extra space

* Remove comment blocks

* Correct comment blocks

* Correct arithmetics

* Recover SNARK verify checks

* Recover sumcheck instance verification check

* Comment out non-existent binaries.

* Remove unused binaries

* Graft in ceno-goldilocks

* Modify pow fn

* Add degree2 extension of goldilocks. Convert to ceno-goldilocks

* Migrate to generic instead of base field

* Migrate to generic instead of base field

* Migrate to generic instead of base field

* Remove unnecessary parameter specification

* Add deserialize trait bound

* fmt

* Resolve conflicts/duplicates/dep versioning from merge

* fmt

* fmt

* Correct itertools version

* Restore transcript consistency

* fmt

* Code improvement

* Code improvement

* Code improvement

* Code improvement

* Import ceno-goldilocks main branch

* fmt

* Reuse Goldilocks random

* Add basefield arithmetics

* fmt

* Use degree 2 ext for soundness

* Specify output

* Correct BaseField trait bound

* Improve arithmetic definition

* Reorder arithmetic definition

* Add arithmetic traits

* Feat/Remove ZK from Spartan Backend (#53)

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Co-authored-by: Yuncong Zhang <[email protected]>
Co-authored-by: Matthias Goergens <[email protected]>