Add Basefold mpcs. (#66)

* Add basefold to master.

* Refactor.

Remove unnecessary module and codes. Refactor the code.

mpcs/Cargo.toml

@@ -7,10 +7,41 @@ license.workspace = true
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
+ctr = { git = "https://github.com/RustCrypto/block-modes", rev = "78fefba" }
 ff_ext = { path = "../ff_ext" }
 serde.workspace = true
 goldilocks.workspace = true
 ff.workspace = true
+ark-std = { version = "0.4" }
+aes = "0.8"
+itertools = "0.12.1"
+num-bigint = "0.4.3"
+num-integer = "0.1.45"
+rand = "0.8"
+bitvec = "1.0.1"
+halo2_curves = { git = "https://github.com/privacy-scaling-explorations/halo2curves", tag = "0.3.3", package = "halo2curves", features = [
+    "derive_serde",
+] }
+blake2b_simd = "1.0.2"
+sha3 = "0.10.6"
+rayon = { version = "1.5.3", optional = true }
+blake2 = { version = "0.10.6" }
+poseidon.workspace = true
+rand_chacha = { version = "0.3.1", features = ["serde1"] }
+generic-array = { version = "0.14.7", features = ["serde"] }
+multilinear_extensions = { path = "../multilinear_extensions" }
+transcript = { path = "../transcript" }
+plonky2 = "0.2.0"
 
-multilinear_extensions = { path = "../multilinear_extensions", features = [ "parallel"] }
-transcript = { path = "../transcript" }
+[dev-dependencies]
+simple-frontend = { path = "../simple-frontend" }
+gkr = { path = "../gkr" }
+
+[features]
+default = ["parallel"]   # Add "sanity-check" to debug
+parallel = ["dep:rayon"]
+benchmark = ["parallel"]
+sanity-check = []
+use-plonky2 = []
+print-trace = [ "ark-std/print-trace" ]
+timer = []