Katana: Add state update DA encodings (#2474)

crates/katana/primitives/Cargo.toml

@@ -11,6 +11,7 @@ anyhow.workspace = true
 base64.workspace = true
 derive_more.workspace = true
 lazy_static.workspace = true
+num-traits.workspace = true
 rand = { workspace = true, features = [ "small_rng" ] }
 serde.workspace = true
 serde_json.workspace = true
@@ -23,10 +24,11 @@ thiserror.workspace = true
 alloy-primitives.workspace = true
 flate2 = { workspace = true, optional = true }
 katana-cairo.workspace = true
+num-bigint = "0.4.6"
 
 [dev-dependencies]
-num-traits.workspace = true
 assert_matches.workspace = true
+rstest.workspace = true
 similar-asserts.workspace = true
 
 [features]

crates/katana/primitives/src/da/blob.rs

@@ -0,0 +1,41 @@
+use num_bigint::BigUint;
+use num_traits::Num;
+
+use super::eip4844::{BLOB_LEN, BLS_MODULUS, GENERATOR};
+use super::math::{fft, ifft};
+
+/// Recovers the original data from a given blob.
+///
+/// This function takes a vector of `BigUint` representing the data of a blob and
+/// returns the recovered original data as a vector of `BigUint`.
+///
+/// # Arguments
+///
+/// * `data` - A vector of `BigUint` representing the blob data.
+///
+/// # Returns
+///
+/// A vector of `BigUint` representing the recovered original data.
+pub fn recover(data: Vec<BigUint>) -> Vec<BigUint> {
+    let xs: Vec<BigUint> = (0..BLOB_LEN)
+        .map(|i| {
+            let bin = format!("{:012b}", i);
+            let bin_rev = bin.chars().rev().collect::<String>();
+            GENERATOR.modpow(&BigUint::from_str_radix(&bin_rev, 2).unwrap(), &BLS_MODULUS)
+        })
+        .collect();
+
+    ifft(data, xs, &BLS_MODULUS)
+}
+
+pub fn transform(data: Vec<BigUint>) -> Vec<BigUint> {
+    let xs: Vec<BigUint> = (0..BLOB_LEN)
+        .map(|i| {
+            let bin = format!("{:012b}", i);
+            let bin_rev = bin.chars().rev().collect::<String>();
+            GENERATOR.modpow(&BigUint::from_str_radix(&bin_rev, 2).unwrap(), &BLS_MODULUS)
+        })
+        .collect();
+
+    fft(data, xs, &BLS_MODULUS)
+}

crates/katana/primitives/src/da/eip4844.rs

@@ -0,0 +1,26 @@
+use std::str::FromStr;
+
+use lazy_static::lazy_static;
+use num_bigint::{BigUint, ToBigUint};
+
+// ****************************************************************************
+// * PARAMETERS & CONSTANTS                                                  *
+// ****************************************************************************
+/// Length of the blob.
+pub const BLOB_LEN: usize = 4096;
+
+lazy_static! {
+    /// EIP-4844 BLS12-381 modulus.
+    ///
+    /// As defined in https://eips.ethereum.org/EIPS/eip-4844
+    pub static ref BLS_MODULUS: BigUint = BigUint::from_str(
+        "52435875175126190479447740508185965837690552500527637822603658699938581184513",
+    )
+    .unwrap();
+    /// Generator of the group of evaluation points (EIP-4844 parameter).
+    pub static ref GENERATOR: BigUint = BigUint::from_str(
+        "39033254847818212395286706435128746857159659164139250548781411570340225835782",
+    )
+    .unwrap();
+    pub static ref TWO: BigUint = 2u32.to_biguint().unwrap();
+}