@@ -15,6 +15,7 @@ ark-ec = "0.4.1"
 ark-ff = "0.4.1"
 ark-r1cs-std = { version = "0.4.0", default-features = false }
 ark-relations = { version = "0.4.0", default-features = false }
+ark-snark = { version = "^0.4.0", default-features = false }
 ark-poly-commit = "^0.4.0"
 ark-crypto-primitives = { version = "^0.4.0", default-features = false, features = [
     "r1cs",

@@ -30,3 +30,10 @@
 ### Repo structure
 - the Circom circuit (that defines the keccak-chain) to be folded is defined at [./circuit/keccak-chain.circom](https://github.com/arnaucube/hash-chain-sonobe/blob/main/circuit/keccak-chain.circom)
 - the logic to fold the circuit using Sonobe is defined at [src/{sha_chain, keccak_chain}.rs](https://github.com/arnaucube/hash-chain-sonobe/blob/main/src)
+
+
+
+## Other
+Additionally there is the `src/naive_approach_sha_chain.rs` file, which mimics the amount of hashes computed by the `src/sha_chain.rs` file, but instead of folding it does it by building a big circuit that does all the hashes at once, as we would do before folding existed.
+
+To run it: `cargo test --release naive_approach_sha_chain -- --nocapture`

@@ -136,7 +136,11 @@ nova.i,
                 start.elapsed()
             );
         }
-        println!("Nova's all steps time: {:?}", start_full.elapsed());
+        println!(
+            "Nova's all {} steps time: {:?}",
+            n_steps,
+            start_full.elapsed()
+        );
 
         // perform the hash chain natively in rust (which uses a rust Keccak256 library)
         let mut z_i_native = z_0.clone();

@@ -3,5 +3,6 @@ #![allow(non_camel_case_types)]
 #![allow(clippy::upper_case_acronyms)]
 
 mod keccak_chain;
+mod naive_approach_sha_chain;
 mod sha_chain;
 mod utils;

@@ -0,0 +1,132 @@
+/// This example does the hash chain but in the naive approach: instead of using folding, it does a
+/// big circuit containing n instantiations of the sha256 constraints.
+
+#[cfg(test)]
+mod tests {
+    use ark_bn254::{Bn254, Fr};
+
+    use ark_groth16::Groth16;
+    use ark_snark::SNARK;
+
+    use ark_ff::PrimeField;
+
+    use std::time::Instant;
+
+    use ark_crypto_primitives::crh::sha256::{constraints::Sha256Gadget, digest::Digest, Sha256};
+    use ark_r1cs_std::fields::fp::FpVar;
+    use ark_r1cs_std::{alloc::AllocVar, eq::EqGadget};
+    use ark_r1cs_std::{bits::uint8::UInt8, boolean::Boolean, ToBitsGadget, ToBytesGadget};
+    use ark_relations::r1cs::{
+        ConstraintSynthesizer, ConstraintSystem, ConstraintSystemRef, SynthesisError,
+    };
+
+    use crate::utils::tests::*;
+
+    /// Test circuit to be folded
+    #[derive(Clone, Debug)]
+    pub struct SHA256ChainCircuit<F: PrimeField, const N: usize, const HASHES_PER_STEP: usize> {
+        z_0: Option<Vec<F>>,
+        z_n: Option<Vec<F>>,
+    }
+    impl<F: PrimeField, const N: usize, const HASHES_PER_STEP: usize> ConstraintSynthesizer<F>
+        for SHA256ChainCircuit<F, N, HASHES_PER_STEP>
+    {
+        fn generate_constraints(self, cs: ConstraintSystemRef<F>) -> Result<(), SynthesisError> {
+            let z_0 = Vec::<FpVar<F>>::new_witness(cs.clone(), || {
+                Ok(self.z_0.unwrap_or(vec![F::zero()]))
+            })?;
+            let z_n =
+                Vec::<FpVar<F>>::new_input(cs.clone(), || Ok(self.z_n.unwrap_or(vec![F::zero()])))?;
+            let mut z_i: Vec<FpVar<F>> = z_0.clone();
+            for _ in 0..N {
+                let mut b: Vec<UInt8<F>> = z_i
+                    .iter()
+                    .map(|f| UInt8::<F>::from_bits_le(&f.to_bits_le().unwrap()[..8]))
+                    .collect::<Vec<_>>();
+
+                for _ in 0..HASHES_PER_STEP {
+                    let mut sha256_var = Sha256Gadget::default();
+                    sha256_var.update(&b).unwrap();
+                    b = sha256_var.finalize()?.to_bytes()?;
+                }
+
+                // update z_i = z_{i+1}
+                z_i = b
+                    .iter()
+                    .map(|e| {
+                        let bits = e.to_bits_le().unwrap();
+                        Boolean::<F>::le_bits_to_fp_var(&bits).unwrap()
+                    })
+                    .collect();
+            }
+
+            z_i.enforce_equal(&z_n)?;
+            Ok(())
+        }
+    }
+    // compute natively in rust the expected result
+    fn rust_native_result(z_0: Vec<Fr>, n_steps: usize, hashes_per_step: usize) -> Vec<Fr> {
+        let mut z_i: Vec<Fr> = z_0.clone();
+        for _ in 0..n_steps {
+            let mut b = f_vec_to_bytes(z_i.to_vec());
+
+            for _ in 0..hashes_per_step {
+                let mut sha256 = Sha256::default();
+                sha256.update(b);
+                b = sha256.finalize().to_vec();
+            }
+
+            z_i = bytes_to_f_vec(b.to_vec()).unwrap();
+        }
+        z_i.clone()
+    }
+
+    #[test]
+    fn full_flow() {
+        // set how many iterations of the SHA256ChainCircuit circuit internal loop we want to
+        // compute
+        const N_STEPS: usize = 50;
+        const HASHES_PER_STEP: usize = 10;
+        println!("running the 'naive' SHA256ChainCircuit, with N_STEPS={}, HASHES_PER_STEP={}. Total hashes = {}", N_STEPS, HASHES_PER_STEP, N_STEPS* HASHES_PER_STEP);
+
+        // set the initial state
+        // let z_0_aux: Vec<u32> = vec![0_u32; 32 * 8];
+        let z_0_aux: Vec<u8> = vec![0_u8; 32];
+        let z_0: Vec<Fr> = z_0_aux.iter().map(|v| Fr::from(*v)).collect::<Vec<Fr>>();
+
+        // run the N iterations 'natively' in rust to compute the expected `z_n`
+        let z_n = rust_native_result(z_0.clone(), N_STEPS, HASHES_PER_STEP);
+
+        let circuit = SHA256ChainCircuit::<Fr, N_STEPS, HASHES_PER_STEP> {
+            z_0: Some(z_0),
+            z_n: Some(z_n.clone()),
+        };
+
+        let cs = ConstraintSystem::<Fr>::new_ref();
+        circuit.clone().generate_constraints(cs.clone()).unwrap();
+        println!(
+            "number of constraints of the (naive) SHA256ChainCircuit with N={} hash iterations: {}",
+            N_STEPS,
+            cs.num_constraints()
+        );
+
+        // now let's generate an actual Groth16 proof
+        let mut rng = rand::rngs::OsRng;
+        let (g16_pk, g16_vk) =
+            Groth16::<Bn254>::circuit_specific_setup(circuit.clone(), &mut rng).unwrap();
+
+        let start = Instant::now();
+        let proof = Groth16::<Bn254>::prove(&g16_pk, circuit.clone(), &mut rng).unwrap();
+        println!(
+            "Groth16 proof generation (for the naive SHA256ChainCircuit): {:?}",
+            start.elapsed()
+        );
+
+        let public_inputs = z_n;
+        let valid_proof = Groth16::<Bn254>::verify(&g16_vk, &public_inputs, &proof).unwrap();
+
+        assert!(valid_proof);
+
+        println!("finished running the 'naive' SHA256ChainCircuit, with N_STEPS={}, HASHES_PER_STEP={}. Total hashes = {}", N_STEPS, HASHES_PER_STEP, N_STEPS* HASHES_PER_STEP);
+    }
+}

@@ -44,10 +44,12 @@ use crate::utils::tests::*;
 
     /// Test circuit to be folded
     #[derive(Clone, Copy, Debug)]
-    pub struct SHA256FoldStepCircuit<F: PrimeField> {
+    pub struct SHA256FoldStepCircuit<F: PrimeField, const HASHES_PER_STEP: usize> {
         _f: PhantomData<F>,
     }
-    impl<F: PrimeField> FCircuit<F> for SHA256FoldStepCircuit<F> {
+    impl<F: PrimeField, const HASHES_PER_STEP: usize> FCircuit<F>
+        for SHA256FoldStepCircuit<F, HASHES_PER_STEP>
+    {
         type Params = ();
         fn new(_params: Self::Params) -> Result<Self, Error> {
             Ok(Self { _f: PhantomData })
@@ -66,12 +68,15 @@ _i: usize,
             z_i: Vec<F>,
             _external_inputs: Vec<F>,
         ) -> Result<Vec<F>, Error> {
-            let b = f_vec_to_bytes(z_i.to_vec());
-            let mut sha256 = Sha256::default();
-            sha256.update(b);
-            let z_i1 = sha256.finalize().to_vec();
+            let mut b = f_vec_to_bytes(z_i.to_vec());
 
-            bytes_to_f_vec(z_i1.to_vec())
+            for _ in 0..HASHES_PER_STEP {
+                let mut sha256 = Sha256::default();
+                sha256.update(b);
+                b = sha256.finalize().to_vec();
+            }
+
+            bytes_to_f_vec(b.to_vec()) // z_{i+1}
         }
         fn generate_step_constraints(
             &self,
@@ -80,14 +85,18 @@ _i: usize,
             z_i: Vec<FpVar<F>>,
             _external_inputs: Vec<FpVar<F>>,
         ) -> Result<Vec<FpVar<F>>, SynthesisError> {
-            let mut sha256_var = Sha256Gadget::default();
-            let z_i_u8: Vec<UInt8<F>> = z_i
+            let mut b: Vec<UInt8<F>> = z_i
                 .iter()
                 .map(|f| UInt8::<F>::from_bits_le(&f.to_bits_le().unwrap()[..8]))
                 .collect::<Vec<_>>();
-            sha256_var.update(&z_i_u8).unwrap();
-            let z_i1_u8 = sha256_var.finalize()?.to_bytes()?;
-            let z_i1: Vec<FpVar<F>> = z_i1_u8
+
+            for _ in 0..HASHES_PER_STEP {
+                let mut sha256_var = Sha256Gadget::default();
+                sha256_var.update(&b).unwrap();
+                b = sha256_var.finalize()?.to_bytes()?;
+            }
+
+            let z_i1: Vec<FpVar<F>> = b
                 .iter()
                 .map(|e| {
                     let bits = e.to_bits_le().unwrap();
@@ -102,14 +111,16 @@
     #[test]
     fn full_flow() {
         // set how many steps of folding we want to compute
-        let n_steps = 100;
+        const N_STEPS: usize = 100;
+        const HASHES_PER_STEP: usize = 10;
+        println!("running Nova folding scheme on SHA256FoldStepCircuit, with N_STEPS={}, HASHES_PER_STEP={}. Total hashes = {}", N_STEPS, HASHES_PER_STEP, N_STEPS* HASHES_PER_STEP);
 
         // set the initial state
         // let z_0_aux: Vec<u32> = vec![0_u32; 32 * 8];
         let z_0_aux: Vec<u8> = vec![0_u8; 32];
         let z_0: Vec<Fr> = z_0_aux.iter().map(|v| Fr::from(*v)).collect::<Vec<Fr>>();
 
-        let f_circuit = SHA256FoldStepCircuit::<Fr>::new(()).unwrap();
+        let f_circuit = SHA256FoldStepCircuit::<Fr, HASHES_PER_STEP>::new(()).unwrap();
 
         // ----------------
         // Sanity check
@@ -128,6 +139,10 @@ let z_1_native = f_circuit.step_native(1, z_0.clone(), vec![]).unwrap();
         assert_eq!(z_1_var.value().unwrap(), z_1_native);
         // check that the constraint system is satisfied
         assert!(cs.is_satisfied().unwrap());
+        println!(
+            "number of constraints of a single instantiation of the SHA256FoldStepCircuit: {}",
+            cs.num_constraints()
+        );
         // ----------------
 
         // define type aliases to avoid writting the whole type each time
@@ -136,7 +151,7 @@ G1,
             GVar,
             G2,
             GVar2,
-            SHA256FoldStepCircuit<Fr>,
+            SHA256FoldStepCircuit<Fr, HASHES_PER_STEP>,
             KZG<'static, Bn254>,
             Pedersen<G2>,
             false,
@@ -146,7 +161,7 @@ G1,
             GVar,
             G2,
             GVar2,
-            SHA256FoldStepCircuit<Fr>,
+            SHA256FoldStepCircuit<Fr, HASHES_PER_STEP>,
             KZG<'static, Bn254>,
             Pedersen<G2>,
             Groth16<Bn254>,
@@ -172,7 +187,7 @@ println!("Decider params generated: {:?}", start.elapsed());
 
         // run n steps of the folding iteration
         let start_full = Instant::now();
-        for _ in 0..n_steps {
+        for _ in 0..N_STEPS {
             let start = Instant::now();
             nova.prove_step(rng, vec![], None).unwrap();
             println!(
@@ -181,7 +196,11 @@ nova.i,
                 start.elapsed()
             );
         }
-        println!("Nova's all steps time: {:?}", start_full.elapsed());
+        println!(
+            "Nova's all {} steps time: {:?}",
+            N_STEPS,
+            start_full.elapsed()
+        );
 
         // ----------------
         // Sanity check