diff --git a/.github/workflows/benchmark.yml b/.github/workflows/benchmark.yml
index 850ac38..61a968e 100644
--- a/.github/workflows/benchmark.yml
+++ b/.github/workflows/benchmark.yml
@@ -17,12 +17,12 @@ jobs:
       - name: Install Nargo
         uses: noir-lang/noirup@v0.1.3
         with:
-          toolchain: 0.34.0
+          toolchain: 0.36.0
 
       - name: Install bb
         run: |
           npm install -g bbup
-          bbup -nv 0.34.0
+          bbup -nv 0.36.0
 
       - name: Build Noir benchmark programs
         run: nargo export
@@ -34,7 +34,7 @@ jobs:
 
       - name: Compare gates reports
         id: gates_diff
-        uses: noir-lang/noir-gates-diff@1931aaaa848a1a009363d6115293f7b7fc72bb87
+        uses: noir-lang/noir-gates-diff@7e4ddaa91c69380f15ccba514eac17bc7432a8cc
         with:
           report: gates_report.json
           summaryQuantile: 0.9 # only display the 10% most significant circuit size diffs in the summary (defaults to 20%)
diff --git a/.github/workflows/nightly-canary.yml b/.github/workflows/nightly-canary.yml
index 4fd5ce1..17a20f7 100644
--- a/.github/workflows/nightly-canary.yml
+++ b/.github/workflows/nightly-canary.yml
@@ -13,7 +13,7 @@ permissions:
 
 jobs:
   test:
-    name: Test on Nargo ${{matrix.toolchain}}
+    name: Test on Nargo Nightly
     runs-on: ubuntu-latest
     steps:
       - name: Checkout sources
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index a3b3dc0..44576e1 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -8,7 +8,7 @@ on:
 
 env:
   CARGO_TERM_COLOR: always
-  MINIMUM_NOIR_VERSION: v0.34.0
+  MINIMUM_NOIR_VERSION: v0.36.0
 
 jobs:
   noir-version-list:
@@ -20,7 +20,7 @@ jobs:
     steps:
       - name: Checkout sources
         id: get_versions
-        run: |         
+        run: |
           # gh returns the Noir releases in reverse chronological order so we keep all releases published after the minimum supported version.
           VERSIONS=$(gh release list -R noir-lang/noir --exclude-pre-releases --json tagName -q 'map(.tagName) | index(env.MINIMUM_NOIR_VERSION) as $index | if $index then .[0:$index+1] else [env.MINIMUM_NOIR_VERSION] end')
           echo "versions=$VERSIONS"
@@ -50,6 +50,32 @@ jobs:
       - name: Run Noir tests
         run: nargo test
 
+  rust-equivalence-tests:
+    name: Test for equivalence against Rust impl
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout sources
+        uses: actions/checkout@v4
+
+      - name: Install Nargo
+        uses: noir-lang/noirup@v0.1.3
+        with:
+          toolchain: ${{ env.MINIMUM_NOIR_VERSION }}
+
+      - name: Install Cargo
+        uses: dtolnay/rust-toolchain@1.74.1
+        with:
+          targets: x86_64-unknown-linux-gnu
+      
+      - name: Cache Cargo dependencies
+        uses: Swatinem/rust-cache@v2
+        with:
+          key: x86_64-unknown-linux-gnu
+          cache-on-failure: true
+
+      - name: Export and Test Noir Functions
+        run: ./scripts/fuzz-test.sh
+
   format:
     runs-on: ubuntu-latest
     steps:
@@ -73,6 +99,7 @@ jobs:
     if: ${{ always() }}
     needs: 
       - test
+      - rust-equivalence-tests
       - format
 
     steps:
diff --git a/Cargo.lock b/Cargo.lock
new file mode 100644
index 0000000..e3d435e
--- /dev/null
+++ b/Cargo.lock
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diff --git a/Cargo.toml b/Cargo.toml
new file mode 100644
index 0000000..5316c13
--- /dev/null
+++ b/Cargo.toml
@@ -0,0 +1,8 @@
+[package]
+name = "noir_library"
+version = "0.1.0"
+edition = "2021"
+
+[dev-dependencies]
+proptest = "1.2.0"
+noir-runner = { git = "https://github.com/noir-lang/noir-runner", branch = "main" }
diff --git a/README.md b/README.md
index abd8a11..a47691a 100644
--- a/README.md
+++ b/README.md
@@ -19,13 +19,19 @@ Add a brief description of the library
 
 ## Noir version compatibility
 
-TODO: Update Noir version numbers tested compatible with
-
-This library is tested to work as of Noir version 1.0.0-beta.x.
+This library is tested to work as of Noir version 0.36.0 & 1.0.0-beta.x.
 
 ## Benchmarks
 
-TODO
+Benchmarks are ignored by `git` and checked on pull-request. As such, benchmarks may be generated
+with the following command.
+
+```bash
+# execute the following
+./scripts/build-gates-report.sh
+```
+
+The benchmark will be generated at `./gates_report.json`.
 
 ## Installation
 
@@ -41,3 +47,4 @@ LIBRARY = { tag = "v0.1.0", git = "https://github.com/noir-lang/LIBRARY_NAME" }
 ### Usage
 
 `PLACEHOLDER`
+
diff --git a/scripts/fuzz-test.sh b/scripts/fuzz-test.sh
new file mode 100755
index 0000000..3e999e9
--- /dev/null
+++ b/scripts/fuzz-test.sh
@@ -0,0 +1,19 @@
+#!/usr/bin/env bash
+set -e
+
+# dependencies:
+#
+# - `nargo`
+# - `cargo`
+
+# export noir functions purely in brillig
+nargo export --force-brillig
+
+# run rust prop tests against brillig functions
+cargo test
+
+# export noir functions as-is
+nargo export
+
+# run rust prop tests against noir functions
+cargo test
diff --git a/src/lib.nr b/src/lib.nr
index 80b968c..a507089 100644
--- a/src/lib.nr
+++ b/src/lib.nr
@@ -13,3 +13,9 @@ fn bench_test(mut x: Field) -> Field {
     }
     x
 }
+
+// This is an example prop test harness.
+#[export]
+fn prop_mul(a: Field, b: Field) -> Field {
+    a * b
+}
diff --git a/tests/differential.rs b/tests/differential.rs
new file mode 100644
index 0000000..91c1158
--- /dev/null
+++ b/tests/differential.rs
@@ -0,0 +1,29 @@
+use std::collections::BTreeMap;
+use std::path::PathBuf;
+
+use noir_runner::{NoirRunner, ToNoir};
+use proptest::{prelude::prop, test_runner::TestRunner};
+
+#[test]
+fn test_prop_mul() {
+    let runner = NoirRunner::try_new(PathBuf::new()).unwrap();
+
+    let mut test_runner = TestRunner::new(Default::default());
+
+    test_runner
+        .run(&(0..1000u32, 0..1000u32), |(a, b)| {
+            let input = BTreeMap::from([
+                ("a".to_string(), a.to_noir()),
+                ("b".to_string(), b.to_noir()),
+            ]);
+
+            let result = runner.run("prop_mul", input).unwrap().unwrap();
+
+            let expected = a * b;
+
+            assert_eq!(result, expected.to_noir());
+
+            Ok(())
+        })
+        .unwrap();
+}