diff --git a/CHANGELOG.md b/CHANGELOG.md
index c152e9ab..8caf16b4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,6 +10,7 @@ and this project adheres to Rust's notion of
 - `halo2::dev::LookupFailure` (used in `VerifyFailure::Lookup`)
 
 ### Changed
+- `halo2::plonk::create_proof` now takes an `R: rand::RngCore` argument.
 - `halo2::plonk::Error` has been overhauled:
   - `Error` now implements `std::fmt::Display` and `std::error::Error`.
   - `Error` no longer implements `PartialEq`. Tests can check for specific error
diff --git a/benches/arithmetic.rs b/benches/arithmetic.rs
index ec13c74b..e6e4f242 100644
--- a/benches/arithmetic.rs
+++ b/benches/arithmetic.rs
@@ -2,14 +2,18 @@
 extern crate criterion;
 
 extern crate halo2;
-use crate::arithmetic::{small_multiexp, FieldExt};
+use crate::arithmetic::small_multiexp;
 use crate::pasta::{EqAffine, Fp};
 use crate::poly::commitment::Params;
+use group::ff::Field;
 use halo2::*;
 
 use criterion::{black_box, Criterion};
+use rand::rngs::OsRng;
 
 fn criterion_benchmark(c: &mut Criterion) {
+    let rng = OsRng;
+
     // small multiexp
     {
         let params: Params<EqAffine> = Params::new(5);
@@ -17,8 +21,8 @@ fn criterion_benchmark(c: &mut Criterion) {
         let len = g.len() / 2;
         let (g_lo, g_hi) = g.split_at_mut(len);
 
-        let coeff_1 = Fp::rand();
-        let coeff_2 = Fp::rand();
+        let coeff_1 = Fp::random(rng);
+        let coeff_2 = Fp::random(rng);
 
         c.bench_function("double-and-add", |b| {
             b.iter(|| {
diff --git a/benches/plonk.rs b/benches/plonk.rs
index 30fe5234..bf0415c4 100644
--- a/benches/plonk.rs
+++ b/benches/plonk.rs
@@ -2,12 +2,14 @@
 extern crate criterion;
 
 extern crate halo2;
+use group::ff::Field;
 use halo2::arithmetic::FieldExt;
 use halo2::circuit::{Cell, Layouter, SimpleFloorPlanner};
 use halo2::pasta::{EqAffine, Fp};
 use halo2::plonk::*;
 use halo2::poly::{commitment::Params, Rotation};
 use halo2::transcript::{Blake2bRead, Blake2bWrite, Challenge255};
+use rand::rngs::OsRng;
 
 use std::marker::PhantomData;
 
@@ -253,13 +255,15 @@ fn criterion_benchmark(c: &mut Criterion) {
     }
 
     fn prover(k: u32, params: &Params<EqAffine>, pk: &ProvingKey<EqAffine>) -> Vec<u8> {
+        let rng = OsRng;
+
         let circuit: MyCircuit<Fp> = MyCircuit {
-            a: Some(Fp::rand()),
+            a: Some(Fp::random(rng)),
             k,
         };
 
         let mut transcript = Blake2bWrite::<_, _, Challenge255<_>>::init(vec![]);
-        create_proof(params, pk, &[circuit], &[&[]], &mut transcript)
+        create_proof(params, pk, &[circuit], &[&[]], rng, &mut transcript)
             .expect("proof generation should not fail");
         transcript.finalize()
     }
diff --git a/examples/sha256/benches.rs b/examples/sha256/benches.rs
index 76ba9099..e24705e5 100644
--- a/examples/sha256/benches.rs
+++ b/examples/sha256/benches.rs
@@ -8,6 +8,7 @@ use halo2::{
     poly::commitment::Params,
     transcript::{Blake2bRead, Blake2bWrite, Challenge255},
 };
+use rand::rngs::OsRng;
 
 use std::{
     fs::File,
@@ -134,7 +135,7 @@ fn bench(name: &str, k: u32, c: &mut Criterion) {
     let proof_path = Path::new("./benches/sha256_assets/sha256_proof");
     if File::open(&proof_path).is_err() {
         let mut transcript = Blake2bWrite::<_, _, Challenge255<_>>::init(vec![]);
-        create_proof(&params, &pk, &[circuit], &[], &mut transcript)
+        create_proof(&params, &pk, &[circuit], &[], OsRng, &mut transcript)
             .expect("proof generation should not fail");
         let proof: Vec<u8> = transcript.finalize();
         let mut file = File::create(&proof_path).expect("Failed to create sha256_proof");
diff --git a/examples/two-chip.rs b/examples/two-chip.rs
index 117eac93..680511ef 100644
--- a/examples/two-chip.rs
+++ b/examples/two-chip.rs
@@ -513,7 +513,9 @@ impl<F: FieldExt> Circuit<F> for MyCircuit<F> {
 
 #[allow(clippy::many_single_char_names)]
 fn main() {
+    use group::ff::Field;
     use halo2::{dev::MockProver, pasta::Fp};
+    use rand::rngs::OsRng;
 
     // ANCHOR: test-circuit
     // The number of rows in our circuit cannot exceed 2^k. Since our example
@@ -521,9 +523,10 @@ fn main() {
     let k = 4;
 
     // Prepare the private and public inputs to the circuit!
-    let a = Fp::rand();
-    let b = Fp::rand();
-    let c = Fp::rand();
+    let rng = OsRng;
+    let a = Fp::random(rng);
+    let b = Fp::random(rng);
+    let c = Fp::random(rng);
     let d = (a + b) * c;
 
     // Instantiate the circuit with the private inputs.
diff --git a/src/arithmetic.rs b/src/arithmetic.rs
index 4d1031ce..0dac0fe2 100644
--- a/src/arithmetic.rs
+++ b/src/arithmetic.rs
@@ -402,13 +402,18 @@ pub fn lagrange_interpolate<F: FieldExt>(points: &[F], evals: &[F]) -> Vec<F> {
     }
 }
 
+#[cfg(test)]
+use rand::rngs::OsRng;
+
 #[cfg(test)]
 use crate::pasta::Fp;
 
 #[test]
 fn test_lagrange_interpolate() {
-    let points = (0..5).map(|_| Fp::rand()).collect::<Vec<_>>();
-    let evals = (0..5).map(|_| Fp::rand()).collect::<Vec<_>>();
+    let rng = OsRng;
+
+    let points = (0..5).map(|_| Fp::random(rng)).collect::<Vec<_>>();
+    let evals = (0..5).map(|_| Fp::random(rng)).collect::<Vec<_>>();
 
     for coeffs in 0..5 {
         let points = &points[0..coeffs];
diff --git a/src/plonk/lookup/prover.rs b/src/plonk/lookup/prover.rs
index 6e7c60d3..80e29a14 100644
--- a/src/plonk/lookup/prover.rs
+++ b/src/plonk/lookup/prover.rs
@@ -16,6 +16,7 @@ use group::{
     ff::{BatchInvert, Field},
     Curve,
 };
+use rand::RngCore;
 use std::{
     collections::BTreeMap,
     iter,
@@ -73,6 +74,7 @@ impl<F: FieldExt> Argument<F> {
         'a,
         C,
         E: EncodedChallenge<C>,
+        R: RngCore,
         T: TranscriptWrite<C, E>,
     >(
         &self,
@@ -86,6 +88,7 @@ impl<F: FieldExt> Argument<F> {
         advice_cosets: &'a [Polynomial<C::Scalar, ExtendedLagrangeCoeff>],
         fixed_cosets: &'a [Polynomial<C::Scalar, ExtendedLagrangeCoeff>],
         instance_cosets: &'a [Polynomial<C::Scalar, ExtendedLagrangeCoeff>],
+        mut rng: R,
         transcript: &mut T,
     ) -> Result<Permuted<C>, Error>
     where
@@ -173,14 +176,6 @@ impl<F: FieldExt> Argument<F> {
             )
         };
 
-        // Closure to construct commitment to vector of values
-        let commit_values = |values: &Polynomial<C::Scalar, LagrangeCoeff>| {
-            let poly = pk.vk.domain.lagrange_to_coeff(values.clone());
-            let blind = Blind(C::Scalar::rand());
-            let commitment = params.commit_lagrange(values, blind).to_affine();
-            (poly, blind, commitment)
-        };
-
         // Get values of input expressions involved in the lookup and compress them
         let (unpermuted_input_expressions, unpermuted_input_cosets, compressed_input_expression) =
             compress_expressions(&self.input_expressions);
@@ -190,14 +185,23 @@ impl<F: FieldExt> Argument<F> {
             compress_expressions(&self.table_expressions);
 
         // Permute compressed (InputExpression, TableExpression) pair
-        let (permuted_input_expression, permuted_table_expression) = permute_expression_pair::<C>(
+        let (permuted_input_expression, permuted_table_expression) = permute_expression_pair::<C, _>(
             pk,
             params,
             domain,
+            &mut rng,
             &compressed_input_expression,
             &compressed_table_expression,
         )?;
 
+        // Closure to construct commitment to vector of values
+        let mut commit_values = |values: &Polynomial<C::Scalar, LagrangeCoeff>| {
+            let poly = pk.vk.domain.lagrange_to_coeff(values.clone());
+            let blind = Blind(C::Scalar::random(&mut rng));
+            let commitment = params.commit_lagrange(values, blind).to_affine();
+            (poly, blind, commitment)
+        };
+
         // Commit to permuted input expression
         let (permuted_input_poly, permuted_input_blind, permuted_input_commitment) =
             commit_values(&permuted_input_expression);
@@ -238,13 +242,18 @@ impl<C: CurveAffine> Permuted<C> {
     /// grand product polynomial over the lookup. The grand product polynomial
     /// is used to populate the Product<C> struct. The Product<C> struct is
     /// added to the Lookup and finally returned by the method.
-    pub(in crate::plonk) fn commit_product<E: EncodedChallenge<C>, T: TranscriptWrite<C, E>>(
+    pub(in crate::plonk) fn commit_product<
+        E: EncodedChallenge<C>,
+        R: RngCore,
+        T: TranscriptWrite<C, E>,
+    >(
         self,
         pk: &ProvingKey<C>,
         params: &Params<C>,
         theta: ChallengeTheta<C>,
         beta: ChallengeBeta<C>,
         gamma: ChallengeGamma<C>,
+        mut rng: R,
         transcript: &mut T,
     ) -> Result<Committed<C>, Error> {
         let blinding_factors = pk.vk.cs.blinding_factors();
@@ -326,7 +335,7 @@ impl<C: CurveAffine> Permuted<C> {
             // be a boolean (and ideally 1, else soundness is broken)
             .take(params.n as usize - blinding_factors)
             // Chain random blinding factors.
-            .chain((0..blinding_factors).map(|_| C::Scalar::rand()))
+            .chain((0..blinding_factors).map(|_| C::Scalar::random(&mut rng)))
             .collect::<Vec<_>>();
         assert_eq!(z.len(), params.n as usize);
         let z = pk.vk.domain.lagrange_from_vec(z);
@@ -376,7 +385,7 @@ impl<C: CurveAffine> Permuted<C> {
             assert_eq!(z[u], C::Scalar::one());
         }
 
-        let product_blind = Blind(C::Scalar::rand());
+        let product_blind = Blind(C::Scalar::random(rng));
         let product_commitment = params.commit_lagrange(&z, product_blind).to_affine();
         let z = pk.vk.domain.lagrange_to_coeff(z);
         let product_coset = pk.vk.domain.coeff_to_extended(z.clone());
@@ -587,10 +596,11 @@ type ExpressionPair<F> = (Polynomial<F, LagrangeCoeff>, Polynomial<F, LagrangeCo
 /// - the first row in a sequence of like values in A' is the row
 ///   that has the corresponding value in S'.
 /// This method returns (A', S') if no errors are encountered.
-fn permute_expression_pair<C: CurveAffine>(
+fn permute_expression_pair<C: CurveAffine, R: RngCore>(
     pk: &ProvingKey<C>,
     params: &Params<C>,
     domain: &EvaluationDomain<C::Scalar>,
+    mut rng: R,
     input_expression: &Polynomial<C::Scalar, LagrangeCoeff>,
     table_expression: &Polynomial<C::Scalar, LagrangeCoeff>,
 ) -> Result<ExpressionPair<C::Scalar>, Error> {
@@ -645,8 +655,9 @@ fn permute_expression_pair<C: CurveAffine>(
     }
     assert!(repeated_input_rows.is_empty());
 
-    permuted_input_expression.extend((0..(blinding_factors + 1)).map(|_| C::Scalar::rand()));
-    permuted_table_coeffs.extend((0..(blinding_factors + 1)).map(|_| C::Scalar::rand()));
+    permuted_input_expression
+        .extend((0..(blinding_factors + 1)).map(|_| C::Scalar::random(&mut rng)));
+    permuted_table_coeffs.extend((0..(blinding_factors + 1)).map(|_| C::Scalar::random(&mut rng)));
     assert_eq!(permuted_input_expression.len(), params.n as usize);
     assert_eq!(permuted_table_coeffs.len(), params.n as usize);
 
diff --git a/src/plonk/permutation/prover.rs b/src/plonk/permutation/prover.rs
index 58c8c69c..fc3a8e7b 100644
--- a/src/plonk/permutation/prover.rs
+++ b/src/plonk/permutation/prover.rs
@@ -2,6 +2,7 @@ use group::{
     ff::{BatchInvert, Field},
     Curve,
 };
+use rand::RngCore;
 use std::iter::{self, ExactSizeIterator};
 
 use super::super::{circuit::Any, ChallengeBeta, ChallengeGamma, ChallengeX};
@@ -44,6 +45,7 @@ impl Argument {
     pub(in crate::plonk) fn commit<
         C: CurveAffine,
         E: EncodedChallenge<C>,
+        R: RngCore,
         T: TranscriptWrite<C, E>,
     >(
         &self,
@@ -55,6 +57,7 @@ impl Argument {
         instance: &[Polynomial<C::Scalar, LagrangeCoeff>],
         beta: ChallengeBeta<C>,
         gamma: ChallengeGamma<C>,
+        mut rng: R,
         transcript: &mut T,
     ) -> Result<Committed<C>, Error> {
         let domain = &pk.vk.domain;
@@ -155,12 +158,12 @@ impl Argument {
             let mut z = domain.lagrange_from_vec(z);
             // Set blinding factors
             for z in &mut z[params.n as usize - blinding_factors..] {
-                *z = C::Scalar::rand();
+                *z = C::Scalar::random(&mut rng);
             }
             // Set new last_z
             last_z = z[params.n as usize - (blinding_factors + 1)];
 
-            let blind = Blind(C::Scalar::rand());
+            let blind = Blind(C::Scalar::random(&mut rng));
 
             let permutation_product_commitment_projective = params.commit_lagrange(&z, blind);
             let permutation_product_blind = blind;
diff --git a/src/plonk/prover.rs b/src/plonk/prover.rs
index 1cfd233e..46503c5a 100644
--- a/src/plonk/prover.rs
+++ b/src/plonk/prover.rs
@@ -1,5 +1,6 @@
 use ff::Field;
 use group::Curve;
+use rand::{rngs::OsRng, RngCore};
 use std::iter;
 use std::ops::RangeTo;
 
@@ -32,6 +33,7 @@ use crate::{
 pub fn create_proof<
     C: CurveAffine,
     E: EncodedChallenge<C>,
+    R: RngCore,
     T: TranscriptWrite<C, E>,
     ConcreteCircuit: Circuit<C::Scalar>,
 >(
@@ -39,6 +41,7 @@ pub fn create_proof<
     pk: &ProvingKey<C>,
     circuits: &[ConcreteCircuit],
     instances: &[&[&[C::Scalar]]],
+    mut rng: R,
     transcript: &mut T,
 ) -> Result<(), Error> {
     for instance in instances.iter() {
@@ -284,12 +287,15 @@ pub fn create_proof<
             // Add blinding factors to advice columns
             for advice in &mut advice {
                 for cell in &mut advice[unusable_rows_start..] {
-                    *cell = C::Scalar::rand();
+                    *cell = C::Scalar::random(&mut rng);
                 }
             }
 
             // Compute commitments to advice column polynomials
-            let advice_blinds: Vec<_> = advice.iter().map(|_| Blind(C::Scalar::rand())).collect();
+            let advice_blinds: Vec<_> = advice
+                .iter()
+                .map(|_| Blind(C::Scalar::random(&mut rng)))
+                .collect();
             let advice_commitments_projective: Vec<_> = advice
                 .iter()
                 .zip(advice_blinds.iter())
@@ -348,6 +354,7 @@ pub fn create_proof<
                         &advice.advice_cosets,
                         &pk.fixed_cosets,
                         &instance.instance_cosets,
+                        &mut rng,
                         transcript,
                     )
                 })
@@ -375,6 +382,7 @@ pub fn create_proof<
                 &instance.instance_values,
                 beta,
                 gamma,
+                &mut rng,
                 transcript,
             )
         })
@@ -386,13 +394,15 @@ pub fn create_proof<
             // Construct and commit to products for each lookup
             lookups
                 .into_iter()
-                .map(|lookup| lookup.commit_product(pk, params, theta, beta, gamma, transcript))
+                .map(|lookup| {
+                    lookup.commit_product(pk, params, theta, beta, gamma, &mut rng, transcript)
+                })
                 .collect::<Result<Vec<_>, _>>()
         })
         .collect::<Result<Vec<_>, _>>()?;
 
     // Commit to the vanishing argument's random polynomial for blinding h(x_3)
-    let vanishing = vanishing::Argument::commit(params, domain, transcript)?;
+    let vanishing = vanishing::Argument::commit(params, domain, &mut rng, transcript)?;
 
     // Obtain challenge for keeping all separate gates linearly independent
     let y: ChallengeY<_> = transcript.squeeze_challenge_scalar();
@@ -473,7 +483,7 @@ pub fn create_proof<
         );
 
     // Construct the vanishing argument's h(X) commitments
-    let vanishing = vanishing.construct(params, domain, expressions, y, transcript)?;
+    let vanishing = vanishing.construct(params, domain, expressions, y, &mut rng, transcript)?;
 
     let x: ChallengeX<_> = transcript.squeeze_challenge_scalar();
     let xn = x.pow(&[params.n as u64, 0, 0, 0]);
@@ -601,5 +611,5 @@ pub fn create_proof<
         // We query the h(X) polynomial at x
         .chain(vanishing.open(x));
 
-    multiopen::create_proof(params, transcript, instances).map_err(|_| Error::Opening)
+    multiopen::create_proof(params, rng, transcript, instances).map_err(|_| Error::Opening)
 }
diff --git a/src/plonk/vanishing/prover.rs b/src/plonk/vanishing/prover.rs
index 02dff0a6..d719947c 100644
--- a/src/plonk/vanishing/prover.rs
+++ b/src/plonk/vanishing/prover.rs
@@ -2,6 +2,7 @@ use std::iter;
 
 use ff::Field;
 use group::Curve;
+use rand::RngCore;
 
 use super::Argument;
 use crate::{
@@ -33,18 +34,19 @@ pub(in crate::plonk) struct Evaluated<C: CurveAffine> {
 }
 
 impl<C: CurveAffine> Argument<C> {
-    pub(in crate::plonk) fn commit<E: EncodedChallenge<C>, T: TranscriptWrite<C, E>>(
+    pub(in crate::plonk) fn commit<E: EncodedChallenge<C>, R: RngCore, T: TranscriptWrite<C, E>>(
         params: &Params<C>,
         domain: &EvaluationDomain<C::Scalar>,
+        mut rng: R,
         transcript: &mut T,
     ) -> Result<Committed<C>, Error> {
         // Sample a random polynomial of degree n - 1
         let mut random_poly = domain.empty_coeff();
         for coeff in random_poly.iter_mut() {
-            *coeff = C::Scalar::rand();
+            *coeff = C::Scalar::random(&mut rng);
         }
         // Sample a random blinding factor
-        let random_blind = Blind(C::Scalar::rand());
+        let random_blind = Blind(C::Scalar::random(rng));
 
         // Commit
         let c = params.commit(&random_poly, random_blind).to_affine();
@@ -58,12 +60,17 @@ impl<C: CurveAffine> Argument<C> {
 }
 
 impl<C: CurveAffine> Committed<C> {
-    pub(in crate::plonk) fn construct<E: EncodedChallenge<C>, T: TranscriptWrite<C, E>>(
+    pub(in crate::plonk) fn construct<
+        E: EncodedChallenge<C>,
+        R: RngCore,
+        T: TranscriptWrite<C, E>,
+    >(
         self,
         params: &Params<C>,
         domain: &EvaluationDomain<C::Scalar>,
         expressions: impl Iterator<Item = Polynomial<C::Scalar, ExtendedLagrangeCoeff>>,
         y: ChallengeY<C>,
+        mut rng: R,
         transcript: &mut T,
     ) -> Result<Constructed<C>, Error> {
         // Evaluate the h(X) polynomial's constraint system expressions for the constraints provided
@@ -81,7 +88,10 @@ impl<C: CurveAffine> Committed<C> {
             .map(|v| domain.coeff_from_vec(v.to_vec()))
             .collect::<Vec<_>>();
         drop(h_poly);
-        let h_blinds: Vec<_> = h_pieces.iter().map(|_| Blind(C::Scalar::rand())).collect();
+        let h_blinds: Vec<_> = h_pieces
+            .iter()
+            .map(|_| Blind(C::Scalar::random(&mut rng)))
+            .collect();
 
         // Compute commitments to each h(X) piece
         let h_commitments_projective: Vec<_> = h_pieces
diff --git a/src/poly/commitment.rs b/src/poly/commitment.rs
index d9e7cba2..30d164ef 100644
--- a/src/poly/commitment.rs
+++ b/src/poly/commitment.rs
@@ -256,6 +256,8 @@ impl<F: FieldExt> MulAssign<F> for Blind<F> {
 fn test_commit_lagrange_epaffine() {
     const K: u32 = 6;
 
+    use rand::rngs::OsRng;
+
     use crate::pasta::{EpAffine, Fq};
     let params = Params::<EpAffine>::new(K);
     let domain = super::EvaluationDomain::new(1, K);
@@ -268,7 +270,7 @@ fn test_commit_lagrange_epaffine() {
 
     let b = domain.lagrange_to_coeff(a.clone());
 
-    let alpha = Blind(Fq::rand());
+    let alpha = Blind(Fq::random(OsRng));
 
     assert_eq!(params.commit(&b, alpha), params.commit_lagrange(&a, alpha));
 }
@@ -277,6 +279,8 @@ fn test_commit_lagrange_epaffine() {
 fn test_commit_lagrange_eqaffine() {
     const K: u32 = 6;
 
+    use rand::rngs::OsRng;
+
     use crate::pasta::{EqAffine, Fp};
     let params = Params::<EqAffine>::new(K);
     let domain = super::EvaluationDomain::new(1, K);
@@ -289,7 +293,7 @@ fn test_commit_lagrange_eqaffine() {
 
     let b = domain.lagrange_to_coeff(a.clone());
 
-    let alpha = Blind(Fp::rand());
+    let alpha = Blind(Fp::random(OsRng));
 
     assert_eq!(params.commit(&b, alpha), params.commit_lagrange(&a, alpha));
 }
@@ -299,6 +303,7 @@ fn test_opening_proof() {
     const K: u32 = 6;
 
     use ff::Field;
+    use rand::rngs::OsRng;
 
     use super::{
         commitment::{Blind, Params},
@@ -310,6 +315,8 @@ fn test_opening_proof() {
         Blake2bRead, Blake2bWrite, Challenge255, Transcript, TranscriptRead, TranscriptWrite,
     };
 
+    let rng = OsRng;
+
     let params = Params::<EpAffine>::new(K);
     let mut params_buffer = vec![];
     params.write(&mut params_buffer).unwrap();
@@ -323,7 +330,7 @@ fn test_opening_proof() {
         *a = Fq::from(i as u64);
     }
 
-    let blind = Blind(Fq::rand());
+    let blind = Blind(Fq::random(rng));
 
     let p = params.commit(&px, blind).to_affine();
 
@@ -335,7 +342,7 @@ fn test_opening_proof() {
     transcript.write_scalar(v).unwrap();
 
     let (proof, ch_prover) = {
-        create_proof(&params, &mut transcript, &px, blind, *x).unwrap();
+        create_proof(&params, rng, &mut transcript, &px, blind, *x).unwrap();
         let ch_prover = transcript.squeeze_challenge();
         (transcript.finalize(), ch_prover)
     };
diff --git a/src/poly/commitment/prover.rs b/src/poly/commitment/prover.rs
index 211b60fe..b393747e 100644
--- a/src/poly/commitment/prover.rs
+++ b/src/poly/commitment/prover.rs
@@ -1,4 +1,5 @@
 use ff::Field;
+use rand::RngCore;
 
 use super::super::{Coeff, Polynomial};
 use super::{Blind, Params};
@@ -23,8 +24,14 @@ use std::io;
 /// opening v, and the point x. It's probably also nice for the transcript
 /// to have seen the elliptic curve description and the URS, if you want to
 /// be rigorous.
-pub fn create_proof<C: CurveAffine, E: EncodedChallenge<C>, T: TranscriptWrite<C, E>>(
+pub fn create_proof<
+    C: CurveAffine,
+    E: EncodedChallenge<C>,
+    R: RngCore,
+    T: TranscriptWrite<C, E>,
+>(
     params: &Params<C>,
+    mut rng: R,
     transcript: &mut T,
     px: &Polynomial<C::Scalar, Coeff>,
     blind: Blind<C::Scalar>,
@@ -37,14 +44,14 @@ pub fn create_proof<C: CurveAffine, E: EncodedChallenge<C>, T: TranscriptWrite<C
     // by setting all coefficients to random values.
     let mut s_poly = (*px).clone();
     for coeff in s_poly.iter_mut() {
-        *coeff = C::Scalar::rand();
+        *coeff = C::Scalar::random(&mut rng);
     }
     // Evaluate the random polynomial at x
     let v_prime = eval_polynomial(&s_poly[..], x);
     // Subtract constant coefficient to get a random polynomial with a root at x
     s_poly[0] = s_poly[0] - &v_prime;
     // And sample a random blind
-    let s_poly_blind = Blind(C::Scalar::rand());
+    let s_poly_blind = Blind(C::Scalar::random(&mut rng));
 
     // Write a commitment to the random polynomial to the transcript
     let s_poly_commitment = params.commit(&s_poly, s_poly_blind).to_affine();
@@ -99,8 +106,8 @@ pub fn create_proof<C: CurveAffine, E: EncodedChallenge<C>, T: TranscriptWrite<C
         let r = best_multiexp(&a[0..half], &g[half..]);
         let value_l = compute_inner_product(&a[half..], &b[0..half]);
         let value_r = compute_inner_product(&a[0..half], &b[half..]);
-        let l_randomness = C::Scalar::rand();
-        let r_randomness = C::Scalar::rand();
+        let l_randomness = C::Scalar::random(&mut rng);
+        let r_randomness = C::Scalar::random(&mut rng);
         let l = l + &best_multiexp(&[value_l * &z, l_randomness], &[params.u, params.h]);
         let r = r + &best_multiexp(&[value_r * &z, r_randomness], &[params.u, params.h]);
         let l = l.to_affine();
diff --git a/src/poly/domain.rs b/src/poly/domain.rs
index 8f449359..fe3e58ba 100644
--- a/src/poly/domain.rs
+++ b/src/poly/domain.rs
@@ -554,14 +554,18 @@ pub struct PinnedEvaluationDomain<'a, G: Group> {
 
 #[test]
 fn test_rotate() {
+    use rand::rngs::OsRng;
+
     use crate::arithmetic::eval_polynomial;
     use crate::pasta::pallas::Scalar;
+
     let domain = EvaluationDomain::<Scalar>::new(1, 3);
+    let rng = OsRng;
 
     let mut poly = domain.empty_lagrange();
     assert_eq!(poly.len(), 8);
     for value in poly.iter_mut() {
-        *value = Scalar::rand();
+        *value = Scalar::random(rng);
     }
 
     let poly_rotated_cur = poly.rotate(Rotation::cur());
@@ -573,7 +577,7 @@ fn test_rotate() {
     let poly_rotated_next = domain.lagrange_to_coeff(poly_rotated_next);
     let poly_rotated_prev = domain.lagrange_to_coeff(poly_rotated_prev);
 
-    let x = Scalar::rand();
+    let x = Scalar::random(rng);
 
     assert_eq!(
         eval_polynomial(&poly[..], x),
@@ -591,6 +595,8 @@ fn test_rotate() {
 
 #[test]
 fn test_l_i() {
+    use rand::rngs::OsRng;
+
     use crate::arithmetic::{eval_polynomial, lagrange_interpolate};
     use crate::pasta::pallas::Scalar;
     let domain = EvaluationDomain::<Scalar>::new(1, 3);
@@ -607,7 +613,7 @@ fn test_l_i() {
         l.push(l_i);
     }
 
-    let x = Scalar::rand();
+    let x = Scalar::random(OsRng);
     let xn = x.pow(&[8, 0, 0, 0]);
 
     let evaluations = domain.l_i_range(x, xn, -7..=7);
diff --git a/src/poly/multiopen.rs b/src/poly/multiopen.rs
index ae8e27ab..7e860e42 100644
--- a/src/poly/multiopen.rs
+++ b/src/poly/multiopen.rs
@@ -250,6 +250,7 @@ where
 #[test]
 fn test_roundtrip() {
     use group::Curve;
+    use rand::rngs::OsRng;
 
     use super::commitment::{Blind, Params};
     use crate::arithmetic::{eval_polynomial, FieldExt};
@@ -260,6 +261,7 @@ fn test_roundtrip() {
 
     let params: Params<EqAffine> = Params::new(K);
     let domain = EvaluationDomain::new(1, K);
+    let rng = OsRng;
 
     let mut ax = domain.empty_coeff();
     for (i, a) in ax.iter_mut().enumerate() {
@@ -276,14 +278,14 @@ fn test_roundtrip() {
         *a = Fp::from(100 + i as u64);
     }
 
-    let blind = Blind(Fp::rand());
+    let blind = Blind(Fp::random(rng));
 
     let a = params.commit(&ax, blind).to_affine();
     let b = params.commit(&bx, blind).to_affine();
     let c = params.commit(&cx, blind).to_affine();
 
-    let x = Fp::rand();
-    let y = Fp::rand();
+    let x = Fp::random(rng);
+    let y = Fp::random(rng);
     let avx = eval_polynomial(&ax, x);
     let bvx = eval_polynomial(&bx, x);
     let cvy = eval_polynomial(&cx, y);
@@ -291,6 +293,7 @@ fn test_roundtrip() {
     let mut transcript = crate::transcript::Blake2bWrite::<_, _, Challenge255<_>>::init(vec![]);
     create_proof(
         &params,
+        rng,
         &mut transcript,
         std::iter::empty()
             .chain(Some(ProverQuery {
diff --git a/src/poly/multiopen/prover.rs b/src/poly/multiopen/prover.rs
index bea21010..a881f201 100644
--- a/src/poly/multiopen/prover.rs
+++ b/src/poly/multiopen/prover.rs
@@ -12,12 +12,21 @@ use crate::transcript::{EncodedChallenge, TranscriptWrite};
 
 use ff::Field;
 use group::Curve;
+use rand::RngCore;
 use std::io;
 use std::marker::PhantomData;
 
 /// Create a multi-opening proof
-pub fn create_proof<'a, I, C: CurveAffine, E: EncodedChallenge<C>, T: TranscriptWrite<C, E>>(
+pub fn create_proof<
+    'a,
+    I,
+    C: CurveAffine,
+    E: EncodedChallenge<C>,
+    R: RngCore,
+    T: TranscriptWrite<C, E>,
+>(
     params: &Params<C>,
+    mut rng: R,
     transcript: &mut T,
     queries: I,
 ) -> io::Result<()>
@@ -78,7 +87,7 @@ where
         })
         .unwrap();
 
-    let f_blind = Blind(C::Scalar::rand());
+    let f_blind = Blind(C::Scalar::random(&mut rng));
     let f_commitment = params.commit(&f_poly, f_blind).to_affine();
 
     transcript.write_point(f_commitment)?;
@@ -106,7 +115,7 @@ where
         },
     );
 
-    commitment::create_proof(params, transcript, &f_poly, f_blind_try, *x_3)
+    commitment::create_proof(params, rng, transcript, &f_poly, f_blind_try, *x_3)
 }
 
 #[doc(hidden)]
diff --git a/src/poly/multiopen/verifier.rs b/src/poly/multiopen/verifier.rs
index ea96a0b8..eec80e51 100644
--- a/src/poly/multiopen/verifier.rs
+++ b/src/poly/multiopen/verifier.rs
@@ -1,4 +1,5 @@
 use ff::Field;
+use rand::rngs::OsRng;
 
 use super::super::{
     commitment::{Guard, Params, MSM},
@@ -31,7 +32,7 @@ where
     // Scale the MSM by a random factor to ensure that if the existing MSM
     // has is_zero() == false then this argument won't be able to interfere
     // with it to make it true, with high probability.
-    msm.scale(C::Scalar::rand());
+    msm.scale(C::Scalar::random(OsRng));
 
     // Sample x_1 for compressing openings at the same point sets together
     let x_1: ChallengeX1<_> = transcript.squeeze_challenge_scalar();
diff --git a/tests/plonk_api.rs b/tests/plonk_api.rs
index 9007a8ec..5ba512af 100644
--- a/tests/plonk_api.rs
+++ b/tests/plonk_api.rs
@@ -12,6 +12,7 @@ use halo2::plonk::{
 };
 use halo2::poly::{commitment::Params, Rotation};
 use halo2::transcript::{Blake2bRead, Blake2bWrite, Challenge255};
+use rand::rngs::OsRng;
 use std::marker::PhantomData;
 
 #[test]
@@ -436,6 +437,7 @@ fn plonk_api() {
             &pk,
             &[circuit.clone(), circuit.clone()],
             &[&[&[instance]], &[&[instance]]],
+            OsRng,
             &mut transcript,
         )
         .expect("proof generation should not fail");