diff --git a/src/plonk.rs b/src/plonk.rs
index b0dc869..e62409f 100644
--- a/src/plonk.rs
+++ b/src/plonk.rs
@@ -345,6 +345,10 @@ fn test_proving() {
         let proof = Proof::create::<DummyHash<Fq>, DummyHash<Fp>, _>(&params, &srs, &circuit)
             .expect("proof generation should not fail");
 
-        assert!(proof.verify::<DummyHash<Fq>, DummyHash<Fp>>(&params, &srs));
+        let msm_default = params.empty_msm();
+        let msm = proof
+            .verify::<DummyHash<Fq>, DummyHash<Fp>>(&params, &srs, msm_default)
+            .unwrap();
+        assert!(msm.is_zero())
     }
 }
diff --git a/src/plonk/verifier.rs b/src/plonk/verifier.rs
index 9c3adca..5197acd 100644
--- a/src/plonk/verifier.rs
+++ b/src/plonk/verifier.rs
@@ -1,15 +1,19 @@
-use super::{hash_point, Proof, SRS};
+use super::{hash_point, Error, Proof, SRS};
 use crate::arithmetic::{get_challenge_scalar, Challenge, Curve, CurveAffine, Field};
-use crate::poly::{commitment::Params, Rotation};
+use crate::poly::{
+    commitment::{Params, MSM},
+    Rotation,
+};
 use crate::transcript::Hasher;
 
-impl<C: CurveAffine> Proof<C> {
+impl<'a, C: CurveAffine> Proof<C> {
     /// Returns a boolean indicating whether or not the proof is valid
     pub fn verify<HBase: Hasher<C::Base>, HScalar: Hasher<C::Scalar>>(
         &self,
-        params: &Params<C>,
+        params: &'a Params<C>,
         srs: &SRS<C>,
-    ) -> bool {
+        msm: MSM<'a, C>,
+    ) -> Result<MSM<'a, C>, Error> {
         // Create a transcript for obtaining Fiat-Shamir challenges.
         let mut transcript = HBase::init(C::Base::one());
 
@@ -133,7 +137,7 @@ impl<C: CurveAffine> Proof<C> {
         }
 
         if h_eval != (expected_h_eval * &(x_3n - &C::Scalar::one())) {
-            return false;
+            return Err(Error::ConstraintSystemFailure);
         }
 
         // We are now convinced the circuit is satisfied so long as the
@@ -261,12 +265,20 @@ impl<C: CurveAffine> Proof<C> {
         }
 
         // Verify the opening proof
-        self.opening.verify(
-            params,
-            &mut transcript,
-            x_6,
-            &f_commitment.to_affine(),
-            f_eval,
-        )
+        let guard = self
+            .opening
+            .verify(
+                params,
+                msm,
+                &mut transcript,
+                x_6,
+                &f_commitment.to_affine(),
+                f_eval,
+            )
+            .unwrap();
+
+        let msm_challenges = guard.use_challenges();
+
+        Ok(msm_challenges)
     }
 }
diff --git a/src/poly.rs b/src/poly.rs
index eef5356..07f32e3 100644
--- a/src/poly.rs
+++ b/src/poly.rs
@@ -13,6 +13,14 @@ mod domain;
 
 pub use domain::*;
 
+/// This is an error that could occur during proving or circuit synthesis.
+// TODO: these errors need to be cleaned up
+#[derive(Debug)]
+pub enum Error {
+    /// OpeningProof is not well-formed
+    OpeningError,
+}
+
 /// The basis over which a polynomial is described.
 pub trait Basis: Clone + Debug + Send + Sync {}
 
diff --git a/src/poly/commitment.rs b/src/poly/commitment.rs
index 1a98548..eb24af9 100644
--- a/src/poly/commitment.rs
+++ b/src/poly/commitment.rs
@@ -4,7 +4,9 @@
 //! [halo]: https://eprint.iacr.org/2019/1021
 
 use super::{Coeff, LagrangeCoeff, Polynomial};
-use crate::arithmetic::{best_fft, best_multiexp, parallelize, Curve, CurveAffine, Field};
+use crate::arithmetic::{
+    best_fft, best_multiexp, parallelize, Challenge, Curve, CurveAffine, Field,
+};
 use crate::transcript::Hasher;
 use std::ops::{Add, AddAssign, Mul, MulAssign};
 
@@ -21,6 +23,96 @@ pub struct OpeningProof<C: CurveAffine> {
     z2: C::Scalar,
 }
 
+/// An accumulator instance consisting of an evaluation claim and a proof.
+#[derive(Debug, Clone)]
+pub struct Accumulator<C: CurveAffine> {
+    /// The claimed output of the linear-time polycommit opening protocol
+    pub g: C,
+
+    /// A vector of 128-bit challenges sampled by the verifier, to be used in
+    /// computing g.
+    pub challenges_sq_packed: Vec<Challenge>,
+}
+
+/// A multiscalar multiplication in the polynomial commitment scheme
+#[derive(Debug, Clone)]
+pub struct MSM<'a, C: CurveAffine> {
+    params: &'a Params<C>,
+    g_scalars: Option<Vec<C::Scalar>>,
+    h_scalar: Option<C::Scalar>,
+    other_scalars: Vec<C::Scalar>,
+    other_bases: Vec<C>,
+}
+
+impl<'a, C: CurveAffine> MSM<'a, C> {
+    /// Add arbitrary term (the scalar and the point)
+    pub fn add_term(&mut self, scalar: C::Scalar, point: C) {
+        &self.other_scalars.push(scalar);
+        &self.other_bases.push(point);
+    }
+
+    /// Add a vector of scalars to `g_scalars`. This function will panic if the
+    /// caller provides a slice of scalars that is not of length `params.n`.
+    // TODO: parallelize
+    pub fn add_to_g(&mut self, scalars: &[C::Scalar]) {
+        assert_eq!(scalars.len(), self.params.n as usize);
+        if let Some(g_scalars) = &mut self.g_scalars {
+            for (g_scalar, scalar) in g_scalars.iter_mut().zip(scalars.iter()) {
+                *g_scalar += &scalar;
+            }
+        } else {
+            self.g_scalars = Some(scalars.to_vec());
+        }
+    }
+
+    /// Add term to h
+    pub fn add_to_h(&mut self, scalar: C::Scalar) {
+        self.h_scalar = self.h_scalar.map_or(Some(scalar), |a| Some(a + &scalar));
+    }
+
+    /// Scale all scalars in the MSM by some scaling factor
+    // TODO: parallelize
+    pub fn scale(&mut self, factor: C::Scalar) {
+        if let Some(g_scalars) = &mut self.g_scalars {
+            for g_scalar in g_scalars.iter_mut() {
+                *g_scalar *= &factor;
+            }
+        }
+
+        // TODO: parallelize
+        for other_scalar in self.other_scalars.iter_mut() {
+            *other_scalar *= &factor;
+        }
+        self.h_scalar = self.h_scalar.map(|a| a * &factor);
+    }
+
+    /// Perform multiexp and check that it results in zero
+    pub fn is_zero(self) -> bool {
+        let len = self.g_scalars.as_ref().map(|v| v.len()).unwrap_or(0)
+            + self.h_scalar.map(|_| 1).unwrap_or(0)
+            + self.other_scalars.len();
+        let mut scalars: Vec<C::Scalar> = Vec::with_capacity(len);
+        let mut bases: Vec<C> = Vec::with_capacity(len);
+
+        scalars.extend(&self.other_scalars);
+        bases.extend(&self.other_bases);
+
+        if let Some(h_scalar) = self.h_scalar {
+            scalars.push(h_scalar);
+            bases.push(self.params.h);
+        }
+
+        if let Some(g_scalars) = &self.g_scalars {
+            scalars.extend(g_scalars);
+            bases.extend(self.params.g.iter());
+        }
+
+        assert_eq!(scalars.len(), len);
+
+        bool::from(best_multiexp(&scalars, &bases).is_zero())
+    }
+}
+
 /// These are the public parameters for the polynomial commitment scheme.
 #[derive(Debug)]
 pub struct Params<C: CurveAffine> {
@@ -152,6 +244,63 @@ impl<C: CurveAffine> Params<C> {
 
         best_multiexp::<C>(&tmp_scalars, &tmp_bases)
     }
+
+    /// Generates an empty multiscalar multiplication struct using the
+    /// appropriate params.
+    pub fn empty_msm(&self) -> MSM<C> {
+        let g_scalars = None;
+        let h_scalar = None;
+        let other_scalars = vec![];
+        let other_bases = vec![];
+
+        MSM {
+            params: &self,
+            g_scalars,
+            h_scalar,
+            other_scalars,
+            other_bases,
+        }
+    }
+}
+
+/// A guard returned by the verifier
+#[derive(Debug, Clone)]
+pub struct Guard<'a, C: CurveAffine> {
+    msm: MSM<'a, C>,
+    neg_z1: C::Scalar,
+    allinv: C::Scalar,
+    challenges_sq: Vec<C::Scalar>,
+    challenges_sq_packed: Vec<Challenge>,
+}
+
+impl<'a, C: CurveAffine> Guard<'a, C> {
+    /// Lets caller supply the challenges and obtain an MSM with updated
+    /// scalars and points.
+    pub fn use_challenges(mut self) -> MSM<'a, C> {
+        let s = compute_s(&self.challenges_sq, self.allinv * &self.neg_z1);
+        self.msm.add_to_g(&s);
+
+        self.msm
+    }
+
+    /// Lets caller supply the purported G point and simply appends it to
+    /// return an updated MSM.
+    pub fn use_g(mut self, g: C) -> (MSM<'a, C>, Accumulator<C>) {
+        &self.msm.add_term(self.neg_z1, g);
+
+        let accumulator = Accumulator {
+            g,
+            challenges_sq_packed: self.challenges_sq_packed,
+        };
+
+        (self.msm, accumulator)
+    }
+
+    /// Computes the g value when given a potential scalar as input.
+    pub fn compute_g(&self) -> C {
+        let s = compute_s(&self.challenges_sq, self.allinv);
+        best_multiexp(&s, &self.msm.params.g).to_affine()
+    }
 }
 
 /// Wrapper type around a blinding factor.
@@ -265,7 +414,7 @@ fn test_opening_proof() {
     transcript.absorb(Fp::from_bytes(&v.to_bytes()).unwrap()); // unlikely to fail since p ~ q
 
     loop {
-        let mut transcript_dup = transcript.clone();
+        let transcript_dup = transcript.clone();
 
         let opening_proof = OpeningProof::create(&params, &mut transcript, &px, blind, x);
         if opening_proof.is_err() {
@@ -273,8 +422,63 @@ fn test_opening_proof() {
             transcript.absorb(Field::one());
         } else {
             let opening_proof = opening_proof.unwrap();
-            assert!(opening_proof.verify(&params, &mut transcript_dup, x, &p, v));
+            // Verify the opening proof
+            let guard = opening_proof
+                .verify(
+                    &params,
+                    params.empty_msm(),
+                    &mut transcript_dup.clone(),
+                    x,
+                    &p,
+                    v,
+                )
+                .unwrap();
+
+            // Test guard behavior prior to checking another proof
+            {
+                // Test use_challenges()
+                let msm_challenges = guard.clone().use_challenges();
+                assert!(msm_challenges.is_zero());
+
+                // Test use_g()
+                let g = guard.compute_g();
+                let (msm_g, _accumulator) = guard.clone().use_g(g);
+                assert!(msm_g.is_zero());
+            }
+
+            // Check another proof to populate `msm.g_scalars`
+            let msm = guard.use_challenges();
+            let guard = opening_proof
+                .verify(&params, msm, &mut transcript_dup.clone(), x, &p, v)
+                .unwrap();
+
+            // Test use_challenges()
+            let msm_challenges = guard.clone().use_challenges();
+            assert!(msm_challenges.is_zero());
+
+            // Test use_g()
+            let g = guard.compute_g();
+            let (msm_g, _accumulator) = guard.clone().use_g(g);
+            assert!(msm_g.is_zero());
+
             break;
         }
     }
 }
+
+// TODO: parallelize
+fn compute_s<F: Field>(challenges_sq: &[F], allinv: F) -> Vec<F> {
+    let lg_n = challenges_sq.len();
+    let n = 1 << lg_n;
+
+    let mut s = Vec::with_capacity(n);
+    s.push(allinv);
+    for i in 1..n {
+        let lg_i = (32 - 1 - (i as u32).leading_zeros()) as usize;
+        let k = 1 << lg_i;
+        let u_lg_i_sq = challenges_sq[(lg_n - 1) - lg_i];
+        s.push(s[i - k] * u_lg_i_sq);
+    }
+
+    s
+}
diff --git a/src/poly/commitment/verifier.rs b/src/poly/commitment/verifier.rs
index a3d7e4d..2e937f9 100644
--- a/src/poly/commitment/verifier.rs
+++ b/src/poly/commitment/verifier.rs
@@ -1,25 +1,25 @@
-use super::{OpeningProof, Params};
+use super::super::Error;
+use super::{Guard, OpeningProof, Params, MSM};
 use crate::transcript::Hasher;
 
-use crate::arithmetic::{
-    best_multiexp, get_challenge_scalar, Challenge, Curve, CurveAffine, Field,
-};
+use crate::arithmetic::{get_challenge_scalar, Challenge, CurveAffine, Field};
 
 impl<C: CurveAffine> OpeningProof<C> {
     /// Checks to see if an [`OpeningProof`] is valid given the current
     /// `transcript`, and a point `x` that the polynomial commitment `p` opens
     /// purportedly to the value `v`.
-    pub fn verify<H: Hasher<C::Base>>(
+    pub fn verify<'a, H: Hasher<C::Base>>(
         &self,
-        params: &Params<C>,
+        params: &'a Params<C>,
+        mut msm: MSM<'a, C>,
         transcript: &mut H,
         x: C::Scalar,
         p: &C,
         v: C::Scalar,
-    ) -> bool {
+    ) -> Result<Guard<'a, C>, Error> {
         // Check for well-formedness
         if self.rounds.len() != params.k as usize {
-            return false;
+            return Err(Error::OpeningError);
         }
 
         transcript.absorb(C::Base::from_u64(self.fork as u64));
@@ -31,7 +31,7 @@ impl<C: CurveAffine> OpeningProof<C> {
             let u_y2 = u_x.square() * &u_x + &C::b();
             let u_y = u_y2.deterministic_sqrt();
             if u_y.is_none() {
-                return false;
+                return Err(Error::OpeningError);
             }
             let u_y = u_y.unwrap();
 
@@ -45,14 +45,15 @@ impl<C: CurveAffine> OpeningProof<C> {
         let mut challenges = Vec::with_capacity(self.rounds.len());
         let mut challenges_inv = Vec::with_capacity(self.rounds.len());
         let mut challenges_sq = Vec::with_capacity(self.rounds.len());
-        let mut allinv = Field::one();
+        let mut challenges_sq_packed: Vec<Challenge> = Vec::with_capacity(self.rounds.len());
+        let mut allinv = C::Scalar::one();
 
         for round in &self.rounds {
             // Feed L and R into the transcript.
             let l = round.0.get_xy();
             let r = round.1.get_xy();
             if bool::from(l.is_none() | r.is_none()) {
-                return false;
+                return Err(Error::OpeningError);
             }
             let l = l.unwrap();
             let r = r.unwrap();
@@ -66,7 +67,7 @@ impl<C: CurveAffine> OpeningProof<C> {
             let challenge = challenge_sq.deterministic_sqrt();
             if challenge.is_none() {
                 // We didn't sample a square.
-                return false;
+                return Err(Error::OpeningError);
             }
             let challenge = challenge.unwrap();
 
@@ -74,10 +75,10 @@ impl<C: CurveAffine> OpeningProof<C> {
             if bool::from(challenge_inv.is_none()) {
                 // We sampled zero for some reason, unlikely to happen by
                 // chance.
-                return false;
+                return Err(Error::OpeningError);
             }
             let challenge_inv = challenge_inv.unwrap();
-            allinv *= challenge_inv;
+            allinv *= &challenge_inv;
 
             let challenge_sq_inv = challenge_inv.square();
 
@@ -89,11 +90,12 @@ impl<C: CurveAffine> OpeningProof<C> {
             challenges.push(challenge);
             challenges_inv.push(challenge_inv);
             challenges_sq.push(challenge_sq);
+            challenges_sq_packed.push(Challenge(challenge_sq_packed));
         }
 
         let delta = self.delta.get_xy();
         if bool::from(delta.is_none()) {
-            return false;
+            return Err(Error::OpeningError);
         }
         let delta = delta.unwrap();
 
@@ -109,40 +111,45 @@ impl<C: CurveAffine> OpeningProof<C> {
         // [c] P + [c * v] U + [c] sum(L_i * u_i^2) + [c] sum(R_i * u_i^-2) + delta - [z1] G - [z1 * b] U - [z2] H
         // = 0
 
+        // 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. It's a way of keeping the MSM's linearly
+        // independent.
+        msm.scale(C::Scalar::random());
+
         for scalar in &mut extra_scalars {
             *scalar *= &c;
         }
 
+        for (scalar, base) in extra_scalars.iter().zip(extra_bases.iter()) {
+            msm.add_term(*scalar, *base);
+        }
+
         let b = compute_b(x, &challenges, &challenges_inv);
 
         let neg_z1 = -self.z1;
 
         // [c] P
-        extra_bases.push(*p);
-        extra_scalars.push(c);
+        msm.add_term(c, *p);
 
         // [c * v] U - [z1 * b] U
-        extra_bases.push(u);
-        extra_scalars.push((c * &v) + &(neg_z1 * &b));
+        msm.add_term((c * &v) + &(neg_z1 * &b), u);
 
         // delta
-        extra_bases.push(self.delta);
-        extra_scalars.push(Field::one());
+        msm.add_term(Field::one(), self.delta);
 
         // - [z2] H
-        extra_bases.push(params.h);
-        extra_scalars.push(-self.z2);
+        msm.add_to_h(-self.z2);
 
-        // - [z1] G
-        extra_bases.extend(&params.g);
-        let mut s = compute_s(&challenges_sq, allinv);
-        // TODO: parallelize
-        for s in &mut s {
-            *s *= &neg_z1;
-        }
-        extra_scalars.extend(s);
+        let guard = Guard {
+            msm,
+            neg_z1,
+            allinv,
+            challenges_sq,
+            challenges_sq_packed,
+        };
 
-        bool::from(best_multiexp(&extra_scalars, &extra_bases).is_zero())
+        Ok(guard)
     }
 }
 
@@ -160,20 +167,3 @@ fn compute_b<F: Field>(x: F, challenges: &[F], challenges_inv: &[F]) -> F {
             )
     }
 }
-
-// TODO: parallelize
-fn compute_s<F: Field>(challenges_sq: &[F], allinv: F) -> Vec<F> {
-    let lg_n = challenges_sq.len();
-    let n = 1 << lg_n;
-
-    let mut s = Vec::with_capacity(n);
-    s.push(allinv);
-    for i in 1..n {
-        let lg_i = (32 - 1 - (i as u32).leading_zeros()) as usize;
-        let k = 1 << lg_i;
-        let u_lg_i_sq = challenges_sq[(lg_n - 1) - lg_i];
-        s.push(s[i - k] * u_lg_i_sq);
-    }
-
-    s
-}