diff --git a/src/constants.rs b/src/constants.rs
new file mode 100644
index 0000000..d8601a6
--- /dev/null
+++ b/src/constants.rs
@@ -0,0 +1,2 @@
+pub(crate) const NUM_CHALLENGE_BITS: usize = 128;
+pub(crate) const NUM_HASH_BITS: usize = 250;
diff --git a/src/lib.rs b/src/lib.rs
index 905c837..df7de20 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -3,10 +3,10 @@
 #![allow(clippy::type_complexity)]
 #![deny(missing_docs)]
 
-mod commitments;
-
 pub mod bellperson;
 mod circuit;
+mod commitments;
+mod constants;
 pub mod errors;
 pub mod gadgets;
 pub mod pasta;
@@ -14,14 +14,13 @@ mod poseidon;
 pub mod r1cs;
 pub mod traits;
 
-use std::marker::PhantomData;
-
 use commitments::CompressedCommitment;
 use errors::NovaError;
 use merlin::Transcript;
 use r1cs::{
   R1CSGens, R1CSInstance, R1CSShape, R1CSWitness, RelaxedR1CSInstance, RelaxedR1CSWitness,
 };
+use std::marker::PhantomData;
 use traits::{AppendToTranscriptTrait, ChallengeTrait, Group};
 
 /// A SNARK that holds the proof of a step of an incremental computation
diff --git a/src/poseidon.rs b/src/poseidon.rs
index d745a95..7b208cc 100644
--- a/src/poseidon.rs
+++ b/src/poseidon.rs
@@ -1,5 +1,8 @@
 //! Poseidon Constants and Poseidon-based RO used in Nova
-use crate::traits::{HashFuncConstantsTrait, HashFuncTrait};
+use super::{
+  constants::{NUM_CHALLENGE_BITS, NUM_HASH_BITS},
+  traits::{HashFuncConstantsTrait, HashFuncTrait},
+};
 use bellperson::{
   gadgets::{
     boolean::{AllocatedBit, Boolean},
@@ -102,11 +105,11 @@ where
   #[allow(dead_code)]
   fn get_challenge(&self) -> Scalar {
     let hash = self.hash_inner();
-    // Only keep 128 bits
+    // Only keep NUM_CHALLENGE_BITS bits
     let bits = hash.to_le_bits();
     let mut res = Scalar::zero();
     let mut coeff = Scalar::one();
-    for bit in bits[0..128].into_iter() {
+    for bit in bits[0..NUM_CHALLENGE_BITS].into_iter() {
       if *bit {
         res += coeff;
       }
@@ -118,11 +121,11 @@ where
   #[allow(dead_code)]
   fn get_hash(&self) -> Scalar {
     let hash = self.hash_inner();
-    // Only keep 250 bits
+    // Only keep NUM_HASH_BITS bits
     let bits = hash.to_le_bits();
     let mut res = Scalar::zero();
     let mut coeff = Scalar::one();
-    for bit in bits[0..250].into_iter() {
+    for bit in bits[0..NUM_HASH_BITS].into_iter() {
       if *bit {
         res += coeff;
       }
@@ -204,8 +207,7 @@ where
     CS: ConstraintSystem<Scalar>,
   {
     let bits = self.hash_inner(cs.namespace(|| "hash"))?;
-    // Only keep 128 bits
-    Ok(bits[..128].into())
+    Ok(bits[..NUM_CHALLENGE_BITS].into())
   }
 
   #[allow(dead_code)]
@@ -214,8 +216,7 @@ where
     CS: ConstraintSystem<Scalar>,
   {
     let bits = self.hash_inner(cs.namespace(|| "hash"))?;
-    // Only keep 250 bits
-    Ok(bits[..250].into())
+    Ok(bits[..NUM_HASH_BITS].into())
   }
 }
 
diff --git a/src/r1cs.rs b/src/r1cs.rs
index 5e03825..3564127 100644
--- a/src/r1cs.rs
+++ b/src/r1cs.rs
@@ -2,6 +2,7 @@
 #![allow(clippy::type_complexity)]
 use super::{
   commitments::{CommitGens, CommitTrait, Commitment, CompressedCommitment},
+  constants::NUM_HASH_BITS,
   errors::NovaError,
   traits::{AppendToTranscriptTrait, Group},
 };
@@ -11,6 +12,7 @@ use itertools::concat;
 use merlin::Transcript;
 use rayon::prelude::*;
 use serde::{Deserialize, Serialize};
+use sha3::{Digest, Sha3_256};
 
 /// Public parameters for a given R1CS
 pub struct R1CSGens<G: Group> {
@@ -328,10 +330,37 @@ impl<G: Group> AppendToTranscriptTrait for R1CSShape<G> {
         .collect(),
     };
 
+    // obtain a vector of bytes representing the R1CS shape
     let mut encoder = ZlibEncoder::new(Vec::new(), Compression::default());
     bincode::serialize_into(&mut encoder, &shape_serialized).unwrap();
     let shape_bytes = encoder.finish().unwrap();
-    transcript.append_message(b"R1CSShape", &shape_bytes);
+
+    // convert shape_bytes into a short digest
+    let mut hasher = Sha3_256::new();
+    hasher.input(&shape_bytes);
+    let shape_digest = hasher.result();
+
+    let shape_digest_trun = {
+      // truncate the digest to 250 bits
+      let bv = (0..NUM_HASH_BITS).map(|i| {
+        let (byte_pos, bit_pos) = (i / 8, i % 8);
+        let bit = (shape_digest[byte_pos] >> bit_pos) & 1;
+        bit == 1
+      });
+
+      // turn the bit vector into a scalar
+      let mut res = G::Scalar::zero();
+      let mut coeff = G::Scalar::one();
+      for bit in bv {
+        if bit {
+          res += coeff;
+        }
+        coeff += coeff;
+      }
+      res
+    };
+
+    shape_digest_trun.append_to_transcript(b"R1CSShape", transcript);
   }
 }