diff --git a/kimchi/src/circuits/constraints.rs b/kimchi/src/circuits/constraints.rs
index f8f2f20555..0e9d61faeb 100644
--- a/kimchi/src/circuits/constraints.rs
+++ b/kimchi/src/circuits/constraints.rs
@@ -639,6 +639,22 @@ impl<F: PrimeField> ConstraintSystem<F> {
     }
 }
 
+/// The default number of chunks in a circuit is one (< 2^16 rows)
+pub const NUM_CHUNKS_BY_DEFAULT: usize = 1;
+
+/// The number of rows required for zero knowledge in circuits with one single chunk
+pub const ZK_ROWS_BY_DEFAULT: u64 = 3;
+
+/// This function computes a strict lower bound in the number of rows required
+/// for zero knowledge in circuits with `num_chunks` chunks. This means that at
+/// least one needs 1 more row than the result of this function to achieve zero
+/// knowledge.
+/// Example:
+///   for 1 chunk, this function returns 2, but at least 3 rows are needed
+/// Note:
+///   the number of zero knowledge rows is usually computed across the codebase
+///   as the formula `(16 * num_chunks + 5) / 7`, which is precisely the formula
+///   in this function plus one.
 pub fn zk_rows_strict_lower_bound(num_chunks: usize) -> usize {
     (2 * (PERMUTS + 1) * num_chunks - 2) / PERMUTS
 }
diff --git a/kimchi/src/prover.rs b/kimchi/src/prover.rs
index 14e043be07..95221b23bc 100644
--- a/kimchi/src/prover.rs
+++ b/kimchi/src/prover.rs
@@ -210,9 +210,17 @@ where
             .ok_or(ProverError::NoRoomForZkInWitness)?;
 
         let zero_knowledge_limit = zk_rows_strict_lower_bound(num_chunks);
-        if (index.cs.zk_rows as usize) < zero_knowledge_limit {
+        // Because the lower bound is strict, the result of the function above
+        // is not a sufficient number of zero knowledge rows, so the error must
+        // be raised anytime the number of zero knowledge rows is not greater
+        // than the strict lower bound.
+        // Example:
+        //   for 1 chunk, `zero_knowledge_limit` is 2, and we need at least 3,
+        //   thus the error should be raised and the message should say that the
+        //   expected number of zero knowledge rows is 3 (hence the + 1).
+        if (index.cs.zk_rows as usize) <= zero_knowledge_limit {
             return Err(ProverError::NotZeroKnowledge(
-                zero_knowledge_limit,
+                zero_knowledge_limit + 1,
                 index.cs.zk_rows as usize,
             ));
         }