diff --git a/evm/src/cpu/bootstrap_kernel.rs b/evm/src/cpu/bootstrap_kernel.rs
index 2d03b3eff9..d1bac762ea 100644
--- a/evm/src/cpu/bootstrap_kernel.rs
+++ b/evm/src/cpu/bootstrap_kernel.rs
@@ -72,13 +72,14 @@ pub(crate) fn eval_bootstrap_kernel_packed<F: Field, P: PackedField<Scalar = F>>
     next_values: &CpuColumnsView<P>,
     yield_constr: &mut ConstraintConsumer<P>,
 ) {
-    // IS_BOOTSTRAP_KERNEL must have an init value of 1, a final value of 0, and a delta in {0, -1}.
+    // IS_BOOTSTRAP_KERNEL must have an init value of 1, a final value of 0,
+    // and a delta = current.is_bootstrap - next.is_bootstrap in {0, 1}.
     let local_is_bootstrap = local_values.is_bootstrap_kernel;
     let next_is_bootstrap = next_values.is_bootstrap_kernel;
     yield_constr.constraint_first_row(local_is_bootstrap - P::ONES);
     yield_constr.constraint_last_row(local_is_bootstrap);
-    let delta_is_bootstrap = next_is_bootstrap - local_is_bootstrap;
-    yield_constr.constraint_transition(delta_is_bootstrap * (delta_is_bootstrap + P::ONES));
+    let delta_is_bootstrap = local_is_bootstrap - next_is_bootstrap;
+    yield_constr.constraint_transition(delta_is_bootstrap * (delta_is_bootstrap - P::ONES));
 
     // If this is a bootloading row and the i'th memory channel is used, it must have the right
     // address, name context = 0, segment = Code, virt = clock * NUM_GP_CHANNELS + i.
@@ -110,6 +111,18 @@ pub(crate) fn eval_bootstrap_kernel_packed<F: Field, P: PackedField<Scalar = F>>
         let diff = expected - actual;
         yield_constr.constraint_transition(delta_is_bootstrap * diff);
     }
+
+    // In addition, validate `is_keccak_sponge`. It must be binary, and be 1 either at the final
+    // boostrap row or during a KECCAK_GENERAL instruction. At the final CPU row, it should be 0.
+    yield_constr
+        .constraint(local_values.is_keccak_sponge * (local_values.is_keccak_sponge - P::ONES));
+    yield_constr.constraint_transition(
+        local_values.is_keccak_sponge
+            - (delta_is_bootstrap
+                + local_values.op.jumpdest_keccak_general
+                    * (P::ONES - local_values.opcode_bits[1])),
+    );
+    yield_constr.constraint_last_row(local_values.is_keccak_sponge);
 }
 
 /// Circuit version of `eval_bootstrap_kernel_packed`.
@@ -122,15 +135,16 @@ pub(crate) fn eval_bootstrap_kernel_ext_circuit<F: RichField + Extendable<D>, co
 ) {
     let one = builder.one_extension();
 
-    // IS_BOOTSTRAP_KERNEL must have an init value of 1, a final value of 0, and a delta in {0, -1}.
+    // IS_BOOTSTRAP_KERNEL must have an init value of 1, a final value of 0,
+    // and a delta = current.is_bootstrap - next.is_bootstrap in {0, 1}.
     let local_is_bootstrap = local_values.is_bootstrap_kernel;
     let next_is_bootstrap = next_values.is_bootstrap_kernel;
     let constraint = builder.sub_extension(local_is_bootstrap, one);
     yield_constr.constraint_first_row(builder, constraint);
     yield_constr.constraint_last_row(builder, local_is_bootstrap);
-    let delta_is_bootstrap = builder.sub_extension(next_is_bootstrap, local_is_bootstrap);
+    let delta_is_bootstrap = builder.sub_extension(local_is_bootstrap, next_is_bootstrap);
     let constraint =
-        builder.mul_add_extension(delta_is_bootstrap, delta_is_bootstrap, delta_is_bootstrap);
+        builder.mul_sub_extension(delta_is_bootstrap, delta_is_bootstrap, delta_is_bootstrap);
     yield_constr.constraint_transition(builder, constraint);
 
     // If this is a bootloading row and the i'th memory channel is used, it must have the right
@@ -182,4 +196,30 @@ pub(crate) fn eval_bootstrap_kernel_ext_circuit<F: RichField + Extendable<D>, co
         let constraint = builder.mul_extension(delta_is_bootstrap, diff);
         yield_constr.constraint_transition(builder, constraint);
     }
+
+    // In addition, validate `is_keccak_sponge`. It must be binary, and be 1 either at the final
+    // boostrap row or during a KECCAK_GENERAL instruction. At the final CPU row, it should be 0.
+    {
+        let constr = builder.mul_sub_extension(
+            local_values.is_keccak_sponge,
+            local_values.is_keccak_sponge,
+            local_values.is_keccak_sponge,
+        );
+        yield_constr.constraint(builder, constr);
+    }
+    {
+        let minus_is_keccak_general = builder.mul_sub_extension(
+            local_values.op.jumpdest_keccak_general,
+            local_values.opcode_bits[1],
+            local_values.op.jumpdest_keccak_general,
+        );
+        let computed_is_keccak_sponge =
+            builder.sub_extension(delta_is_bootstrap, minus_is_keccak_general);
+        let constr =
+            builder.sub_extension(local_values.is_keccak_sponge, computed_is_keccak_sponge);
+        yield_constr.constraint_transition(builder, constr);
+    }
+    {
+        yield_constr.constraint_last_row(builder, local_values.is_keccak_sponge);
+    }
 }