diff --git a/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/ProductSIntList.java b/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/ProductSIntList.java
index 6860b90e5..f88be1fc0 100644
--- a/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/ProductSIntList.java
+++ b/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/ProductSIntList.java
@@ -7,46 +7,58 @@
 import dk.alexandra.fresco.framework.value.SInt;
 import java.util.ArrayList;
 import java.util.List;
+import java.util.Objects;
 
 /**
- * ComputationBuilder for multiplying a list of SInts.
+ * Builder for a {@link Computation}s that computes the product of a list of {@link SInts}
+ * secret-shared values.
+ *
+ * <p>Empty lists are allowed, and will always produce a value of {@code 1}.
  */
 public class ProductSIntList implements Computation<SInt, ProtocolBuilderNumeric> {
 
   private final List<DRes<SInt>> input;
 
   /**
-   * Creates a new ProductSIntList.
+   * Creates a new {@link ProductSIntList}.
    *
-   * @param list the list to sum
+   * @param list the list to sum. Not nullable.
    */
   public ProductSIntList(List<DRes<SInt>> list) {
-    input = list;
+    input = Objects.requireNonNull(list);
   }
 
   @Override
   public DRes<SInt> buildComputation(ProtocolBuilderNumeric iterationBuilder) {
-    return iterationBuilder.seq(seq ->
-        () -> input
-    ).whileLoop(
-        (inputs) -> inputs.size() > 1,
-        (seq, inputs) -> seq.par(parallel -> {
-          List<DRes<SInt>> out = new ArrayList<>();
-          Numeric numericBuilder = parallel.numeric();
-          DRes<SInt> left = null;
-          for (DRes<SInt> input1 : inputs) {
-            if (left == null) {
-              left = input1;
-            } else {
-              out.add(numericBuilder.mult(left, input1));
-              left = null;
-            }
-          }
-          if (left != null) {
-            out.add(left);
-          }
-          return () -> out;
-        })
-    ).seq((builder, currentInput) -> currentInput.get(0));
+    // Fast case if there is nothing to compute.
+    if (input.isEmpty()) {
+      return iterationBuilder.seq(seq -> seq.numeric().known(1));
+    }
+
+    // Slow case when there are elements to compute on.
+    return iterationBuilder
+        .seq(seq -> () -> input)
+        .whileLoop(
+            (inputs) -> inputs.size() > 1,
+            (seq, inputs) ->
+                seq.par(
+                    parallel -> {
+                      List<DRes<SInt>> out = new ArrayList<>();
+                      Numeric numericBuilder = parallel.numeric();
+                      DRes<SInt> left = null;
+                      for (DRes<SInt> input1 : inputs) {
+                        if (left == null) {
+                          left = input1;
+                        } else {
+                          out.add(numericBuilder.mult(left, input1));
+                          left = null;
+                        }
+                      }
+                      if (left != null) {
+                        out.add(left);
+                      }
+                      return () -> out;
+                    }))
+        .seq((builder, currentInput) -> currentInput.get(0));
   }
 }
diff --git a/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/SumSIntList.java b/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/SumSIntList.java
index 9092d413d..b03b8f826 100644
--- a/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/SumSIntList.java
+++ b/lib/common/src/main/java/dk/alexandra/fresco/lib/common/math/integer/SumSIntList.java
@@ -7,46 +7,57 @@
 import dk.alexandra.fresco.framework.value.SInt;
 import java.util.ArrayList;
 import java.util.List;
+import java.util.Objects;
 
 /**
- * ComputationBuilder for summing a list of SInts.
+ * Builder for a {@link Computation}s that sum lists of {@link SInts} secret-shared values.
+ *
+ * <p>Empty lists are allowed, and will always produce a value of {@code 0}.
  */
 public class SumSIntList implements Computation<SInt, ProtocolBuilderNumeric> {
 
   private final List<DRes<SInt>> input;
 
   /**
-   * Creates a new SumSIntList.
+   * Creates a new {@link SumSIntList}.
    *
-   * @param list the list to sum
+   * @param list the list to sum. Not nullable.
    */
   public SumSIntList(List<DRes<SInt>> list) {
-    input = list;
+    input = Objects.requireNonNull(list);
   }
 
   @Override
   public DRes<SInt> buildComputation(ProtocolBuilderNumeric iterationBuilder) {
-    return iterationBuilder.seq(seq ->
-        () -> input
-    ).whileLoop(
-        (inputs) -> inputs.size() > 1,
-        (seq, inputs) -> seq.par(parallel -> {
-          List<DRes<SInt>> out = new ArrayList<>();
-          Numeric numericBuilder = parallel.numeric();
-          DRes<SInt> left = null;
-          for (DRes<SInt> input1 : inputs) {
-            if (left == null) {
-              left = input1;
-            } else {
-              out.add(numericBuilder.add(left, input1));
-              left = null;
-            }
-          }
-          if (left != null) {
-            out.add(left);
-          }
-          return () -> out;
-        })
-    ).seq((builder, currentInput) -> currentInput.get(0));
+    // Fast case if there is nothing to sum.
+    if (input.isEmpty()) {
+      return iterationBuilder.seq(seq -> seq.numeric().known(0));
+    }
+
+    // Slow case when there are elements to sum.
+    return iterationBuilder
+        .seq(seq -> () -> input)
+        .whileLoop(
+            (inputs) -> inputs.size() > 1,
+            (seq, inputs) ->
+                seq.par(
+                    parallel -> {
+                      List<DRes<SInt>> out = new ArrayList<>();
+                      Numeric numericBuilder = parallel.numeric();
+                      DRes<SInt> left = null;
+                      for (DRes<SInt> input1 : inputs) {
+                        if (left == null) {
+                          left = input1;
+                        } else {
+                          out.add(numericBuilder.add(left, input1));
+                          left = null;
+                        }
+                      }
+                      if (left != null) {
+                        out.add(left);
+                      }
+                      return () -> out;
+                    }))
+        .seq((builder, currentInput) -> currentInput.get(0));
   }
 }
diff --git a/lib/common/src/test/java/dk/alexandra/fresco/lib/common/math/integer/TestProductAndSum.java b/lib/common/src/test/java/dk/alexandra/fresco/lib/common/math/integer/TestProductAndSum.java
index 65bb34a7a..9b541e62a 100644
--- a/lib/common/src/test/java/dk/alexandra/fresco/lib/common/math/integer/TestProductAndSum.java
+++ b/lib/common/src/test/java/dk/alexandra/fresco/lib/common/math/integer/TestProductAndSum.java
@@ -15,13 +15,45 @@
 import java.util.List;
 import java.util.stream.Collectors;
 
+/** Test of {@link ProductSIntList} and {@link SumSIntList}. */
 public class TestProductAndSum {
 
-  public static class TestProduct<ResourcePoolT extends ResourcePool>
-      extends TestThreadFactory<ResourcePoolT, ProtocolBuilderNumeric> {
+  private static final class TestCase {
+    public final BigInteger expectedOutput;
+    public final List<BigInteger> inputs;
+
+    public TestCase(long expectedOutput, long... inputs) {
+      this.expectedOutput = BigInteger.valueOf(expectedOutput);
+      this.inputs =
+          Arrays.stream(inputs)
+              .mapToObj(BigInteger::valueOf)
+              .collect(Collectors.toUnmodifiableList());
+    }
+  }
 
-    List<BigInteger> inputs = Arrays.asList(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L).stream().map(
-        BigInteger::valueOf).collect(Collectors.toList());
+  private static final List<TestCase> TEST_CASES_SUM =
+      List.of(
+          new TestCase(0),
+          new TestCase(123, 123),
+          new TestCase(2, 1, 1),
+          new TestCase(4, 2, 2),
+          new TestCase(6, 3, 3),
+          new TestCase(15, 1, 2, 4, 8),
+          new TestCase(55, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10));
+
+  private static final List<TestCase> TEST_CASES_PRODUCT =
+      List.of(
+          new TestCase(1),
+          new TestCase(123, 123),
+          new TestCase(1, 1, 1),
+          new TestCase(4, 2, 2),
+          new TestCase(9, 3, 3),
+          new TestCase(64, 1, 2, 4, 8),
+          new TestCase(3628800, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10));
+
+  /** Test of {@link ProductSIntList}. */
+  public static final class TestProduct<ResourcePoolT extends ResourcePool>
+      extends TestThreadFactory<ResourcePoolT, ProtocolBuilderNumeric> {
 
     @Override
     public TestThread<ResourcePoolT, ProtocolBuilderNumeric> next() {
@@ -29,45 +61,51 @@ public TestThread<ResourcePoolT, ProtocolBuilderNumeric> next() {
 
         @Override
         public void test() throws Exception {
-          // define functionality to be tested
-          Application<BigInteger, ProtocolBuilderNumeric> testApplication =
-              root -> {
-                List<DRes<SInt>> closed = inputs.stream().map(root.numeric()::known)
-                    .collect(Collectors.toList());
-                DRes<SInt> result = AdvancedNumeric.using(root).product(closed);
-                DRes<BigInteger> open = root.numeric().open(result);
-                return () -> open.out();
-              };
-          BigInteger output = runApplication(testApplication);
-          assertEquals(output, inputs.stream().reduce(BigInteger.ONE, (a, b) -> a.multiply(b)));
+          for (final TestCase testCase : TEST_CASES_PRODUCT) {
+            // define functionality to be tested
+            Application<BigInteger, ProtocolBuilderNumeric> testApplication =
+                root -> {
+                  List<DRes<SInt>> closed =
+                      testCase.inputs.stream()
+                          .map(root.numeric()::known)
+                          .collect(Collectors.toUnmodifiableList());
+                  DRes<SInt> result = AdvancedNumeric.using(root).product(closed);
+                  DRes<BigInteger> open = root.numeric().open(result);
+                  return () -> open.out();
+                };
+            BigInteger output = runApplication(testApplication);
+            assertEquals(testCase.expectedOutput, output);
+          }
         }
       };
     }
   }
 
-  public static class TestSum<ResourcePoolT extends ResourcePool>
+  /** Test of {@link SumSIntList}. */
+  public static final class TestSum<ResourcePoolT extends ResourcePool>
       extends TestThreadFactory<ResourcePoolT, ProtocolBuilderNumeric> {
 
-    List<BigInteger> inputs = Arrays.asList(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L).stream().map(
-        BigInteger::valueOf).collect(Collectors.toList());
-
     @Override
     public TestThread<ResourcePoolT, ProtocolBuilderNumeric> next() {
       return new TestThread<ResourcePoolT, ProtocolBuilderNumeric>() {
 
         @Override
         public void test() throws Exception {
-          // define functionality to be tested
-          Application<BigInteger, ProtocolBuilderNumeric> testApplication =
-              root -> {
-                List<DRes<SInt>> closed = inputs.stream().map(root.numeric()::known)
-                    .collect(Collectors.toList());
-                DRes<SInt> result = AdvancedNumeric.using(root).sum(closed);
-                DRes<BigInteger> open = root.numeric().open(result);
-                return () -> open.out();
-              };
-          BigInteger output = runApplication(testApplication);
-          assertEquals(output, inputs.stream().reduce(BigInteger.ZERO, (a, b) -> a.add(b)));
+          for (final TestCase testCase : TEST_CASES_SUM) {
+            // define functionality to be tested
+            Application<BigInteger, ProtocolBuilderNumeric> testApplication =
+                root -> {
+                  List<DRes<SInt>> closed =
+                      testCase.inputs.stream()
+                          .map(root.numeric()::known)
+                          .collect(Collectors.toUnmodifiableList());
+                  DRes<SInt> result = AdvancedNumeric.using(root).sum(closed);
+                  DRes<BigInteger> open = root.numeric().open(result);
+                  return () -> open.out();
+                };
+            BigInteger output = runApplication(testApplication);
+            assertEquals(testCase.expectedOutput, output);
+          }
         }
       };
     }