diff --git a/util/encoding/encoding_test.go b/util/encoding/encoding_test.go
index f1a0cccdc..a7d230a64 100644
--- a/util/encoding/encoding_test.go
+++ b/util/encoding/encoding_test.go
@@ -2,6 +2,7 @@ package encoding
 
 import (
 	"bytes"
+	"io"
 	"testing"
 
 	"github.com/stretchr/testify/require"
@@ -60,3 +61,40 @@ func TestScalarHexString(t *testing.T) {
 	ErrFatal(err)
 	require.True(t, sc.Equal(s2))
 }
+
+// Tests for error cases
+type MockFailingReader struct {
+	data []byte
+}
+type MockEmptyReader struct {
+	data []byte
+}
+
+func (m *MockFailingReader) Read(p []byte) (n int, err error) {
+	return copy(p, m.data), io.EOF
+}
+func (m *MockEmptyReader) Read(p []byte) (n int, err error) {
+	return 0, nil
+}
+
+func TestReadHexPointErrorInvalidHexEnc(t *testing.T) {
+	// Test case: invalid hex encoding
+	reader := bytes.NewReader([]byte("invalidhex"))
+	_, err := ReadHexPoint(s, reader)
+	require.Error(t, err, "Expected error when reading invalid hex encoding, but got nil")
+}
+
+func TestReadHexPointErrorReaderFails(t *testing.T) {
+	// Test case: reader fails
+	mockReader1 := &MockFailingReader{data: []byte("abc")}
+	_, err := ReadHexPoint(s, mockReader1)
+	require.Error(t, err, "Expected error when reader fails, but got nil")
+}
+
+func TestReadHexPointErrorNotEnoughBytes(t *testing.T) {
+	// Test case: not enough bytes from stream
+	mockReader2 := &MockEmptyReader{data: []byte("abc")}
+	_, err := ReadHexPoint(s, mockReader2)
+	require.Error(t, err, "Expected error when not enough bytes from stream, but got nil")
+	require.EqualError(t, err, "didn't get enough bytes from stream", "Expected error message: didn't get enough bytes from stream, but got %s", err.Error())
+}
diff --git a/util/random/rand_test.go b/util/random/rand_test.go
index 42b50ac03..36f62f76e 100644
--- a/util/random/rand_test.go
+++ b/util/random/rand_test.go
@@ -3,14 +3,18 @@ package random
 import (
 	"bytes"
 	"crypto/rand"
+	"fmt"
+	"math/big"
+	"strconv"
 	"strings"
 	"testing"
 )
 
 const size = 32
+const readerStream = "some io.Reader stream to be used for testing"
 
 func TestMixedEntropy(t *testing.T) {
-	r := strings.NewReader("some io.Reader stream to be used for testing")
+	r := strings.NewReader(readerStream)
 	cipher := New(r, rand.Reader)
 
 	src := make([]byte, size)
@@ -57,13 +61,12 @@ func TestCryptoOnly(t *testing.T) {
 }
 
 func TestUserOnly(t *testing.T) {
-	seed := "some io.Reader stream to be used for testing"
-	cipher1 := New(strings.NewReader(seed))
+	cipher1 := New(strings.NewReader(readerStream))
 	src := make([]byte, size)
 	copy(src, []byte("hello"))
 	dst1 := make([]byte, size)
 	cipher1.XORKeyStream(dst1, src)
-	cipher2 := New(strings.NewReader(seed))
+	cipher2 := New(strings.NewReader(readerStream))
 	dst2 := make([]byte, size)
 	cipher2.XORKeyStream(dst2, src)
 	if !bytes.Equal(dst1, dst2) {
@@ -84,3 +87,63 @@ func TestIncorrectSize(t *testing.T) {
 	dst := make([]byte, size+1)
 	cipher.XORKeyStream(dst, src)
 }
+
+func TestBits(t *testing.T) {
+	testCases := []struct {
+		bitlen uint // input bit length
+		exact  bool // whether the exact bit length should be enforced
+	}{
+		{bitlen: 128, exact: false},
+		{bitlen: 256, exact: true},
+		{bitlen: 512, exact: false},
+		{bitlen: 1024, exact: true},
+	}
+
+	for _, tc := range testCases {
+		t.Run(fmt.Sprintf("bitlen: %d exact: %s", tc.bitlen, strconv.FormatBool(tc.exact)), func(t *testing.T) {
+			r := strings.NewReader(readerStream)
+			cipher := New(r, rand.Reader)
+
+			bigIntBytes := Bits(tc.bitlen, tc.exact, cipher)
+			bigInt := new(big.Int).SetBytes(bigIntBytes)
+
+			// Check if the bit length matches the expected length
+			expectedBitLen := tc.bitlen
+			if tc.exact && uint(bigInt.BitLen()) != expectedBitLen {
+				t.Errorf("Generated BigInt with exact bits doesn't match the expected bit length: got %d, expected %d", bigInt.BitLen(), expectedBitLen)
+			} else if !tc.exact && uint(bigInt.BitLen()) > expectedBitLen {
+				t.Errorf("Generated BigInt with more bits than maximum bit length: got %d, expected at most %d", bigInt.BitLen(), expectedBitLen)
+			}
+		})
+	}
+}
+
+func TestInt(t *testing.T) {
+	testCases := []struct {
+		modulusBitLen uint // Bit length of the modulus
+	}{
+		{128},
+		{256},
+		{512},
+		{1024},
+	}
+
+	for _, tc := range testCases {
+		t.Run(fmt.Sprintf("modulusBitlen: %d", tc.modulusBitLen), func(t *testing.T) {
+			modulus, err := rand.Prime(rand.Reader, int(tc.modulusBitLen))
+			if err != nil {
+				t.Fatalf("Failed to generate random prime: %v", err)
+			}
+
+			r := strings.NewReader(readerStream)
+			cipher := New(r, rand.Reader)
+
+			randomInt := Int(modulus, cipher)
+
+			// Check if the generated BigInt is less than the modulus
+			if randomInt.Cmp(modulus) >= 0 {
+				t.Errorf("Generated BigInt %v is not less than the modulus %v", randomInt, modulus)
+			}
+		})
+	}
+}