diff --git a/src/bignum/bignum.cc b/src/bignum/bignum.cc
index 5d6ccb2..cf0d6b6 100644
--- a/src/bignum/bignum.cc
+++ b/src/bignum/bignum.cc
@@ -18,6 +18,57 @@ bool do_less_than(digits_type const& lhs, digits_type const& rhs) {
                                         rhs.rend());
 }
 
+digits_type do_addition(digits_type const& lhs, digits_type const& rhs) {
+    int carry = 0;
+    digits_type res;
+
+    auto it1 = lhs.begin();
+    auto it2 = rhs.begin();
+
+    auto const end1 = lhs.end();
+    auto const end2 = rhs.end();
+
+    while (it1 != end1 && it2 != end2) {
+        int addition = *it1 + *it2 + carry;
+        carry = addition / 10;
+        res.push_back(addition % 10);
+        ++it1;
+        ++it2;
+    }
+
+    auto it = it1;
+    auto end = end1;
+    if (it1 == end1) {
+        it = it2;
+        end = end2;
+    }
+
+    while (it != end) {
+        int addition = *it + carry;
+        carry = addition / 10;
+        res.push_back(addition % 10);
+        ++it;
+    }
+
+    return res;
+}
+
+digits_type do_substraction(digits_type const& lhs, digits_type const& rhs) {
+    assert(!do_less_than(lhs, rhs));
+
+    digits_type complement;
+    auto const take_complement = [](auto num) { return 9 - num; };
+    std::transform(lhs.begin(), lhs.end(), std::back_inserter(complement),
+                   take_complement);
+
+    complement = do_addition(complement, rhs);
+
+    std::transform(complement.begin(), complement.end(), complement.begin(),
+                   take_complement);
+
+    return complement;
+}
+
 } // namespace
 
 BigNum::BigNum(std::int64_t number) {
@@ -60,6 +111,48 @@ void BigNum::flip_sign() {
     sign_ *= -1;
 }
 
+void BigNum::add(BigNum const& rhs) {
+    assert(is_canonicalized());
+    assert(rhs.is_canonicalized());
+
+    if (rhs.sign_ == 0) {
+        return;
+    }
+
+    if (sign_ == 0) {
+        *this = rhs;
+        return;
+    }
+
+    if (sign_ == rhs.sign_) {
+        digits_ = do_addition(digits_, rhs.digits_);
+    } else {
+        bool flipped = do_less_than(digits_, rhs.digits_);
+        if (flipped) {
+            digits_ = do_substraction(rhs.digits_, digits_);
+        } else {
+            digits_ = do_substraction(digits_, rhs.digits_);
+        }
+        if (flipped) {
+            flip_sign();
+        }
+        canonicalize();
+    }
+
+    assert(is_canonicalized());
+}
+
+void BigNum::substract(BigNum const& rhs) {
+    assert(is_canonicalized());
+    assert(rhs.is_canonicalized());
+
+    flip_sign();
+    add(rhs);
+    flip_sign();
+
+    assert(is_canonicalized());
+}
+
 bool BigNum::equal(BigNum const& rhs) const {
     assert(is_canonicalized());
     assert(rhs.is_canonicalized());
diff --git a/src/bignum/bignum.hh b/src/bignum/bignum.hh
index 8774eb0..149e962 100644
--- a/src/bignum/bignum.hh
+++ b/src/bignum/bignum.hh
@@ -25,6 +25,28 @@ public:
         return ret;
     }
 
+    friend BigNum& operator+=(BigNum& lhs, BigNum const& rhs) {
+        lhs.add(rhs);
+        return lhs;
+    }
+
+    friend BigNum operator+(BigNum const& lhs, BigNum const& rhs) {
+        auto ret = lhs;
+        ret += rhs;
+        return ret;
+    }
+
+    friend BigNum& operator-=(BigNum& lhs, BigNum const& rhs) {
+        lhs.substract(rhs);
+        return lhs;
+    }
+
+    friend BigNum operator-(BigNum const& lhs, BigNum const& rhs) {
+        auto ret = lhs;
+        ret -= rhs;
+        return ret;
+    }
+
     friend bool operator==(BigNum const& lhs, BigNum const& rhs) {
         return lhs.equal(rhs);
     }
@@ -53,6 +75,8 @@ private:
     std::ostream& dump(std::ostream& out) const;
 
     void flip_sign();
+    void add(BigNum const& rhs);
+    void substract(BigNum const& rhs);
 
     bool equal(BigNum const& rhs) const;
     bool less_than(BigNum const& rhs) const;
diff --git a/tests/unit/bignum.cc b/tests/unit/bignum.cc
index 65ff7d5..bf788b6 100644
--- a/tests/unit/bignum.cc
+++ b/tests/unit/bignum.cc
@@ -56,3 +56,89 @@ TEST(BigNum, unary) {
     auto const minus_one = BigNum(-1);
     EXPECT_EQ(minus_one, -one);
 }
+
+TEST(BigNum, addition_positive) {
+    auto const zero = BigNum(0);
+    auto const one = BigNum(1);
+    auto const two = BigNum(2);
+
+    EXPECT_EQ(zero + zero, zero);
+    EXPECT_EQ(zero + one, one);
+    EXPECT_EQ(one + zero, one);
+    EXPECT_EQ(one + one, two);
+}
+
+TEST(BigNum, addition_negative) {
+    auto const zero = BigNum(0);
+    auto const minus_one = BigNum(-1);
+    auto const minus_two = BigNum(-2);
+
+    EXPECT_EQ(zero + zero, zero);
+    EXPECT_EQ(zero + minus_one, minus_one);
+    EXPECT_EQ(minus_one + zero, minus_one);
+    EXPECT_EQ(minus_one + minus_one, minus_two);
+}
+
+TEST(BigNum, addition_mixed_signs) {
+    auto const zero = BigNum(0);
+    auto const one = BigNum(1);
+    auto const minus_one = BigNum(-1);
+
+    EXPECT_EQ(one + minus_one, zero);
+    EXPECT_EQ(minus_one + one, zero);
+}
+
+TEST(BigNum, addition_flips_sign) {
+    auto const one = BigNum(1);
+    auto const two = BigNum(2);
+    auto const minus_one = BigNum(-1);
+    auto const minus_two = BigNum(-2);
+
+    EXPECT_EQ(one + minus_two, minus_one);
+    EXPECT_EQ(minus_two + one, minus_one);
+
+    EXPECT_EQ(minus_one + two, one);
+    EXPECT_EQ(two + minus_one, one);
+}
+
+TEST(BigNum, substraction_positive) {
+    auto const zero = BigNum(0);
+    auto const one = BigNum(1);
+    auto const two = BigNum(2);
+
+    EXPECT_EQ(zero - zero, zero);
+    EXPECT_EQ(two - zero, two);
+    EXPECT_EQ(two - one, one);
+    EXPECT_EQ(one - one, zero);
+}
+
+TEST(BigNum, substraction_negative) {
+    auto const zero = BigNum(0);
+    auto const minus_one = BigNum(-1);
+    auto const one = BigNum(1);
+
+    EXPECT_EQ(zero - zero, zero);
+    EXPECT_EQ(zero - minus_one, one);
+    EXPECT_EQ(zero - one, minus_one);
+}
+
+TEST(BigNum, substraction_mixed_signs) {
+    auto const zero = BigNum(0);
+    auto const one = BigNum(1);
+    auto const two = BigNum(2);
+    auto const minus_one = BigNum(-1);
+    auto const minus_two = BigNum(-2);
+
+    EXPECT_EQ(one - minus_one, two);
+    EXPECT_EQ(minus_one - one, minus_two);
+}
+
+TEST(BigNum, substraction_flips_sign) {
+    auto const one = BigNum(1);
+    auto const two = BigNum(2);
+    auto const minus_one = BigNum(-1);
+    auto const minus_two = BigNum(-2);
+
+    EXPECT_EQ(one - two, minus_one);
+    EXPECT_EQ(minus_one - minus_two, one);
+}