Libraries: Move to Userland/Libraries/

Userland/Libraries/LibCrypto/BigInt/SignedBigInteger.cpp

@@ -0,0 +1,272 @@
+/*
+ * Copyright (c) 2020, the SerenityOS developers.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this
+ *    list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ *    this list of conditions and the following disclaimer in the documentation
+ *    and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#include "SignedBigInteger.h"
+#include <AK/StringBuilder.h>
+
+namespace Crypto {
+
+SignedBigInteger SignedBigInteger::import_data(const u8* ptr, size_t length)
+{
+    bool sign = *ptr;
+    auto unsigned_data = UnsignedBigInteger::import_data(ptr + 1, length - 1);
+    return { move(unsigned_data), sign };
+}
+
+size_t SignedBigInteger::export_data(Bytes data, bool remove_leading_zeros) const
+{
+    // FIXME: Support this:
+    //        m <0XX> -> m <XX> (if remove_leading_zeros)
+    ASSERT(!remove_leading_zeros);
+
+    data[0] = m_sign;
+    auto bytes_view = data.slice(1, data.size() - 1);
+    return m_unsigned_data.export_data(bytes_view, remove_leading_zeros) + 1;
+}
+
+SignedBigInteger SignedBigInteger::from_base10(StringView str)
+{
+    bool sign = false;
+    if (str.length() > 1) {
+        auto maybe_sign = str[0];
+        if (maybe_sign == '-') {
+            str = str.substring_view(1, str.length() - 1);
+            sign = true;
+        }
+        if (maybe_sign == '+')
+            str = str.substring_view(1, str.length() - 1);
+    }
+    auto unsigned_data = UnsignedBigInteger::from_base10(str);
+    return { move(unsigned_data), sign };
+}
+
+String SignedBigInteger::to_base10() const
+{
+    StringBuilder builder;
+
+    if (m_sign)
+        builder.append('-');
+
+    builder.append(m_unsigned_data.to_base10());
+
+    return builder.to_string();
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::plus(const SignedBigInteger& other) const
+{
+    // If both are of the same sign, just add the unsigned data and return.
+    if (m_sign == other.m_sign)
+        return { other.m_unsigned_data.plus(m_unsigned_data), m_sign };
+
+    // One value is signed while the other is not.
+    return m_sign ? other.minus(this->m_unsigned_data) : minus(other.m_unsigned_data);
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::minus(const SignedBigInteger& other) const
+{
+    // If the signs are different, convert the op to an addition.
+    if (m_sign != other.m_sign) {
+        // -x - y = - (x + y)
+        // x - -y = (x + y)
+        SignedBigInteger result { other.m_unsigned_data.plus(this->m_unsigned_data) };
+        if (m_sign)
+            result.negate();
+        return result;
+    }
+
+    if (!m_sign) {
+        // Both operands are positive.
+        // x - y = - (y - x)
+        if (m_unsigned_data < other.m_unsigned_data) {
+            // The result will be negative.
+            return { other.m_unsigned_data.minus(m_unsigned_data), true };
+        }
+
+        // The result will be either zero, or positive.
+        return SignedBigInteger { m_unsigned_data.minus(other.m_unsigned_data) };
+    }
+
+    // Both operands are negative.
+    // -x - -y = y - x
+    if (m_unsigned_data < other.m_unsigned_data) {
+        // The result will be positive.
+        return SignedBigInteger { other.m_unsigned_data.minus(m_unsigned_data), true };
+    }
+    // The result will be either zero, or negative.
+    // y - x = - (x - y)
+    return SignedBigInteger { m_unsigned_data.minus(other.m_unsigned_data) };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::plus(const UnsignedBigInteger& other) const
+{
+    if (m_sign) {
+        if (other < m_unsigned_data)
+            return { m_unsigned_data.minus(other), true };
+
+        return { other.minus(m_unsigned_data), false };
+    }
+
+    return { m_unsigned_data.plus(other), false };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::minus(const UnsignedBigInteger& other) const
+{
+    if (m_sign)
+        return { m_unsigned_data.plus(m_unsigned_data), true };
+
+    if (other < m_unsigned_data)
+        return { m_unsigned_data.minus(other), false };
+
+    return { other.minus(m_unsigned_data), true };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::bitwise_or(const UnsignedBigInteger& other) const
+{
+    return { unsigned_value().bitwise_or(other), m_sign };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::bitwise_and(const UnsignedBigInteger& other) const
+{
+    return { unsigned_value().bitwise_and(other), false };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::bitwise_xor(const UnsignedBigInteger& other) const
+{
+    return { unsigned_value().bitwise_xor(other), m_sign };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::bitwise_not() const
+{
+    return { unsigned_value().bitwise_not(), !m_sign };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::bitwise_or(const SignedBigInteger& other) const
+{
+    auto result = bitwise_or(other.unsigned_value());
+
+    // The sign bit will have to be OR'd manually.
+    if (other.is_negative())
+        result.negate();
+
+    return result;
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::bitwise_and(const SignedBigInteger& other) const
+{
+    auto result = bitwise_and(other.unsigned_value());
+
+    // The sign bit will have to be AND'd manually.
+    result.m_sign = is_negative() || other.is_negative();
+
+    return result;
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::bitwise_xor(const SignedBigInteger& other) const
+{
+    auto result = bitwise_xor(other.unsigned_value());
+
+    // The sign bit will have to be XOR'd manually.
+    result.m_sign = is_negative() ^ other.is_negative();
+
+    return result;
+}
+
+bool SignedBigInteger::operator==(const UnsignedBigInteger& other) const
+{
+    if (m_sign)
+        return false;
+    return m_unsigned_data == other;
+}
+
+bool SignedBigInteger::operator!=(const UnsignedBigInteger& other) const
+{
+    if (m_sign)
+        return true;
+    return m_unsigned_data != other;
+}
+
+bool SignedBigInteger::operator<(const UnsignedBigInteger& other) const
+{
+    if (m_sign)
+        return true;
+    return m_unsigned_data < other;
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::shift_left(size_t num_bits) const
+{
+    return SignedBigInteger { m_unsigned_data.shift_left(num_bits), m_sign };
+}
+
+FLATTEN SignedBigInteger SignedBigInteger::multiplied_by(const SignedBigInteger& other) const
+{
+    bool result_sign = m_sign ^ other.m_sign;
+    return { m_unsigned_data.multiplied_by(other.m_unsigned_data), result_sign };
+}
+
+FLATTEN SignedDivisionResult SignedBigInteger::divided_by(const SignedBigInteger& divisor) const
+{
+    // Aa / Bb -> (A^B)q, Ar
+    bool result_sign = m_sign ^ divisor.m_sign;
+    auto unsigned_division_result = m_unsigned_data.divided_by(divisor.m_unsigned_data);
+    return {
+        { move(unsigned_division_result.quotient), result_sign },
+        { move(unsigned_division_result.remainder), m_sign }
+    };
+}
+
+void SignedBigInteger::set_bit_inplace(size_t bit_index)
+{
+    m_unsigned_data.set_bit_inplace(bit_index);
+}
+
+bool SignedBigInteger::operator==(const SignedBigInteger& other) const
+{
+    if (is_invalid() != other.is_invalid())
+        return false;
+
+    if (m_unsigned_data == 0 && other.m_unsigned_data == 0)
+        return true;
+
+    return m_sign == other.m_sign && m_unsigned_data == other.m_unsigned_data;
+}
+
+bool SignedBigInteger::operator!=(const SignedBigInteger& other) const
+{
+    return !(*this == other);
+}
+
+bool SignedBigInteger::operator<(const SignedBigInteger& other) const
+{
+    if (m_sign ^ other.m_sign)
+        return m_sign;
+
+    if (m_sign)
+        return other.m_unsigned_data < m_unsigned_data;
+
+    return m_unsigned_data < other.m_unsigned_data;
+}
+
+}

Userland/Libraries/LibCrypto/BigInt/SignedBigInteger.h

@@ -0,0 +1,162 @@
+/*
+ * Copyright (c) 2020, the SerenityOS developers.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this
+ *    list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ *    this list of conditions and the following disclaimer in the documentation
+ *    and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#pragma once
+
+#include <AK/Span.h>
+#include <LibCrypto/BigInt/UnsignedBigInteger.h>
+
+namespace Crypto {
+
+struct SignedDivisionResult;
+
+class SignedBigInteger {
+public:
+    SignedBigInteger(i32 x)
+        : m_sign(x < 0)
+        , m_unsigned_data(abs(x))
+    {
+    }
+
+    SignedBigInteger(UnsignedBigInteger&& unsigned_data, bool sign)
+        : m_sign(sign)
+        , m_unsigned_data(move(unsigned_data))
+    {
+    }
+
+    explicit SignedBigInteger(UnsignedBigInteger unsigned_data)
+        : m_sign(false)
+        , m_unsigned_data(move(unsigned_data))
+    {
+    }
+
+    SignedBigInteger()
+        : m_sign(false)
+        , m_unsigned_data()
+    {
+    }
+
+    static SignedBigInteger create_invalid()
+    {
+        return { UnsignedBigInteger::create_invalid(), false };
+    }
+
+    static SignedBigInteger import_data(const AK::StringView& data) { return import_data((const u8*)data.characters_without_null_termination(), data.length()); }
+    static SignedBigInteger import_data(const u8* ptr, size_t length);
+
+    size_t export_data(Bytes, bool remove_leading_zeros = false) const;
+
+    static SignedBigInteger from_base10(StringView str);
+    String to_base10() const;
+
+    const UnsignedBigInteger& unsigned_value() const { return m_unsigned_data; }
+    const Vector<u32, STARTING_WORD_SIZE> words() const { return m_unsigned_data.words(); }
+    bool is_negative() const { return m_sign; }
+
+    void negate() { m_sign = !m_sign; }
+
+    void set_to_0() { m_unsigned_data.set_to_0(); }
+    void set_to(i32 other)
+    {
+        m_unsigned_data.set_to((u32)other);
+        m_sign = other < 0;
+    }
+    void set_to(const SignedBigInteger& other)
+    {
+        m_unsigned_data.set_to(other.m_unsigned_data);
+        m_sign = other.m_sign;
+    }
+
+    void invalidate()
+    {
+        m_unsigned_data.invalidate();
+    }
+
+    bool is_invalid() const { return m_unsigned_data.is_invalid(); }
+
+    // These get + 1 byte for the sign.
+    size_t length() const { return m_unsigned_data.length() + 1; }
+    size_t trimmed_length() const { return m_unsigned_data.trimmed_length() + 1; };
+
+    SignedBigInteger plus(const SignedBigInteger& other) const;
+    SignedBigInteger minus(const SignedBigInteger& other) const;
+    SignedBigInteger bitwise_or(const SignedBigInteger& other) const;
+    SignedBigInteger bitwise_and(const SignedBigInteger& other) const;
+    SignedBigInteger bitwise_xor(const SignedBigInteger& other) const;
+    SignedBigInteger bitwise_not() const;
+    SignedBigInteger shift_left(size_t num_bits) const;
+    SignedBigInteger multiplied_by(const SignedBigInteger& other) const;
+    SignedDivisionResult divided_by(const SignedBigInteger& divisor) const;
+
+    SignedBigInteger plus(const UnsignedBigInteger& other) const;
+    SignedBigInteger minus(const UnsignedBigInteger& other) const;
+    SignedBigInteger bitwise_or(const UnsignedBigInteger& other) const;
+    SignedBigInteger bitwise_and(const UnsignedBigInteger& other) const;
+    SignedBigInteger bitwise_xor(const UnsignedBigInteger& other) const;
+    SignedBigInteger multiplied_by(const UnsignedBigInteger& other) const;
+    SignedDivisionResult divided_by(const UnsignedBigInteger& divisor) const;
+
+    void set_bit_inplace(size_t bit_index);
+
+    bool operator==(const SignedBigInteger& other) const;
+    bool operator!=(const SignedBigInteger& other) const;
+    bool operator<(const SignedBigInteger& other) const;
+
+    bool operator==(const UnsignedBigInteger& other) const;
+    bool operator!=(const UnsignedBigInteger& other) const;
+    bool operator<(const UnsignedBigInteger& other) const;
+
+private:
+    bool m_sign { false };
+    UnsignedBigInteger m_unsigned_data;
+};
+
+struct SignedDivisionResult {
+    Crypto::SignedBigInteger quotient;
+    Crypto::SignedBigInteger remainder;
+};
+
+}
+
+inline const LogStream&
+operator<<(const LogStream& stream, const Crypto::SignedBigInteger value)
+{
+    if (value.is_invalid()) {
+        stream << "Invalid BigInt";
+        return stream;
+    }
+    if (value.is_negative())
+        stream << "-";
+
+    stream << value.unsigned_value();
+    return stream;
+}
+
+inline Crypto::SignedBigInteger
+operator""_sbigint(const char* string, size_t length)
+{
+    return Crypto::SignedBigInteger::from_base10({ string, length });
+}

Userland/Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp

@@ -0,0 +1,745 @@
+/*
+ * Copyright (c) 2020, Itamar S. <itamar8910@gmail.com>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this
+ *    list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ *    this list of conditions and the following disclaimer in the documentation
+ *    and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#include "UnsignedBigInteger.h"
+#include <AK/StringBuilder.h>
+
+namespace Crypto {
+
+UnsignedBigInteger::UnsignedBigInteger(const u8* ptr, size_t length)
+{
+    m_words.resize_and_keep_capacity((length + sizeof(u32) - 1) / sizeof(u32));
+    size_t in = length, out = 0;
+    while (in >= sizeof(u32)) {
+        in -= sizeof(u32);
+        u32 word = ((u32)ptr[in] << 24) | ((u32)ptr[in + 1] << 16) | ((u32)ptr[in + 2] << 8) | (u32)ptr[in + 3];
+        m_words[out++] = word;
+    }
+    if (in > 0) {
+        u32 word = 0;
+        for (size_t i = 0; i < in; i++) {
+            word <<= 8;
+            word |= (u32)ptr[i];
+        }
+        m_words[out++] = word;
+    }
+}
+
+UnsignedBigInteger UnsignedBigInteger::create_invalid()
+{
+    UnsignedBigInteger invalid(0);
+    invalid.invalidate();
+    return invalid;
+}
+
+size_t UnsignedBigInteger::export_data(Bytes data, bool remove_leading_zeros) const
+{
+    size_t word_count = trimmed_length();
+    size_t out = 0;
+    if (word_count > 0) {
+        ssize_t leading_zeros = -1;
+        if (remove_leading_zeros) {
+            u32 word = m_words[word_count - 1];
+            for (size_t i = 0; i < sizeof(u32); i++) {
+                u8 byte = (u8)(word >> ((sizeof(u32) - i - 1) * 8));
+                data[out++] = byte;
+                if (leading_zeros < 0 && byte != 0)
+                    leading_zeros = (int)i;
+            }
+        }
+        for (size_t i = word_count - (remove_leading_zeros ? 1 : 0); i > 0; i--) {
+            auto word = m_words[i - 1];
+            data[out++] = (u8)(word >> 24);
+            data[out++] = (u8)(word >> 16);
+            data[out++] = (u8)(word >> 8);
+            data[out++] = (u8)word;
+        }
+        if (leading_zeros > 0)
+            out -= leading_zeros;
+    }
+    return out;
+}
+
+UnsignedBigInteger UnsignedBigInteger::from_base10(const String& str)
+{
+    UnsignedBigInteger result;
+    UnsignedBigInteger ten { 10 };
+
+    for (auto& c : str) {
+        result = result.multiplied_by(ten).plus(c - '0');
+    }
+    return result;
+}
+
+String UnsignedBigInteger::to_base10() const
+{
+    if (*this == UnsignedBigInteger { 0 })
+        return "0";
+
+    StringBuilder builder;
+    UnsignedBigInteger temp(*this);
+    UnsignedBigInteger quotient;
+    UnsignedBigInteger remainder;
+
+    while (temp != UnsignedBigInteger { 0 }) {
+        divide_u16_without_allocation(temp, 10, quotient, remainder);
+        ASSERT(remainder.words()[0] < 10);
+        builder.append(static_cast<char>(remainder.words()[0] + '0'));
+        temp.set_to(quotient);
+    }
+
+    auto reversed_string = builder.to_string();
+    builder.clear();
+    for (int i = reversed_string.length() - 1; i >= 0; --i) {
+        builder.append(reversed_string[i]);
+    }
+
+    return builder.to_string();
+}
+
+void UnsignedBigInteger::set_to_0()
+{
+    m_words.clear_with_capacity();
+    m_is_invalid = false;
+    m_cached_trimmed_length = {};
+}
+
+void UnsignedBigInteger::set_to(u32 other)
+{
+    m_is_invalid = false;
+    m_words.resize_and_keep_capacity(1);
+    m_words[0] = other;
+    m_cached_trimmed_length = {};
+}
+
+void UnsignedBigInteger::set_to(const UnsignedBigInteger& other)
+{
+    m_is_invalid = other.m_is_invalid;
+    m_words.resize_and_keep_capacity(other.m_words.size());
+    __builtin_memcpy(m_words.data(), other.m_words.data(), other.m_words.size() * sizeof(u32));
+    m_cached_trimmed_length = {};
+}
+
+size_t UnsignedBigInteger::trimmed_length() const
+{
+    if (!m_cached_trimmed_length.has_value()) {
+        size_t num_leading_zeroes = 0;
+        for (int i = length() - 1; i >= 0; --i, ++num_leading_zeroes) {
+            if (m_words[i] != 0)
+                break;
+        }
+        m_cached_trimmed_length = length() - num_leading_zeroes;
+    }
+    return m_cached_trimmed_length.value();
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+
+    add_without_allocation(*this, other, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::minus(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+
+    subtract_without_allocation(*this, other, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_or(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+
+    bitwise_or_without_allocation(*this, other, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_and(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+
+    bitwise_and_without_allocation(*this, other, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_xor(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+
+    bitwise_xor_without_allocation(*this, other, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::bitwise_not() const
+{
+    UnsignedBigInteger result;
+
+    bitwise_not_without_allocation(*this, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
+{
+    UnsignedBigInteger output;
+    UnsignedBigInteger temp_result;
+    UnsignedBigInteger temp_plus;
+
+    shift_left_without_allocation(*this, num_bits, temp_result, temp_plus, output);
+
+    return output;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+    UnsignedBigInteger temp_shift_result;
+    UnsignedBigInteger temp_shift_plus;
+    UnsignedBigInteger temp_shift;
+    UnsignedBigInteger temp_plus;
+
+    multiply_without_allocation(*this, other, temp_shift_result, temp_shift_plus, temp_shift, temp_plus, result);
+
+    return result;
+}
+
+FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigInteger& divisor) const
+{
+    UnsignedBigInteger quotient;
+    UnsignedBigInteger remainder;
+
+    // If we actually have a u16-compatible divisor, short-circuit to the
+    // less computationally-intensive "divide_u16_without_allocation" method.
+    if (divisor.trimmed_length() == 1 && divisor.m_words[0] < (1 << 16)) {
+        divide_u16_without_allocation(*this, divisor.m_words[0], quotient, remainder);
+        return UnsignedDivisionResult { quotient, remainder };
+    }
+
+    UnsignedBigInteger temp_shift_result;
+    UnsignedBigInteger temp_shift_plus;
+    UnsignedBigInteger temp_shift;
+    UnsignedBigInteger temp_minus;
+
+    divide_without_allocation(*this, divisor, temp_shift_result, temp_shift_plus, temp_shift, temp_minus, quotient, remainder);
+
+    return UnsignedDivisionResult { quotient, remainder };
+}
+
+void UnsignedBigInteger::set_bit_inplace(size_t bit_index)
+{
+    const size_t word_index = bit_index / UnsignedBigInteger::BITS_IN_WORD;
+    const size_t inner_word_index = bit_index % UnsignedBigInteger::BITS_IN_WORD;
+
+    m_words.ensure_capacity(word_index);
+
+    for (size_t i = length(); i <= word_index; ++i) {
+        m_words.unchecked_append(0);
+    }
+    m_words[word_index] |= (1 << inner_word_index);
+
+    m_cached_trimmed_length = {};
+}
+
+bool UnsignedBigInteger::operator==(const UnsignedBigInteger& other) const
+{
+    if (is_invalid() != other.is_invalid())
+        return false;
+
+    auto length = trimmed_length();
+
+    if (length != other.trimmed_length())
+        return false;
+
+    return !__builtin_memcmp(m_words.data(), other.words().data(), length);
+}
+
+bool UnsignedBigInteger::operator!=(const UnsignedBigInteger& other) const
+{
+    return !(*this == other);
+}
+
+bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
+{
+    auto length = trimmed_length();
+    auto other_length = other.trimmed_length();
+
+    if (length < other_length) {
+        return true;
+    }
+
+    if (length > other_length) {
+        return false;
+    }
+
+    if (length == 0) {
+        return false;
+    }
+    for (int i = length - 1; i >= 0; --i) {
+        if (m_words[i] == other.m_words[i])
+            continue;
+        return m_words[i] < other.m_words[i];
+    }
+    return false;
+}
+
+/**
+ * Complexity: O(N) where N is the number of words in the larger number
+ */
+void UnsignedBigInteger::add_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
+{
+    const UnsignedBigInteger* const longer = (left.length() > right.length()) ? &left : &right;
+    const UnsignedBigInteger* const shorter = (longer == &right) ? &left : &right;
+
+    u8 carry = 0;
+
+    output.set_to_0();
+    output.m_words.resize_and_keep_capacity(longer->length());
+
+    for (size_t i = 0; i < shorter->length(); ++i) {
+        u32 word_addition_result = shorter->m_words[i] + longer->m_words[i];
+        u8 carry_out = 0;
+        // if there was a carry, the result will be smaller than any of the operands
+        if (word_addition_result + carry < shorter->m_words[i]) {
+            carry_out = 1;
+        }
+        if (carry) {
+            word_addition_result++;
+        }
+        carry = carry_out;
+        output.m_words[i] = word_addition_result;
+    }
+
+    for (size_t i = shorter->length(); i < longer->length(); ++i) {
+        u32 word_addition_result = longer->m_words[i] + carry;
+
+        carry = 0;
+        if (word_addition_result < longer->m_words[i]) {
+            carry = 1;
+        }
+        output.m_words[i] = word_addition_result;
+    }
+    if (carry) {
+        output.m_words.append(carry);
+    }
+}
+
+/**
+ * Complexity: O(N) where N is the number of words in the larger number
+ */
+void UnsignedBigInteger::subtract_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
+{
+    if (left < right) {
+        output.invalidate();
+        return;
+    }
+
+    u8 borrow = 0;
+    auto own_length = left.length();
+    auto other_length = right.length();
+
+    output.set_to_0();
+    output.m_words.resize_and_keep_capacity(own_length);
+
+    for (size_t i = 0; i < own_length; ++i) {
+        u32 other_word = (i < other_length) ? right.m_words[i] : 0;
+        i64 temp = static_cast<i64>(left.m_words[i]) - static_cast<i64>(other_word) - static_cast<i64>(borrow);
+        // If temp < 0, we had an underflow
+        borrow = (temp >= 0) ? 0 : 1;
+        if (temp < 0) {
+            temp += (UINT32_MAX + 1);
+        }
+        output.m_words[i] = temp;
+    }
+
+    // This assertion should not fail, because we verified that *this>=other at the beginning of the function
+    ASSERT(borrow == 0);
+}
+
+/**
+ * Complexity: O(N) where N is the number of words in the shorter value
+ * Method:
+ * Apply <op> word-wise until words in the shorter value are used up
+ * then copy the rest of the words verbatim from the longer value.
+ */
+FLATTEN void UnsignedBigInteger::bitwise_or_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
+{
+    // If either of the BigInts are invalid, the output is just the other one.
+    if (left.is_invalid()) {
+        output.set_to(right);
+        return;
+    }
+    if (right.is_invalid()) {
+        output.set_to(left);
+        return;
+    }
+
+    const UnsignedBigInteger *shorter, *longer;
+    if (left.length() < right.length()) {
+        shorter = &left;
+        longer = &right;
+    } else {
+        shorter = &right;
+        longer = &left;
+    }
+
+    output.m_words.resize_and_keep_capacity(longer->length());
+
+    size_t longer_offset = longer->length() - shorter->length();
+    for (size_t i = 0; i < shorter->length(); ++i)
+        output.m_words[i] = longer->words()[i] | shorter->words()[i];
+
+    __builtin_memcpy(output.m_words.data() + shorter->length(), longer->words().data() + shorter->length(), sizeof(u32) * longer_offset);
+}
+
+/**
+ * Complexity: O(N) where N is the number of words in the shorter value
+ * Method:
+ * Apply 'and' word-wise until words in the shorter value are used up
+ * and zero the rest.
+ */
+FLATTEN void UnsignedBigInteger::bitwise_and_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
+{
+    // If either of the BigInts are invalid, the output is just the other one.
+    if (left.is_invalid()) {
+        output.set_to(right);
+        return;
+    }
+    if (right.is_invalid()) {
+        output.set_to(left);
+        return;
+    }
+
+    const UnsignedBigInteger *shorter, *longer;
+    if (left.length() < right.length()) {
+        shorter = &left;
+        longer = &right;
+    } else {
+        shorter = &right;
+        longer = &left;
+    }
+
+    output.m_words.resize_and_keep_capacity(longer->length());
+
+    size_t longer_offset = longer->length() - shorter->length();
+    for (size_t i = 0; i < shorter->length(); ++i)
+        output.m_words[i] = longer->words()[i] & shorter->words()[i];
+
+    __builtin_memset(output.m_words.data() + shorter->length(), 0, sizeof(u32) * longer_offset);
+}
+
+/**
+ * Complexity: O(N) where N is the number of words in the shorter value
+ * Method:
+ * Apply 'xor' word-wise until words in the shorter value are used up
+ * and copy the rest.
+ */
+FLATTEN void UnsignedBigInteger::bitwise_xor_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
+{
+    // If either of the BigInts are invalid, the output is just the other one.
+    if (left.is_invalid()) {
+        output.set_to(right);
+        return;
+    }
+    if (right.is_invalid()) {
+        output.set_to(left);
+        return;
+    }
+
+    const UnsignedBigInteger *shorter, *longer;
+    if (left.length() < right.length()) {
+        shorter = &left;
+        longer = &right;
+    } else {
+        shorter = &right;
+        longer = &left;
+    }
+
+    output.m_words.resize_and_keep_capacity(longer->length());
+
+    size_t longer_offset = longer->length() - shorter->length();
+    for (size_t i = 0; i < shorter->length(); ++i)
+        output.m_words[i] = longer->words()[i] ^ shorter->words()[i];
+
+    __builtin_memcpy(output.m_words.data() + shorter->length(), longer->words().data() + shorter->length(), sizeof(u32) * longer_offset);
+}
+
+/**
+ * Complexity: O(N) where N is the number of words
+ */
+FLATTEN void UnsignedBigInteger::bitwise_not_without_allocation(
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
+{
+    // If the value is invalid, the output value is invalid as well.
+    if (right.is_invalid()) {
+        output.invalidate();
+        return;
+    }
+    if (right.length() == 0) {
+        output.set_to_0();
+        return;
+    }
+
+    output.m_words.resize_and_keep_capacity(right.length());
+
+    if (right.length() > 1) {
+        for (size_t i = 0; i < right.length() - 1; ++i)
+            output.m_words[i] = ~right.words()[i];
+    }
+
+    auto last_word_index = right.length() - 1;
+    auto last_word = right.words()[last_word_index];
+
+    output.m_words[last_word_index] = ((u32)0xffffffffffffffff >> __builtin_clz(last_word)) & ~last_word;
+}
+
+/**
+ * Complexity : O(N + num_bits % 8) where N is the number of words in the number
+ * Shift method :
+ * Start by shifting by whole words in num_bits (by putting missing words at the start),
+ * then shift the number's words two by two by the remaining amount of bits.
+ */
+FLATTEN void UnsignedBigInteger::shift_left_without_allocation(
+    const UnsignedBigInteger& number,
+    size_t num_bits,
+    UnsignedBigInteger& temp_result,
+    UnsignedBigInteger& temp_plus,
+    UnsignedBigInteger& output)
+{
+    // We can only do shift operations on individual words
+    // where the shift amount is <= size of word (32).
+    // But we do know how to shift by a multiple of word size (e.g 64=32*2)
+    // So we first shift the result by how many whole words fit in 'num_bits'
+    shift_left_by_n_words(number, num_bits / UnsignedBigInteger::BITS_IN_WORD, temp_result);
+
+    output.set_to(temp_result);
+
+    // And now we shift by the leftover amount of bits
+    num_bits %= UnsignedBigInteger::BITS_IN_WORD;
+
+    if (num_bits == 0) {
+        return;
+    }
+
+    for (size_t i = 0; i < temp_result.length(); ++i) {
+        u32 current_word_of_temp_result = shift_left_get_one_word(temp_result, num_bits, i);
+        output.m_words[i] = current_word_of_temp_result;
+    }
+
+    // Shifting the last word can produce a carry
+    u32 carry_word = shift_left_get_one_word(temp_result, num_bits, temp_result.length());
+    if (carry_word != 0) {
+
+        // output += (carry_word << temp_result.length())
+        // FIXME : Using temp_plus this way to transform carry_word into a bigint is not
+        // efficient nor pretty. Maybe we should have an "add_with_shift" method ?
+        temp_plus.set_to_0();
+        temp_plus.m_words.append(carry_word);
+        shift_left_by_n_words(temp_plus, temp_result.length(), temp_result);
+        add_without_allocation(output, temp_result, temp_plus);
+        output.set_to(temp_plus);
+    }
+}
+
+/**
+ * Complexity: O(N^2) where N is the number of words in the larger number
+ * Multiplication method:
+ * An integer is equal to the sum of the powers of two
+ * according to the indexes of its 'on' bits.
+ * So to multiple x*y, we go over each '1' bit in x (say the i'th bit), 
+ * and add y<<i to the result.
+ */
+FLATTEN void UnsignedBigInteger::multiply_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& temp_shift_result,
+    UnsignedBigInteger& temp_shift_plus,
+    UnsignedBigInteger& temp_shift,
+    UnsignedBigInteger& temp_plus,
+    UnsignedBigInteger& output)
+{
+    output.set_to_0();
+
+    // iterate all bits
+    for (size_t word_index = 0; word_index < left.length(); ++word_index) {
+        for (size_t bit_index = 0; bit_index < UnsignedBigInteger::BITS_IN_WORD; ++bit_index) {
+            // If the bit is off - skip over it
+            if (!(left.m_words[word_index] & (1 << bit_index)))
+                continue;
+
+            const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
+
+            // output += (right << shift_amount);
+            shift_left_without_allocation(right, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
+            add_without_allocation(output, temp_shift, temp_plus);
+            output.set_to(temp_plus);
+        }
+    }
+}
+
+/**
+ * Complexity: O(N^2) where N is the number of words in the larger number
+ * Division method:
+ * We loop over the bits of the divisor, attempting to subtract divisor<<i from the dividend.
+ * If the result is non-negative, it means that divisor*2^i "fits" in the dividend,
+ * so we set the ith bit in the quotient and reduce divisor<<i from the dividend.
+ * When we're done, what's left from the dividend is the remainder.
+ */
+FLATTEN void UnsignedBigInteger::divide_without_allocation(
+    const UnsignedBigInteger& numerator,
+    const UnsignedBigInteger& denominator,
+    UnsignedBigInteger& temp_shift_result,
+    UnsignedBigInteger& temp_shift_plus,
+    UnsignedBigInteger& temp_shift,
+    UnsignedBigInteger& temp_minus,
+    UnsignedBigInteger& quotient,
+    UnsignedBigInteger& remainder)
+{
+    quotient.set_to_0();
+    remainder.set_to(numerator);
+
+    // iterate all bits
+    for (int word_index = numerator.trimmed_length() - 1; word_index >= 0; --word_index) {
+        for (int bit_index = UnsignedBigInteger::BITS_IN_WORD - 1; bit_index >= 0; --bit_index) {
+            const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
+            shift_left_without_allocation(denominator, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
+
+            subtract_without_allocation(remainder, temp_shift, temp_minus);
+            if (!temp_minus.is_invalid()) {
+                remainder.set_to(temp_minus);
+                quotient.set_bit_inplace(shift_amount);
+            }
+        }
+    }
+}
+
+/**
+ * Complexity : O(N) where N is the number of digits in the numerator
+ * Division method :
+ * Starting from the most significant one, for each half-word of the numerator, combine it
+ * with the existing remainder if any, divide the combined number as a u32 operation and
+ * update the quotient / remainder as needed.
+ */
+FLATTEN void UnsignedBigInteger::divide_u16_without_allocation(
+    const UnsignedBigInteger& numerator,
+    u32 denominator,
+    UnsignedBigInteger& quotient,
+    UnsignedBigInteger& remainder)
+{
+    ASSERT(denominator < (1 << 16));
+    u32 remainder_word = 0;
+    auto numerator_length = numerator.trimmed_length();
+    quotient.set_to_0();
+    quotient.m_words.resize(numerator_length);
+    for (int word_index = numerator_length - 1; word_index >= 0; --word_index) {
+        auto word_high = numerator.m_words[word_index] >> 16;
+        auto word_low = numerator.m_words[word_index] & ((1 << 16) - 1);
+
+        auto number_to_divide_high = (remainder_word << 16) | word_high;
+        auto quotient_high = number_to_divide_high / denominator;
+        remainder_word = number_to_divide_high % denominator;
+
+        auto number_to_divide_low = remainder_word << 16 | word_low;
+        auto quotient_low = number_to_divide_low / denominator;
+        remainder_word = number_to_divide_low % denominator;
+
+        quotient.m_words[word_index] = (quotient_high << 16) | quotient_low;
+    }
+    remainder.set_to(remainder_word);
+}
+
+ALWAYS_INLINE void UnsignedBigInteger::shift_left_by_n_words(
+    const UnsignedBigInteger& number,
+    const size_t number_of_words,
+    UnsignedBigInteger& output)
+{
+    // shifting left by N words means just inserting N zeroes to the beginning of the words vector
+    output.set_to_0();
+    output.m_words.resize_and_keep_capacity(number_of_words + number.length());
+
+    __builtin_memset(output.m_words.data(), 0, number_of_words * sizeof(unsigned));
+    __builtin_memcpy(&output.m_words.data()[number_of_words], number.m_words.data(), number.m_words.size() * sizeof(unsigned));
+}
+
+/**
+ * Returns the word at a requested index in the result of a shift operation
+ */
+ALWAYS_INLINE u32 UnsignedBigInteger::shift_left_get_one_word(
+    const UnsignedBigInteger& number,
+    const size_t num_bits,
+    const size_t result_word_index)
+{
+    // "<= length()" (rather than length() - 1) is intentional,
+    // The result inedx of length() is used when calculating the carry word
+    ASSERT(result_word_index <= number.length());
+    ASSERT(num_bits <= UnsignedBigInteger::BITS_IN_WORD);
+    u32 result = 0;
+
+    // we need to check for "num_bits != 0" since shifting right by 32 is apparently undefined behaviour!
+    if (result_word_index > 0 && num_bits != 0) {
+        result += number.m_words[result_word_index - 1] >> (UnsignedBigInteger::BITS_IN_WORD - num_bits);
+    }
+    if (result_word_index < number.length() && num_bits < 32) {
+        result += number.m_words[result_word_index] << num_bits;
+    }
+    return result;
+}
+}
+
+void AK::Formatter<Crypto::UnsignedBigInteger>::format(FormatBuilder& fmtbuilder, const Crypto::UnsignedBigInteger& value)
+{
+    if (value.is_invalid())
+        return Formatter<StringView>::format(fmtbuilder, "invalid");
+
+    StringBuilder builder;
+    for (int i = value.length() - 1; i >= 0; --i)
+        builder.appendff("{}|", value.words()[i]);
+
+    return Formatter<StringView>::format(fmtbuilder, builder.string_view());
+}

Userland/Libraries/LibCrypto/BigInt/UnsignedBigInteger.h

@@ -0,0 +1,156 @@
+/*
+ * Copyright (c) 2020, Itamar S. <itamar8910@gmail.com>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this
+ *    list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ *    this list of conditions and the following disclaimer in the documentation
+ *    and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#pragma once
+
+#include <AK/ByteBuffer.h>
+#include <AK/LogStream.h>
+#include <AK/Span.h>
+#include <AK/String.h>
+#include <AK/Types.h>
+#include <AK/Vector.h>
+
+namespace Crypto {
+
+struct UnsignedDivisionResult;
+constexpr size_t STARTING_WORD_SIZE = 512;
+
+class UnsignedBigInteger {
+public:
+    UnsignedBigInteger(u32 x) { m_words.append(x); }
+
+    explicit UnsignedBigInteger(AK::Vector<u32, STARTING_WORD_SIZE>&& words)
+        : m_words(move(words))
+    {
+    }
+
+    explicit UnsignedBigInteger(const u8* ptr, size_t length);
+
+    UnsignedBigInteger() { }
+
+    static UnsignedBigInteger create_invalid();
+
+    static UnsignedBigInteger import_data(const AK::StringView& data) { return import_data((const u8*)data.characters_without_null_termination(), data.length()); }
+    static UnsignedBigInteger import_data(const u8* ptr, size_t length)
+    {
+        return UnsignedBigInteger(ptr, length);
+    }
+
+    size_t export_data(Bytes, bool remove_leading_zeros = false) const;
+
+    static UnsignedBigInteger from_base10(const String& str);
+    String to_base10() const;
+
+    const AK::Vector<u32, STARTING_WORD_SIZE>& words() const { return m_words; }
+
+    void set_to_0();
+    void set_to(u32 other);
+    void set_to(const UnsignedBigInteger& other);
+
+    void invalidate()
+    {
+        m_is_invalid = true;
+        m_cached_trimmed_length = {};
+    }
+
+    bool is_invalid() const { return m_is_invalid; }
+
+    size_t length() const { return m_words.size(); }
+    // The "trimmed length" is the number of words after trimming leading zeroed words
+    size_t trimmed_length() const;
+
+    UnsignedBigInteger plus(const UnsignedBigInteger& other) const;
+    UnsignedBigInteger minus(const UnsignedBigInteger& other) const;
+    UnsignedBigInteger bitwise_or(const UnsignedBigInteger& other) const;
+    UnsignedBigInteger bitwise_and(const UnsignedBigInteger& other) const;
+    UnsignedBigInteger bitwise_xor(const UnsignedBigInteger& other) const;
+    UnsignedBigInteger bitwise_not() const;
+    UnsignedBigInteger shift_left(size_t num_bits) const;
+    UnsignedBigInteger multiplied_by(const UnsignedBigInteger& other) const;
+    UnsignedDivisionResult divided_by(const UnsignedBigInteger& divisor) const;
+
+    void set_bit_inplace(size_t bit_index);
+
+    static void add_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& output);
+    static void subtract_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& output);
+    static void bitwise_or_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& output);
+    static void bitwise_and_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& output);
+    static void bitwise_xor_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& output);
+    static void bitwise_not_without_allocation(const UnsignedBigInteger& left, UnsignedBigInteger& output);
+    static void shift_left_without_allocation(const UnsignedBigInteger& number, size_t bits_to_shift_by, UnsignedBigInteger& temp_result, UnsignedBigInteger& temp_plus, UnsignedBigInteger& output);
+    static void multiply_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& temp_shift_result, UnsignedBigInteger& temp_shift_plus, UnsignedBigInteger& temp_shift, UnsignedBigInteger& temp_plus, UnsignedBigInteger& output);
+    static void divide_without_allocation(const UnsignedBigInteger& numerator, const UnsignedBigInteger& denominator, UnsignedBigInteger& temp_shift_result, UnsignedBigInteger& temp_shift_plus, UnsignedBigInteger& temp_shift, UnsignedBigInteger& temp_minus, UnsignedBigInteger& quotient, UnsignedBigInteger& remainder);
+    static void divide_u16_without_allocation(const UnsignedBigInteger& numerator, u32 denominator, UnsignedBigInteger& quotient, UnsignedBigInteger& remainder);
+
+    bool operator==(const UnsignedBigInteger& other) const;
+    bool operator!=(const UnsignedBigInteger& other) const;
+    bool operator<(const UnsignedBigInteger& other) const;
+
+private:
+    ALWAYS_INLINE static void shift_left_by_n_words(const UnsignedBigInteger& number, size_t number_of_words, UnsignedBigInteger& output);
+    ALWAYS_INLINE static u32 shift_left_get_one_word(const UnsignedBigInteger& number, size_t num_bits, size_t result_word_index);
+
+    static constexpr size_t BITS_IN_WORD = 32;
+    // Little endian
+    // m_word[0] + m_word[1] * 256 + m_word[2] * 65536 + ...
+    AK::Vector<u32, STARTING_WORD_SIZE> m_words;
+
+    // Used to indicate a negative result, or a result of an invalid operation
+    bool m_is_invalid { false };
+
+    mutable Optional<size_t> m_cached_trimmed_length;
+};
+
+struct UnsignedDivisionResult {
+    Crypto::UnsignedBigInteger quotient;
+    Crypto::UnsignedBigInteger remainder;
+};
+
+}
+
+inline const LogStream&
+operator<<(const LogStream& stream, const Crypto::UnsignedBigInteger& value)
+{
+    if (value.is_invalid()) {
+        stream << "Invalid BigInt";
+        return stream;
+    }
+    for (int i = value.length() - 1; i >= 0; --i) {
+        stream << value.words()[i] << "|";
+    }
+    return stream;
+}
+
+template<>
+struct AK::Formatter<Crypto::UnsignedBigInteger> : Formatter<StringView> {
+    void format(FormatBuilder&, const Crypto::UnsignedBigInteger&);
+};
+
+inline Crypto::UnsignedBigInteger
+operator""_bigint(const char* string, size_t length)
+{
+    return Crypto::UnsignedBigInteger::from_base10({ string, length });
+}