/* * Copyright (c) 2020, Itamar S. * Copyright (c) 2020-2021, Dex♪ * * SPDX-License-Identifier: BSD-2-Clause */ #include "UnsignedBigIntegerAlgorithms.h" #include #include namespace Crypto { /** * Complexity: O(N) where N is the number of words in the shorter value * Method: * Apply 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 UnsignedBigIntegerAlgorithms::bitwise_or_without_allocation( UnsignedBigInteger const& left, UnsignedBigInteger const& 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; } UnsignedBigInteger const *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 UnsignedBigIntegerAlgorithms::bitwise_and_without_allocation( UnsignedBigInteger const& left, UnsignedBigInteger const& 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; } UnsignedBigInteger const *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 UnsignedBigIntegerAlgorithms::bitwise_xor_without_allocation( UnsignedBigInteger const& left, UnsignedBigInteger const& 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; } UnsignedBigInteger const *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 UnsignedBigIntegerAlgorithms::bitwise_not_fill_to_one_based_index_without_allocation( UnsignedBigInteger const& right, size_t index, UnsignedBigInteger& output) { // If the value is invalid, the output value is invalid as well. if (right.is_invalid()) { output.invalidate(); return; } if (index == 0) { output.set_to_0(); return; } size_t size = (index + UnsignedBigInteger::BITS_IN_WORD - 1) / UnsignedBigInteger::BITS_IN_WORD; output.m_words.resize_and_keep_capacity(size); VERIFY(size > 0); for (size_t i = 0; i < size - 1; ++i) output.m_words[i] = ~(i < right.length() ? right.words()[i] : 0); index -= (size - 1) * UnsignedBigInteger::BITS_IN_WORD; auto last_word_index = size - 1; auto last_word = last_word_index < right.length() ? right.words()[last_word_index] : 0; output.m_words[last_word_index] = (NumericLimits::max() >> (UnsignedBigInteger::BITS_IN_WORD - index)) & ~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 UnsignedBigIntegerAlgorithms::shift_left_without_allocation( UnsignedBigInteger const& 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_into_accumulator_without_allocation(output, temp_result); } } void UnsignedBigIntegerAlgorithms::shift_left_by_n_words( UnsignedBigInteger const& number, 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)); } void UnsignedBigIntegerAlgorithms::shift_right_by_n_words( UnsignedBigInteger const& number, size_t number_of_words, UnsignedBigInteger& output) { // shifting right by N words means just not copying the first words output.set_to_0(); output.m_words.resize_and_keep_capacity(number.length() - number_of_words); __builtin_memcpy(output.m_words.data(), &number.m_words.data()[number_of_words], (number.m_words.size() - number_of_words) * sizeof(unsigned)); } /** * Returns the word at a requested index in the result of a shift operation */ ALWAYS_INLINE UnsignedBigInteger::Word UnsignedBigIntegerAlgorithms::shift_left_get_one_word( UnsignedBigInteger const& number, size_t num_bits, size_t result_word_index) { // "<= length()" (rather than length() - 1) is intentional, // The result index of length() is used when calculating the carry word VERIFY(result_word_index <= number.length()); VERIFY(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 behavior! 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; } }