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/*
* BigInt Base
* (C) 1999-2011,2012,2014,2019 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/bigint.h>
#include <botan/internal/mp_core.h>
#include <botan/internal/rounding.h>
#include <botan/internal/bit_ops.h>
#include <botan/internal/ct_utils.h>
#include <botan/loadstor.h>
namespace Botan {
BigInt::BigInt(const word words[], size_t length)
{
m_data.set_words(words, length);
}
/*
* Construct a BigInt from a regular number
*/
BigInt::BigInt(uint64_t n)
{
if(n > 0)
{
#if BOTAN_MP_WORD_BITS == 32
m_data.set_word_at(0, static_cast<word>(n));
m_data.set_word_at(1, static_cast<word>(n >> 32));
#else
m_data.set_word_at(0, n);
#endif
}
}
/*
* Construct a BigInt of the specified size
*/
BigInt::BigInt(Sign s, size_t size)
{
m_data.set_size(size);
m_signedness = s;
}
/*
* Construct a BigInt from a string
*/
BigInt::BigInt(const std::string& str)
{
Base base = Decimal;
size_t markers = 0;
bool negative = false;
if(str.length() > 0 && str[0] == '-')
{
markers += 1;
negative = true;
}
if(str.length() > markers + 2 && str[markers ] == '0' &&
str[markers + 1] == 'x')
{
markers += 2;
base = Hexadecimal;
}
*this = decode(cast_char_ptr_to_uint8(str.data()) + markers,
str.length() - markers, base);
if(negative) set_sign(Negative);
else set_sign(Positive);
}
BigInt::BigInt(const uint8_t input[], size_t length)
{
binary_decode(input, length);
}
/*
* Construct a BigInt from an encoded BigInt
*/
BigInt::BigInt(const uint8_t input[], size_t length, Base base)
{
*this = decode(input, length, base);
}
BigInt::BigInt(const uint8_t buf[], size_t length, size_t max_bits)
{
if(8 * length > max_bits)
length = (max_bits + 7) / 8;
binary_decode(buf, length);
if(8 * length > max_bits)
*this >>= (8 - (max_bits % 8));
}
/*
* Construct a BigInt from an encoded BigInt
*/
BigInt::BigInt(RandomNumberGenerator& rng, size_t bits, bool set_high_bit)
{
randomize(rng, bits, set_high_bit);
}
uint8_t BigInt::byte_at(size_t n) const
{
return get_byte(sizeof(word) - (n % sizeof(word)) - 1,
word_at(n / sizeof(word)));
}
int32_t BigInt::cmp_word(word other) const
{
if(is_negative())
return -1; // other is positive ...
const size_t sw = this->sig_words();
if(sw > 1)
return 1; // must be larger since other is just one word ...
return bigint_cmp(this->data(), sw, &other, 1);
}
/*
* Comparison Function
*/
int32_t BigInt::cmp(const BigInt& other, bool check_signs) const
{
if(check_signs)
{
if(other.is_positive() && this->is_negative())
return -1;
if(other.is_negative() && this->is_positive())
return 1;
if(other.is_negative() && this->is_negative())
return (-bigint_cmp(this->data(), this->size(),
other.data(), other.size()));
}
return bigint_cmp(this->data(), this->size(),
other.data(), other.size());
}
bool BigInt::is_equal(const BigInt& other) const
{
if(this->sign() != other.sign())
return false;
return bigint_ct_is_eq(this->data(), this->sig_words(),
other.data(), other.sig_words()).is_set();
}
bool BigInt::is_less_than(const BigInt& other) const
{
if(this->is_negative() && other.is_positive())
return true;
if(this->is_positive() && other.is_negative())
return false;
if(other.is_negative() && this->is_negative())
{
return bigint_ct_is_lt(other.data(), other.sig_words(),
this->data(), this->sig_words()).is_set();
}
return bigint_ct_is_lt(this->data(), this->sig_words(),
other.data(), other.sig_words()).is_set();
}
void BigInt::encode_words(word out[], size_t size) const
{
const size_t words = sig_words();
if(words > size)
throw Encoding_Error("BigInt::encode_words value too large to encode");
clear_mem(out, size);
copy_mem(out, data(), words);
}
size_t BigInt::Data::calc_sig_words() const
{
const size_t sz = m_reg.size();
size_t sig = sz;
word sub = 1;
for(size_t i = 0; i != sz; ++i)
{
const word w = m_reg[sz - i - 1];
sub &= ct_is_zero(w);
sig -= sub;
}
/*
* This depends on the data so is poisoned, but unpoison it here as
* later conditionals are made on the size.
*/
CT::unpoison(sig);
return sig;
}
/*
* Return bits {offset...offset+length}
*/
uint32_t BigInt::get_substring(size_t offset, size_t length) const
{
if(length == 0 || length > 32)
throw Invalid_Argument("BigInt::get_substring invalid substring length");
const uint32_t mask = 0xFFFFFFFF >> (32 - length);
const size_t word_offset = offset / BOTAN_MP_WORD_BITS;
const size_t wshift = (offset % BOTAN_MP_WORD_BITS);
/*
* The substring is contained within one or at most two words. The
* offset and length are not secret, so we can perform conditional
* operations on those values.
*/
const word w0 = word_at(word_offset);
if(wshift == 0 || (offset + length) / BOTAN_MP_WORD_BITS == word_offset)
{
return static_cast<uint32_t>(w0 >> wshift) & mask;
}
else
{
const word w1 = word_at(word_offset + 1);
return static_cast<uint32_t>((w0 >> wshift) | (w1 << (BOTAN_MP_WORD_BITS - wshift))) & mask;
}
}
/*
* Convert this number to a uint32_t, if possible
*/
uint32_t BigInt::to_u32bit() const
{
if(is_negative())
throw Encoding_Error("BigInt::to_u32bit: Number is negative");
if(bits() > 32)
throw Encoding_Error("BigInt::to_u32bit: Number is too big to convert");
uint32_t out = 0;
for(size_t i = 0; i != 4; ++i)
out = (out << 8) | byte_at(3-i);
return out;
}
/*
* Set bit number n
*/
void BigInt::conditionally_set_bit(size_t n, bool set_it)
{
const size_t which = n / BOTAN_MP_WORD_BITS;
const word mask = static_cast<word>(set_it) << (n % BOTAN_MP_WORD_BITS);
m_data.set_word_at(which, word_at(which) | mask);
}
/*
* Clear bit number n
*/
void BigInt::clear_bit(size_t n)
{
const size_t which = n / BOTAN_MP_WORD_BITS;
if(which < size())
{
const word mask = ~(static_cast<word>(1) << (n % BOTAN_MP_WORD_BITS));
m_data.set_word_at(which, word_at(which) & mask);
}
}
size_t BigInt::bytes() const
{
return round_up(bits(), 8) / 8;
}
size_t BigInt::top_bits_free() const
{
const size_t words = sig_words();
const word top_word = word_at(words - 1);
const size_t bits_used = high_bit(top_word);
CT::unpoison(bits_used);
return BOTAN_MP_WORD_BITS - bits_used;
}
size_t BigInt::bits() const
{
const size_t words = sig_words();
if(words == 0)
return 0;
const size_t full_words = (words - 1) * BOTAN_MP_WORD_BITS;
const size_t top_bits = BOTAN_MP_WORD_BITS - top_bits_free();
return full_words + top_bits;
}
/*
* Calcluate the size in a certain base
*/
size_t BigInt::encoded_size(Base base) const
{
static const double LOG_2_BASE_10 = 0.30102999566;
if(base == Binary)
return bytes();
else if(base == Hexadecimal)
return 2*bytes();
else if(base == Decimal)
return static_cast<size_t>((bits() * LOG_2_BASE_10) + 1);
else
throw Invalid_Argument("Unknown base for BigInt encoding");
}
/*
* Return the negation of this number
*/
BigInt BigInt::operator-() const
{
BigInt x = (*this);
x.flip_sign();
return x;
}
size_t BigInt::reduce_below(const BigInt& p, secure_vector<word>& ws)
{
if(p.is_negative() || this->is_negative())
throw Invalid_Argument("BigInt::reduce_below both values must be positive");
const size_t p_words = p.sig_words();
if(size() < p_words + 1)
grow_to(p_words + 1);
if(ws.size() < p_words + 1)
ws.resize(p_words + 1);
clear_mem(ws.data(), ws.size());
size_t reductions = 0;
for(;;)
{
word borrow = bigint_sub3(ws.data(), data(), p_words + 1, p.data(), p_words);
if(borrow)
break;
++reductions;
swap_reg(ws);
}
return reductions;
}
void BigInt::ct_reduce_below(const BigInt& mod, secure_vector<word>& ws, size_t bound)
{
if(mod.is_negative() || this->is_negative())
throw Invalid_Argument("BigInt::ct_reduce_below both values must be positive");
const size_t mod_words = mod.sig_words();
grow_to(mod_words);
const size_t sz = size();
ws.resize(sz);
clear_mem(ws.data(), sz);
for(size_t i = 0; i != bound; ++i)
{
word borrow = bigint_sub3(ws.data(), data(), sz, mod.data(), mod_words);
CT::Mask<word>::is_zero(borrow).select_n(mutable_data(), ws.data(), data(), sz);
}
}
/*
* Return the absolute value of this number
*/
BigInt BigInt::abs() const
{
BigInt x = (*this);
x.set_sign(Positive);
return x;
}
void BigInt::binary_encode(uint8_t buf[]) const
{
this->binary_encode(buf, bytes());
}
/*
* Encode this number into bytes
*/
void BigInt::binary_encode(uint8_t output[], size_t len) const
{
const size_t full_words = len / sizeof(word);
const size_t extra_bytes = len % sizeof(word);
for(size_t i = 0; i != full_words; ++i)
{
const word w = word_at(i);
store_be(w, output + (len - (i+1)*sizeof(word)));
}
if(extra_bytes > 0)
{
const word w = word_at(full_words);
for(size_t i = 0; i != extra_bytes; ++i)
{
output[extra_bytes - i - 1] = get_byte(sizeof(word) - i - 1, w);
}
}
}
/*
* Set this number to the value in buf
*/
void BigInt::binary_decode(const uint8_t buf[], size_t length)
{
clear();
const size_t full_words = length / sizeof(word);
const size_t extra_bytes = length % sizeof(word);
secure_vector<word> reg((round_up(full_words + (extra_bytes > 0 ? 1 : 0), 8)));
for(size_t i = 0; i != full_words; ++i)
{
reg[i] = load_be<word>(buf + length - sizeof(word)*(i+1), 0);
}
if(extra_bytes > 0)
{
for(size_t i = 0; i != extra_bytes; ++i)
reg[full_words] = (reg[full_words] << 8) | buf[i];
}
m_data.swap(reg);
}
void BigInt::ct_cond_add(bool predicate, const BigInt& value)
{
if(this->is_negative() || value.is_negative())
throw Invalid_Argument("BigInt::ct_cond_add requires both values to be positive");
this->grow_to(1 + value.sig_words());
bigint_cnd_add(static_cast<word>(predicate),
this->mutable_data(), this->size(),
value.data(), value.sig_words());
}
void BigInt::ct_cond_swap(bool predicate, BigInt& other)
{
const size_t max_words = std::max(size(), other.size());
grow_to(max_words);
other.grow_to(max_words);
bigint_cnd_swap(predicate, this->mutable_data(), other.mutable_data(), max_words);
}
void BigInt::cond_flip_sign(bool predicate)
{
// This code is assuming Negative == 0, Positive == 1
const auto mask = CT::Mask<uint8_t>::expand(predicate);
const uint8_t current_sign = static_cast<uint8_t>(sign());
const uint8_t new_sign = mask.select(current_sign ^ 1, current_sign);
set_sign(static_cast<Sign>(new_sign));
}
void BigInt::ct_cond_assign(bool predicate, const BigInt& other)
{
const size_t t_words = size();
const size_t o_words = other.size();
if(o_words < t_words)
grow_to(o_words);
const size_t r_words = std::max(t_words, o_words);
const auto mask = CT::Mask<word>::expand(predicate);
for(size_t i = 0; i != r_words; ++i)
{
const word o_word = other.word_at(i);
const word t_word = this->word_at(i);
this->set_word_at(i, mask.select(o_word, t_word));
}
const bool different_sign = sign() != other.sign();
cond_flip_sign(predicate && different_sign);
}
#if defined(BOTAN_HAS_VALGRIND)
void BigInt::const_time_poison() const
{
CT::poison(m_data.const_data(), m_data.size());
}
void BigInt::const_time_unpoison() const
{
CT::unpoison(m_data.const_data(), m_data.size());
}
#endif
void BigInt::const_time_lookup(secure_vector<word>& output,
const std::vector<BigInt>& vec,
size_t idx)
{
const size_t words = output.size();
clear_mem(output.data(), output.size());
CT::poison(&idx, sizeof(idx));
for(size_t i = 0; i != vec.size(); ++i)
{
BOTAN_ASSERT(vec[i].size() >= words,
"Word size as expected in const_time_lookup");
const auto mask = CT::Mask<word>::is_equal(i, idx);
for(size_t w = 0; w != words; ++w)
{
const word viw = vec[i].word_at(w);
output[w] = mask.if_set_return(viw);
}
}
CT::unpoison(idx);
CT::unpoison(output.data(), output.size());
}
}