randombit/botan | Build 13011071422 | source/src/lib/math/bigint/divide.cpp | Coveralls

21

void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r) {

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22

   q.cond_flip_sign(x.sign() != y.sign());

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24

   if(x.is_negative() && r.is_nonzero()) {

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25

      q -= 1;

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26

      r = y.abs() - r;

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28

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30

inline bool division_check(word q, word y2, word y1, word x3, word x2, word x1) {

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36

   word y3 = 0;

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37

   y1 = word_madd2(q, y1, &y3);

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38

   y2 = word_madd2(q, y2, &y3);

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40

   const word x[3] = {x1, x2, x3};

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41

   const word y[3] = {y1, y2, y3};

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43

   return bigint_ct_is_lt(x, 3, y, 3).as_bool();

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48

void ct_divide(const BigInt& x, const BigInt& y, BigInt& q_out, BigInt& r_out) {

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49

   if(y.is_zero()) {

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53

   const size_t x_words = x.sig_words();

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54

   const size_t y_words = y.sig_words();

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56

   const size_t x_bits = x.bits();

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58

   BigInt q = BigInt::with_capacity(x_words);

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59

   BigInt r = BigInt::with_capacity(y_words);

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60

   BigInt t = BigInt::with_capacity(y_words);  // a temporary

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62

   for(size_t i = 0; i != x_bits; ++i) {

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63

      const size_t b = x_bits - 1 - i;

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64

      const bool x_b = x.get_bit(b);

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66

      r <<= 1;

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67

      r.conditionally_set_bit(0, x_b);

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69

      const bool r_gte_y = bigint_sub3(t.mutable_data(), r._data(), r.size(), y._data(), y_words) == 0;

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71

      q.conditionally_set_bit(b, r_gte_y);

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72

      r.ct_cond_swap(r_gte_y, t);

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75

   sign_fixup(x, y, q, r);

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76

   r_out = r;

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77

   q_out = q;

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78

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80

BigInt ct_divide_pow2k(size_t k, const BigInt& y) {

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81

   BOTAN_ARG_CHECK(!y.is_zero(), "Cannot divide by zero");

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82

   BOTAN_ARG_CHECK(!y.is_negative(), "Negative divisor not supported");

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83

   BOTAN_ARG_CHECK(k > 1, "Invalid k");

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85

   const size_t x_bits = k + 1;

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86

   const size_t y_bits = y.bits();

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88

   if(x_bits < y_bits) {

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89

      return BigInt::zero();

258✔

92

   BOTAN_ASSERT_NOMSG(y_bits >= 1);

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93

   const size_t x_words = (x_bits + BOTAN_MP_WORD_BITS - 1) / BOTAN_MP_WORD_BITS;

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94

   const size_t y_words = y.sig_words();

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96

   BigInt q = BigInt::with_capacity(x_words);

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97

   BigInt r = BigInt::with_capacity(y_words + 1);

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98

   BigInt t = BigInt::with_capacity(y_words + 1);  // a temporary

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100

   r.set_bit(y_bits - 1);

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101

   for(size_t i = y_bits - 1; i != x_bits; ++i) {

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102

      const size_t b = x_bits - 1 - i;

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104

      if(i >= y_bits) {

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105

         bigint_shl1(r.mutable_data(), r.size(), r.size(), 1);

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108

      const bool r_gte_y = bigint_sub3(t.mutable_data(), r._data(), r.size(), y._data(), y_words) == 0;

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110

      q.conditionally_set_bit(b, r_gte_y);

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112

      bigint_cnd_swap(static_cast<word>(r_gte_y), r.mutable_data(), t.mutable_data(), y_words + 1);

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117

   return q;

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118

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120

void ct_divide_word(const BigInt& x, word y, BigInt& q_out, word& r_out) {

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121

   if(y == 0) {

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125

   const size_t x_words = x.sig_words();

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126

   const size_t x_bits = x.bits();

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128

   BigInt q = BigInt::with_capacity(x_words);

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131

   for(size_t i = 0; i != x_bits; ++i) {

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132

      const size_t b = x_bits - 1 - i;

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133

      const bool x_b = x.get_bit(b);

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135

      const auto r_carry = CT::Mask<word>::expand_top_bit(r);

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137

      r <<= 1;

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138

      r += x_b;

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140

      const auto r_gte_y = CT::Mask<word>::is_gte(r, y) | r_carry;

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141

      q.conditionally_set_bit(b, r_gte_y.as_bool());

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142

      r = r_gte_y.select(r - y, r);

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145

   if(x.is_negative()) {

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146

      q.flip_sign();

19✔

147

      if(r != 0) {

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148

         --q;

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149

         r = y - r;

15✔

153

   r_out = r;

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154

   q_out = q;

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155

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157

word ct_mod_word(const BigInt& x, word y) {

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158

   BOTAN_ARG_CHECK(x.is_positive(), "The argument x must be positive");

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159

   BOTAN_ARG_CHECK(y != 0, "Cannot divide by zero");

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161

   const size_t x_bits = x.bits();

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163

   word r = 0;

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165

   for(size_t i = 0; i != x_bits; ++i) {

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166

      const size_t b = x_bits - 1 - i;

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167

      const bool x_b = x.get_bit(b);

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169

      const auto r_carry = CT::Mask<word>::expand_top_bit(r);

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171

      r <<= 1;

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172

      r += x_b;

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174

      const auto r_gte_y = CT::Mask<word>::is_gte(r, y) | r_carry;

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175

      r = r_gte_y.select(r - y, r);

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178

   return r;

4,334✔

181

BigInt ct_modulo(const BigInt& x, const BigInt& y) {

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182

   if(y.is_negative() || y.is_zero()) {

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186

   const size_t y_words = y.sig_words();

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188

   const size_t x_bits = x.bits();

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190

   BigInt r = BigInt::with_capacity(y_words);

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191

   BigInt t = BigInt::with_capacity(y_words);

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193

   for(size_t i = 0; i != x_bits; ++i) {

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194

      const size_t b = x_bits - 1 - i;

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195

      const bool x_b = x.get_bit(b);

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197

      r <<= 1;

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198

      r.conditionally_set_bit(0, x_b);

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200

      const bool r_gte_y = bigint_sub3(t.mutable_data(), r._data(), r.size(), y._data(), y_words) == 0;

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202

      r.ct_cond_swap(r_gte_y, t);

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205

   if(x.is_negative()) {

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206

      if(r.is_nonzero()) {

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207

         r = y - r;

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211

   return r;

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212

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219

void vartime_divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out) {

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220

   if(y_arg.is_zero()) {

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224

   const size_t y_words = y_arg.sig_words();

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226

   BOTAN_ASSERT_NOMSG(y_words > 0);

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228

   BigInt y = y_arg;

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230

   BigInt r = x;

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231

   BigInt q = BigInt::zero();

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232

   secure_vector<word> ws;

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234

   r.set_sign(BigInt::Positive);

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235

   y.set_sign(BigInt::Positive);

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238

   const size_t shifts = y.top_bits_free();

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240

   y <<= shifts;

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241

   r <<= shifts;

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   const size_t t = y_words - 1;

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245

   const size_t n = std::max(y_words, r.sig_words()) - 1;  // r may have changed size however

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247

   BOTAN_ASSERT_NOMSG(n >= t);

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249

   q.grow_to(n - t + 1);

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251

   word* q_words = q.mutable_data();

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253

   BigInt shifted_y = y << (BOTAN_MP_WORD_BITS * (n - t));

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256

   q_words[n - t] = r.reduce_below(shifted_y, ws);

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258

   const word y_t0 = y.word_at(t);

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259

   const word y_t1 = y.word_at(t - 1);

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260

   BOTAN_DEBUG_ASSERT((y_t0 >> (BOTAN_MP_WORD_BITS - 1)) == 1);

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262

   for(size_t j = n; j != t; --j) {

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      const word x_j0 = r.word_at(j);

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      const word x_j1 = r.word_at(j - 1);

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265

      const word x_j2 = r.word_at(j - 2);

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267

      word qjt = bigint_divop_vartime(x_j0, x_j1, y_t0);

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269

      qjt = CT::Mask<word>::is_equal(x_j0, y_t0).select(WordInfo<word>::max, qjt);

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272

      qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);

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273

      qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);

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274

      BOTAN_DEBUG_ASSERT(division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2) == false);

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276

      shifted_y >>= BOTAN_MP_WORD_BITS;

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280

      r -= qjt * shifted_y;

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281

      qjt -= r.is_negative();

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282

      r += static_cast<word>(r.is_negative()) * shifted_y;

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284

      q_words[j - t - 1] = qjt;

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287

   r >>= shifts;

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289

   sign_fixup(x, y_arg, q, r);

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291

   r_out = r;

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292

   q_out = q;

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293

1,744,180✔

randombit / botan / 13011071422

Source File
Press 'n' to go to next uncovered line, 'b' for previous

1	/*
2	* Division Algorithms
3	* (C) 1999-2007,2012,2018,2021 Jack Lloyd
4	*
5	* Botan is released under the Simplified BSD License (see license.txt)
6	*/
7
8	#include <botan/internal/divide.h>
9
10	#include <botan/internal/bit_ops.h>
11	#include <botan/internal/ct_utils.h>
12	#include <botan/internal/mp_core.h>
13
14	namespace Botan {
15
16	namespace {
17
18	/*
19	* Handle signed operands, if necessary
20	*/
21	void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r) {	355,478✔
22	q.cond_flip_sign(x.sign() != y.sign());	355,478✔
23
24	if(x.is_negative() && r.is_nonzero()) {	357,051✔
25	q -= 1;	1,569✔
26	r = y.abs() - r;	4,707✔
27	}
28	}	355,478✔
29
30	inline bool division_check(word q, word y2, word y1, word x3, word x2, word x1) {	2,817,666✔
31	/*
32	Compute (y3,y2,y1) = (y2,y1) * q
33	and return true if (y3,y2,y1) > (x3,x2,x1)
34	*/
35
36	word y3 = 0;	2,817,666✔
37	y1 = word_madd2(q, y1, &y3);	2,817,666✔
38	y2 = word_madd2(q, y2, &y3);	2,817,666✔
39
40	const word x[3] = {x1, x2, x3};	2,817,666✔
41	const word y[3] = {y1, y2, y3};	2,817,666✔
42
43	return bigint_ct_is_lt(x, 3, y, 3).as_bool();	2,817,666✔
44	}
45
46	} // namespace
47
48	void ct_divide(const BigInt& x, const BigInt& y, BigInt& q_out, BigInt& r_out) {	6,642✔
49	if(y.is_zero()) {	11,260✔
50	throw Invalid_Argument("ct_divide: cannot divide by zero");	×
51	}
52
53	const size_t x_words = x.sig_words();	6,642✔
54	const size_t y_words = y.sig_words();	6,642✔
55
56	const size_t x_bits = x.bits();	6,642✔
57
58	BigInt q = BigInt::with_capacity(x_words);	6,642✔
59	BigInt r = BigInt::with_capacity(y_words);	6,642✔
60	BigInt t = BigInt::with_capacity(y_words); // a temporary	6,642✔
61
62	for(size_t i = 0; i != x_bits; ++i) {	6,043,280✔
63	const size_t b = x_bits - 1 - i;	6,036,638✔
64	const bool x_b = x.get_bit(b);	6,036,638✔
65
66	r <<= 1;	6,036,638✔
67	r.conditionally_set_bit(0, x_b);	6,036,638✔
68
69	const bool r_gte_y = bigint_sub3(t.mutable_data(), r._data(), r.size(), y._data(), y_words) == 0;	6,036,638✔
70
71	q.conditionally_set_bit(b, r_gte_y);	6,036,638✔
72	r.ct_cond_swap(r_gte_y, t);	6,036,638✔
73	}
74
75	sign_fixup(x, y, q, r);	6,642✔
76	r_out = r;	6,642✔
77	q_out = q;	6,642✔
78	}	19,921✔
79
80	BigInt ct_divide_pow2k(size_t k, const BigInt& y) {	114,893✔
81	BOTAN_ARG_CHECK(!y.is_zero(), "Cannot divide by zero");	115,271✔
82	BOTAN_ARG_CHECK(!y.is_negative(), "Negative divisor not supported");	114,893✔
83	BOTAN_ARG_CHECK(k > 1, "Invalid k");	114,893✔
84
85	const size_t x_bits = k + 1;	114,893✔
86	const size_t y_bits = y.bits();	114,893✔
87
88	if(x_bits < y_bits) {	114,893✔
89	return BigInt::zero();	258✔
90	}
91
92	BOTAN_ASSERT_NOMSG(y_bits >= 1);	114,635✔
93	const size_t x_words = (x_bits + BOTAN_MP_WORD_BITS - 1) / BOTAN_MP_WORD_BITS;	114,635✔
94	const size_t y_words = y.sig_words();	114,635✔
95
96	BigInt q = BigInt::with_capacity(x_words);	114,635✔
97	BigInt r = BigInt::with_capacity(y_words + 1);	114,635✔
98	BigInt t = BigInt::with_capacity(y_words + 1); // a temporary	114,635✔
99
100	r.set_bit(y_bits - 1);	114,635✔
101	for(size_t i = y_bits - 1; i != x_bits; ++i) {	34,374,655✔
102	const size_t b = x_bits - 1 - i;	34,260,020✔
103
104	if(i >= y_bits) {	34,260,020✔
105	bigint_shl1(r.mutable_data(), r.size(), r.size(), 1);	34,145,385✔
106	}
107
108	const bool r_gte_y = bigint_sub3(t.mutable_data(), r._data(), r.size(), y._data(), y_words) == 0;	34,260,020✔
109
110	q.conditionally_set_bit(b, r_gte_y);	34,260,020✔
111
112	bigint_cnd_swap(static_cast<word>(r_gte_y), r.mutable_data(), t.mutable_data(), y_words + 1);	34,260,020✔
113	}
114
115	// No need for sign fixup
116
117	return q;	114,635✔
118	}	229,270✔
119
120	void ct_divide_word(const BigInt& x, word y, BigInt& q_out, word& r_out) {	594,685✔
121	if(y == 0) {	594,685✔
122	throw Invalid_Argument("ct_divide_word: cannot divide by zero");	×
123	}
124
125	const size_t x_words = x.sig_words();	594,685✔
126	const size_t x_bits = x.bits();	594,685✔
127
128	BigInt q = BigInt::with_capacity(x_words);	594,685✔
129	word r = 0;
130
131	for(size_t i = 0; i != x_bits; ++i) {	59,200,113✔
132	const size_t b = x_bits - 1 - i;	58,605,428✔
133	const bool x_b = x.get_bit(b);	58,605,428✔
134
135	const auto r_carry = CT::Mask<word>::expand_top_bit(r);	58,605,428✔
136
137	r <<= 1;	58,605,428✔
138	r += x_b;	58,605,428✔
139
140	const auto r_gte_y = CT::Mask<word>::is_gte(r, y) \| r_carry;	58,605,428✔
141	q.conditionally_set_bit(b, r_gte_y.as_bool());	58,605,428✔
142	r = r_gte_y.select(r - y, r);	58,605,428✔
143	}
144
145	if(x.is_negative()) {	594,685✔
146	q.flip_sign();	19✔
147	if(r != 0) {	19✔
148	--q;	15✔
149	r = y - r;	15✔
150	}
151	}
152
153	r_out = r;	594,685✔
154	q_out = q;	594,685✔
155	}	594,685✔
156
157	word ct_mod_word(const BigInt& x, word y) {	4,334✔
158	BOTAN_ARG_CHECK(x.is_positive(), "The argument x must be positive");	4,334✔
159	BOTAN_ARG_CHECK(y != 0, "Cannot divide by zero");	4,334✔
160
161	const size_t x_bits = x.bits();	4,334✔
162
163	word r = 0;	4,334✔
164
165	for(size_t i = 0; i != x_bits; ++i) {	3,018,772✔
166	const size_t b = x_bits - 1 - i;	3,014,438✔
167	const bool x_b = x.get_bit(b);	3,014,438✔
168
169	const auto r_carry = CT::Mask<word>::expand_top_bit(r);	3,014,438✔
170
171	r <<= 1;	3,014,438✔
172	r += x_b;	3,014,438✔
173
174	const auto r_gte_y = CT::Mask<word>::is_gte(r, y) \| r_carry;	3,014,438✔
175	r = r_gte_y.select(r - y, r);	3,014,438✔
176	}
177
178	return r;	4,334✔
179	}
180
181	BigInt ct_modulo(const BigInt& x, const BigInt& y) {	6,476✔
182	if(y.is_negative() \|\| y.is_zero()) {	12,952✔
183	throw Invalid_Argument("ct_modulo requires y > 0");	×
184	}
185
186	const size_t y_words = y.sig_words();	6,476✔
187
188	const size_t x_bits = x.bits();	6,476✔
189
190	BigInt r = BigInt::with_capacity(y_words);	6,476✔
191	BigInt t = BigInt::with_capacity(y_words);	6,476✔
192
193	for(size_t i = 0; i != x_bits; ++i) {	8,605,675✔
194	const size_t b = x_bits - 1 - i;	8,599,199✔
195	const bool x_b = x.get_bit(b);	8,599,199✔
196
197	r <<= 1;	8,599,199✔
198	r.conditionally_set_bit(0, x_b);	8,599,199✔
199
200	const bool r_gte_y = bigint_sub3(t.mutable_data(), r._data(), r.size(), y._data(), y_words) == 0;	8,599,199✔
201
202	r.ct_cond_swap(r_gte_y, t);	8,599,199✔
203	}
204
205	if(x.is_negative()) {	6,476✔
206	if(r.is_nonzero()) {	1,208✔
207	r = y - r;	1,204✔
208	}
209	}
210
211	return r;	6,476✔
212	}	6,476✔
213
214	/*
215	* Solve x = q * y + r
216	*
217	* See Handbook of Applied Cryptography section 14.2.5
218	*/
219	void vartime_divide(const BigInt& x, const BigInt& y_arg, BigInt& q_out, BigInt& r_out) {	348,836✔
220	if(y_arg.is_zero()) {	348,912✔
221	throw Invalid_Argument("vartime_divide: cannot divide by zero");	×
222	}
223
224	const size_t y_words = y_arg.sig_words();	348,836✔
225
226	BOTAN_ASSERT_NOMSG(y_words > 0);	348,836✔
227
228	BigInt y = y_arg;	348,836✔
229
230	BigInt r = x;	348,836✔
231	BigInt q = BigInt::zero();	348,836✔
232	secure_vector<word> ws;	348,836✔
233
234	r.set_sign(BigInt::Positive);	348,836✔
235	y.set_sign(BigInt::Positive);	348,836✔
236
237	// Calculate shifts needed to normalize y with high bit set
238	const size_t shifts = y.top_bits_free();	348,836✔
239
240	y <<= shifts;	348,836✔
241	r <<= shifts;	348,836✔
242
243	// we know y has not changed size, since we only shifted up to set high bit
244	const size_t t = y_words - 1;	348,836✔
245	const size_t n = std::max(y_words, r.sig_words()) - 1; // r may have changed size however	697,672✔
246
247	BOTAN_ASSERT_NOMSG(n >= t);	348,836✔
248
249	q.grow_to(n - t + 1);	348,836✔
250
251	word* q_words = q.mutable_data();	348,836✔
252
253	BigInt shifted_y = y << (BOTAN_MP_WORD_BITS * (n - t));	348,836✔
254
255	// Set q_{n-t} to number of times r > shifted_y
256	q_words[n - t] = r.reduce_below(shifted_y, ws);	348,836✔
257
258	const word y_t0 = y.word_at(t);	348,836✔
259	const word y_t1 = y.word_at(t - 1);	348,836✔
260	BOTAN_DEBUG_ASSERT((y_t0 >> (BOTAN_MP_WORD_BITS - 1)) == 1);	348,836✔
261
262	for(size_t j = n; j != t; --j) {	1,757,669✔
263	const word x_j0 = r.word_at(j);	1,408,833✔
264	const word x_j1 = r.word_at(j - 1);	1,408,833✔
265	const word x_j2 = r.word_at(j - 2);	1,408,833✔
266
267	word qjt = bigint_divop_vartime(x_j0, x_j1, y_t0);	1,408,833✔
268
269	qjt = CT::Mask<word>::is_equal(x_j0, y_t0).select(WordInfo<word>::max, qjt);	1,408,833✔
270
271	// Per HAC 14.23, this operation is required at most twice
272	qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);	1,408,833✔
273	qjt -= division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2);	1,408,833✔
274	BOTAN_DEBUG_ASSERT(division_check(qjt, y_t0, y_t1, x_j0, x_j1, x_j2) == false);	1,408,833✔
275
276	shifted_y >>= BOTAN_MP_WORD_BITS;	1,408,833✔
277	// Now shifted_y == y << (BOTAN_MP_WORD_BITS * (j-t-1))
278
279	// TODO this sequence could be better
280	r -= qjt * shifted_y;	1,408,833✔
281	qjt -= r.is_negative();	1,408,833✔
282	r += static_cast<word>(r.is_negative()) * shifted_y;	1,408,833✔
283
284	q_words[j - t - 1] = qjt;	1,408,833✔
285	}
286
287	r >>= shifts;	348,836✔
288
289	sign_fixup(x, y_arg, q, r);	348,836✔
290
291	r_out = r;	348,836✔
292	q_out = q;	348,836✔
293	}	1,744,180✔
294
295	} // namespace Botan

randombit / botan / 13011071422

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