Botan  1.10.9
powm_mnt.cpp
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1 /*
2 * Montgomery Exponentiation
3 * (C) 1999-2010 Jack Lloyd
4 *
5 * Distributed under the terms of the Botan license
6 */
7 
8 #include <botan/internal/def_powm.h>
9 #include <botan/numthry.h>
10 #include <botan/internal/mp_core.h>
11 
12 namespace Botan {
13 
14 /*
15 * Set the exponent
16 */
18  {
19  this->exp = exp;
20  exp_bits = exp.bits();
21  }
22 
23 /*
24 * Set the base
25 */
27  {
28  window_bits = Power_Mod::window_bits(exp.bits(), base.bits(), hints);
29 
30  g.resize((1 << window_bits));
31 
32  SecureVector<word> z(2 * (mod_words + 1));
33  SecureVector<word> workspace(z.size());
34 
35  g[0] = 1;
36 
37  bigint_monty_mul(&z[0], z.size(),
38  g[0].data(), g[0].size(), g[0].sig_words(),
39  R2.data(), R2.size(), R2.sig_words(),
40  modulus.data(), mod_words, mod_prime,
41  &workspace[0]);
42 
43  g[0].assign(&z[0], mod_words + 1);
44 
45  g[1] = (base >= modulus) ? (base % modulus) : base;
46 
47  bigint_monty_mul(&z[0], z.size(),
48  g[1].data(), g[1].size(), g[1].sig_words(),
49  R2.data(), R2.size(), R2.sig_words(),
50  modulus.data(), mod_words, mod_prime,
51  &workspace[0]);
52 
53  g[1].assign(&z[0], mod_words + 1);
54 
55  const BigInt& x = g[1];
56  const size_t x_sig = x.sig_words();
57 
58  for(size_t i = 1; i != g.size(); ++i)
59  {
60  const BigInt& y = g[i-1];
61  const size_t y_sig = y.sig_words();
62 
63  zeroise(z);
64  bigint_monty_mul(&z[0], z.size(),
65  x.data(), x.size(), x_sig,
66  y.data(), y.size(), y_sig,
67  modulus.data(), mod_words, mod_prime,
68  &workspace[0]);
69 
70  g[i].assign(&z[0], mod_words + 1);
71  }
72  }
73 
74 /*
75 * Compute the result
76 */
78  {
79  const size_t exp_nibbles = (exp_bits + window_bits - 1) / window_bits;
80 
81  BigInt x = R_mod;
82  SecureVector<word> z(2 * (mod_words + 1));
83  SecureVector<word> workspace(2 * (mod_words + 1));
84 
85  for(size_t i = exp_nibbles; i > 0; --i)
86  {
87  for(size_t k = 0; k != window_bits; ++k)
88  {
89  zeroise(z);
90 
91  bigint_monty_sqr(&z[0], z.size(),
92  x.data(), x.size(), x.sig_words(),
93  modulus.data(), mod_words, mod_prime,
94  &workspace[0]);
95 
96  x.assign(&z[0], mod_words + 1);
97  }
98 
99  const u32bit nibble = exp.get_substring(window_bits*(i-1), window_bits);
100 
101  const BigInt& y = g[nibble];
102 
103  zeroise(z);
104  bigint_monty_mul(&z[0], z.size(),
105  x.data(), x.size(), x.sig_words(),
106  y.data(), y.size(), y.sig_words(),
107  modulus.data(), mod_words, mod_prime,
108  &workspace[0]);
109 
110  x.assign(&z[0], mod_words + 1);
111  }
112 
113  x.get_reg().resize(2*mod_words+1);
114 
115  bigint_monty_redc(&x[0], x.size(),
116  modulus.data(), mod_words, mod_prime,
117  &workspace[0]);
118 
119  x.get_reg().resize(mod_words+1);
120 
121  return x;
122  }
123 
124 /*
125 * Montgomery_Exponentiator Constructor
126 */
129  {
130  // Montgomery reduction only works for positive odd moduli
131  if(!mod.is_positive() || mod.is_even())
132  throw Invalid_Argument("Montgomery_Exponentiator: invalid modulus");
133 
134  window_bits = 0;
135  this->hints = hints;
136  modulus = mod;
137  exp_bits = 0;
138 
139  mod_words = modulus.sig_words();
140 
141  BigInt r(BigInt::Power2, mod_words * BOTAN_MP_WORD_BITS);
142  mod_prime = (((r * inverse_mod(r, mod)) - 1) / mod).word_at(0);
143 
144  R_mod = r % modulus;
145 
146  R2 = (R_mod * R_mod) % modulus;
147  }
148 
149 }
size_t sig_words() const
Definition: bigint.h:290
void resize(size_t n)
Definition: secmem.h:211
bool is_even() const
Definition: bigint.h:158
void assign(const word x[], size_t length)
Definition: bigint.h:337
void set_exponent(const BigInt &)
Definition: powm_mnt.cpp:17
SecureVector< word > & get_reg()
Definition: bigint.h:325
std::invalid_argument Invalid_Argument
Definition: exceptn.h:20
size_t size() const
Definition: bigint.h:284
void bigint_monty_sqr(word z[], size_t z_size, const word x[], size_t x_size, size_t x_sw, const word p[], size_t p_size, word p_dash, word workspace[])
Definition: mp_monty.cpp:84
u32bit get_substring(size_t offset, size_t length) const
Definition: bigint.cpp:168
size_t bits() const
Definition: bigint.cpp:253
void bigint_monty_redc(word z[], size_t z_size, const word p[], size_t p_size, word p_dash, word workspace[])
Definition: mp_monty.cpp:21
Montgomery_Exponentiator(const BigInt &, Power_Mod::Usage_Hints)
Definition: powm_mnt.cpp:127
GMP_MPZ exp
Definition: gmp_powm.cpp:29
const word * data() const
Definition: bigint.h:317
GMP_MPZ mod
Definition: gmp_powm.cpp:29
size_t size() const
Definition: secmem.h:29
static size_t window_bits(size_t exp_bits, size_t base_bits, Power_Mod::Usage_Hints hints)
Definition: pow_mod.cpp:119
void bigint_monty_mul(word z[], size_t z_size, const word x[], size_t x_size, size_t x_sw, const word y[], size_t y_size, size_t y_sw, const word p[], size_t p_size, word p_dash, word workspace[])
Definition: mp_monty.cpp:69
BigInt inverse_mod(const BigInt &n, const BigInt &mod)
Definition: numthry.cpp:202
void set_base(const BigInt &)
Definition: powm_mnt.cpp:26
bool is_positive() const
Definition: bigint.h:251
BigInt r
Definition: numthry.cpp:26
void zeroise(MemoryRegion< T > &vec)
Definition: secmem.h:415
unsigned int u32bit
Definition: types.h:32
GMP_MPZ base
Definition: gmp_powm.cpp:29