Botan  1.10.17
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  g[i].grow_to(mod_words);
72  }
73  }
74 
75 /*
76 * Compute the result
77 */
79  {
80  const size_t exp_nibbles = (exp_bits + window_bits - 1) / window_bits;
81 
82  BigInt x = R_mod;
83  SecureVector<word> z(2 * (mod_words + 1));
84  SecureVector<word> workspace(2 * (mod_words + 1));
85  SecureVector<word> e(mod_words);
86 
87  for(size_t i = exp_nibbles; i > 0; --i)
88  {
89  for(size_t k = 0; k != window_bits; ++k)
90  {
91  zeroise(z);
92 
93  bigint_monty_sqr(&z[0], z.size(),
94  x.data(), x.size(), x.sig_words(),
95  modulus.data(), mod_words, mod_prime,
96  &workspace[0]);
97 
98  x.assign(&z[0], mod_words + 1);
99  }
100 
101  const u32bit nibble = exp.get_substring(window_bits*(i-1), window_bits);
102 
103  zeroise(z);
104 
105  BigInt::const_time_lookup(e, g, nibble);
106 
107  bigint_monty_mul(&z[0], z.size(),
108  x.data(), x.size(), x.sig_words(),
109  e.data(), e.size(), e.size(),
110  modulus.data(), mod_words, mod_prime,
111  &workspace[0]);
112 
113  x.assign(&z[0], mod_words + 1);
114  }
115 
116  x.get_reg().resize(2*mod_words+1);
117 
118  bigint_monty_redc(&x[0], x.size(),
119  modulus.data(), mod_words, mod_prime,
120  &workspace[0]);
121 
122  x.get_reg().resize(mod_words+1);
123 
124  return x;
125  }
126 
127 /*
128 * Montgomery_Exponentiator Constructor
129 */
132  {
133  // Montgomery reduction only works for positive odd moduli
134  if(!mod.is_positive() || mod.is_even())
135  throw Invalid_Argument("Montgomery_Exponentiator: invalid modulus");
136 
137  window_bits = 0;
138  this->hints = hints;
139  modulus = mod;
140  exp_bits = 0;
141 
142  mod_words = modulus.sig_words();
143 
144  BigInt r(BigInt::Power2, mod_words * BOTAN_MP_WORD_BITS);
145  mod_prime = (((r * inverse_mod(r, mod)) - 1) / mod).word_at(0);
146 
147  R_mod = r % modulus;
148 
149  R2 = (R_mod * R_mod) % modulus;
150  }
151 
152 }
void resize(size_t n)
Definition: secmem.h:217
void assign(const word x[], size_t length)
Definition: bigint.h:337
size_t bits() const
Definition: bigint.cpp:254
u32bit get_substring(size_t offset, size_t length) const
Definition: bigint.cpp:169
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
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
const word * data() const
Definition: bigint.h:317
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:130
size_t size() const
Definition: bigint.h:284
size_t sig_words() const
Definition: bigint.h:290
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
size_t size() const
Definition: secmem.h:29
BigInt inverse_mod(const BigInt &n, const BigInt &mod)
Definition: numthry.cpp:314
void set_base(const BigInt &)
Definition: powm_mnt.cpp:26
static void const_time_lookup(SecureVector< word > &output, const std::vector< BigInt > &vec, size_t idx)
Definition: bigint.cpp:382
void zeroise(MemoryRegion< T > &vec)
Definition: secmem.h:428
unsigned int u32bit
Definition: types.h:32