      1
      2
      3
      4
      5
      6
      7
      8
      9
     10
     11
     12
     13
     14
     15
     16
     17
     18
     19
     20
     21
     22
     23
     24
     25
     26
     27
     28
     29
     30
     31
     32
     33
     34
     35
     36
     37
     38
     39
     40
     41
     42
     43
     44
     45
     46
     47
     48
     49
     50
     51
     52
     53
     54
     55
     56
     57
     58
     59
     60
     61
     62
     63
     64
     65
     66
     67
     68
     69
     70
     71
     72
     73
     74
     75
     76
     77
     78
     79
     80
     81
     82
     83
     84
     85
     86
     87
     88
     89
     90
     91
     92
     93
     94
     95
     96
     97
     98
     99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    241
    242
    243
    244
    245
    246
    247
    248
    249
    250
    251
    252
    253
    254
    255
    256
    257
    258
    259
    260
    261
    262
    263
    264
    265
    266
    267
    268
    269
    270
    271
    272
    273
    274
    275
    276
    277
    278
    279
    280
    281
    282
    283
    284
    285
    286
    287
    288
    289
    290
    291
    292
    293
    294
    295
    296
    297
    298
    299
    300
    301
    302
    303
    304
    305
    306
    307
    308
    309
    310
    311
    312
    313
    314
    315
    316
    317
    318
    319
    320
    321
    322
    323
    324
    325
    326
    327
    328
    329
    330
    331
    332
    333
    334
    335

    // Copyright 2016 Brian Smith.
    //
    // Permission to use, copy, modify, and/or distribute this software for any
    // purpose with or without fee is hereby granted, provided that the above
    // copyright notice and this permission notice appear in all copies.
    //
    // THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES
    // WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    // MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY
    // SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    // WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
    // OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
    // CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

    use c;
    use core::marker::PhantomData;
    use super::*;
    use super::{Mont, elem_sqr_mul, elem_sqr_mul_acc};
    use super::elem::{binary_op, binary_op_assign};

    macro_rules! p256_limbs {
        [$limb_7:expr, $limb_6:expr, $limb_5:expr, $limb_4:expr,
         $limb_3:expr, $limb_2:expr, $limb_1:expr, $limb_0:expr] => {
            limbs![0, 0, 0, 0,
                   $limb_7, $limb_6, $limb_5, $limb_4,
                   $limb_3, $limb_2, $limb_1, $limb_0]
        };
    }

    pub static COMMON_OPS: CommonOps = CommonOps {
        num_limbs: 256 / LIMB_BITS,

        q: Mont {
            p: p256_limbs![0xffffffff, 0x00000001, 0x00000000, 0x00000000,
                           0x00000000, 0xffffffff, 0xffffffff, 0xffffffff],
            rr: p256_limbs![0x00000004, 0xfffffffd, 0xffffffff, 0xfffffffe,
                            0xfffffffb, 0xffffffff, 0x00000000, 0x00000003],
        },

        n: Elem {
            limbs: p256_limbs![0xffffffff, 0x00000000, 0xffffffff, 0xffffffff,
                               0xbce6faad, 0xa7179e84, 0xf3b9cac2, 0xfc632551],
            m: PhantomData,
            encoding: PhantomData, // Unencoded
        },

        a: Elem {
            limbs: p256_limbs![0xfffffffc, 0x00000004, 0x00000000, 0x00000000,
                               0x00000003, 0xffffffff, 0xffffffff, 0xfffffffc],
            m: PhantomData,
            encoding: PhantomData, // R
        },
        b: Elem {
            limbs: p256_limbs![0xdc30061d, 0x04874834, 0xe5a220ab, 0xf7212ed6,
                               0xacf005cd, 0x78843090, 0xd89cdf62, 0x29c4bddf],
            m: PhantomData,
            encoding: PhantomData, // R
        },

        elem_add_impl: GFp_nistz256_add,
        elem_mul_mont: GFp_nistz256_mul_mont,
        elem_sqr_mont: GFp_nistz256_sqr_mont,

        point_add_jacobian_impl: GFp_nistz256_point_add,
    };

    pub static PRIVATE_KEY_OPS: PrivateKeyOps = PrivateKeyOps {
        common: &COMMON_OPS,
        elem_inv_squared: p256_elem_inv_squared,
        point_mul_base_impl: p256_point_mul_base_impl,
        point_mul_impl: GFp_nistz256_point_mul,
    };

    fn p256_elem_inv_squared(a: &Elem<R>) -> Elem<R> {
        // Calculate a**-2 (mod q) == a**(q - 3) (mod q)
        //
        // The exponent (q - 3) is:
        //
        //    0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc

        #[inline]
        fn sqr_mul(a: &Elem<R>, squarings: usize, b: &Elem<R>) -> Elem<R> {
            elem_sqr_mul(&COMMON_OPS, a, squarings, b)
        }

        #[inline]
        fn sqr_mul_acc(a: &mut Elem<R>, squarings: usize, b: &Elem<R>) {
            elem_sqr_mul_acc(&COMMON_OPS, a, squarings, b)
        }

        let b_1 = &a;
        let b_11       = sqr_mul(b_1,          1, b_1);
        let b_111      = sqr_mul(&b_11,        1, b_1);
        let f_11       = sqr_mul(&b_111,       3, &b_111);
        let fff        = sqr_mul(&f_11,        6, &f_11);
        let fff_111    = sqr_mul(&fff,         3, &b_111);
        let fffffff_11 = sqr_mul(&fff_111,    15, &fff_111);
        let ffffffff   = sqr_mul(&fffffff_11,  2, &b_11);

        // ffffffff00000001
        let mut acc = sqr_mul(&ffffffff, 31 + 1, b_1);

        // ffffffff00000001000000000000000000000000ffffffff
        sqr_mul_acc(&mut acc, 96 + 32, &ffffffff);

        // ffffffff00000001000000000000000000000000ffffffffffffffff
        sqr_mul_acc(&mut acc, 32, &ffffffff);

        // ffffffff00000001000000000000000000000000fffffffffffffffffffffff_11
        sqr_mul_acc(&mut acc, 30, &fffffff_11);

        // ffffffff00000001000000000000000000000000fffffffffffffffffffffffc
        COMMON_OPS.elem_square(&mut acc);
        COMMON_OPS.elem_square(&mut acc);

        acc
    }

    fn p256_point_mul_base_impl(g_scalar: &Scalar) -> Point {
        let mut r = Point::new_at_infinity();
        unsafe {
            GFp_nistz256_point_mul_base(r.xyz.as_mut_ptr(),
                                        g_scalar.limbs.as_ptr());
        }
        r
    }

    pub static PUBLIC_KEY_OPS: PublicKeyOps = PublicKeyOps { common: &COMMON_OPS };

    pub static SCALAR_OPS: ScalarOps = ScalarOps {
        common: &COMMON_OPS,
        scalar_inv_to_mont_impl: p256_scalar_inv_to_mont,
        scalar_mul_mont: GFp_p256_scalar_mul_mont,
    };

    pub static PUBLIC_SCALAR_OPS: PublicScalarOps = PublicScalarOps {
        scalar_ops: &SCALAR_OPS,
        public_key_ops: &PUBLIC_KEY_OPS,
        private_key_ops: &PRIVATE_KEY_OPS,

        q_minus_n: Elem {
            limbs: p256_limbs![0, 0, 0, 0, 0x43190553, 0x58e8617b, 0x0c46353d,
                               0x039cdaae],
            m: PhantomData,
            encoding: PhantomData, // Unencoded
        },
    };

    fn p256_scalar_inv_to_mont(a: &Scalar<Unencoded>) -> Scalar<R> {
        // Calculate the modular inverse of scalar |a| using Fermat's Little
        // Theorem:
        //
        //    a**-1 (mod n) == a**(n - 2) (mod n)
        //
        // The exponent (n - 2) is:
        //
        //    0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254f

        #[inline]
        fn mul(a: &Scalar<R>, b: &Scalar<R>) -> Scalar<R> {
            binary_op(GFp_p256_scalar_mul_mont, a, b)
        }

        #[inline]
        fn sqr(a: &Scalar<R>) -> Scalar<R> {
            unary_op(GFp_p256_scalar_sqr_mont, a)
        }

        // Returns (`a` squared `squarings` times) * `b`.
        fn sqr_mul(a: &Scalar<R>, squarings: c::int, b: &Scalar<R>) -> Scalar<R> {
            debug_assert!(squarings >= 1);
            let mut tmp = Scalar::zero();
            unsafe {
                GFp_p256_scalar_sqr_rep_mont(tmp.limbs.as_mut_ptr(),
                                             a.limbs.as_ptr(), squarings)
            }
            mul(&tmp, b)
        }

        // Sets `acc` = (`acc` squared `squarings` times) * `b`.
        fn sqr_mul_acc(acc: &mut Scalar<R>, squarings: c::int, b: &Scalar<R>) {
            debug_assert!(squarings >= 1);
            unsafe {
                GFp_p256_scalar_sqr_rep_mont(acc.limbs.as_mut_ptr(),
                                             acc.limbs.as_ptr(), squarings)
            }
            binary_op_assign(GFp_p256_scalar_mul_mont, acc, b);
        }

        fn to_mont(a: &Scalar) -> Scalar<R> {
            static N_RR: Scalar<Unencoded> = Scalar {
                limbs: p256_limbs![0x66e12d94, 0xf3d95620, 0x2845b239, 0x2b6bec59,
                                   0x4699799c, 0x49bd6fa6, 0x83244c95, 0xbe79eea2],
                m: PhantomData,
                encoding: PhantomData,
            };
            binary_op(GFp_p256_scalar_mul_mont, a, &N_RR)
        }

        // Indexes into `d`.
        const B_1: usize = 0;
        const B_10: usize = 1;
        const B_11: usize = 2;
        const B_101: usize = 3;
        const B_111: usize = 4;
        const B_1111: usize = 5;
        const B_10101: usize = 6;
        const B_101111: usize = 7;
        const DIGIT_COUNT: usize = 8;

        let mut d = [Scalar::zero(); DIGIT_COUNT];

        d[B_1] = to_mont(a);
        d[B_10] = sqr(&d[B_1]);
        d[B_11] = mul(&d[B_10], &d[B_1]);
        d[B_101] = mul(&d[B_10], &d[B_11]);
        d[B_111] = mul(&d[B_101], &d[B_10]);
        let b_1010 = sqr(&d[B_101]);
        d[B_1111] = mul(&b_1010, &d[B_101]);
        d[B_10101] = sqr_mul(&b_1010, 0 + 1, &d[B_1]);
        let b_101010 = sqr(&d[B_10101]);
        d[B_101111] = mul(&b_101010, &d[B_101]);
        let b_111111 = mul(&b_101010, &d[B_10101]);

        let ff       = sqr_mul(&b_111111,  0 + 2,  &d[B_11]);
        let ffff     = sqr_mul(&ff,        0 + 8,  &ff);
        let ffffffff = sqr_mul(&ffff,      0 + 16, &ffff);

        // ffffffff00000000ffffffff
        let mut acc = sqr_mul(&ffffffff, 32 + 32, &ffffffff);

        // ffffffff00000000ffffffffffffffff
        sqr_mul_acc(&mut acc, 0 + 32, &ffffffff);

        // The rest of the exponent, in binary, is:
        //
        //    1011110011100110111110101010110110100111000101111001111010000100
        //    1111001110111001110010101100001011111100011000110010010101001111

        static REMAINING_WINDOWS: [(u8, u8); 26] = [
            (    6, B_101111 as u8),
            (2 + 3, B_111 as u8),
            (2 + 2, B_11 as u8),
            (1 + 4, B_1111 as u8),
            (    5, B_10101 as u8),
            (1 + 3, B_101 as u8),
            (    3, B_101 as u8),
            (    3, B_101 as u8),
            (2 + 3, B_111 as u8),
            (3 + 6, B_101111 as u8),
            (2 + 4, B_1111 as u8),
            (1 + 1, B_1 as u8),
            (4 + 1, B_1 as u8),
            (2 + 4, B_1111 as u8),
            (2 + 3, B_111 as u8),
            (1 + 3, B_111 as u8),
            (2 + 3, B_111 as u8),
            (2 + 3, B_101 as u8),
            (1 + 2, B_11 as u8),
            (4 + 6, B_101111 as u8),
            (    2, B_11 as u8),
            (3 + 2, B_11 as u8),
            (3 + 2, B_11 as u8),
            (2 + 1, B_1 as u8),
            (2 + 5, B_10101 as u8),
            (2 + 4, B_1111 as u8),
        ];

        for &(squarings, digit) in &REMAINING_WINDOWS {
            sqr_mul_acc(&mut acc, squarings as c::int, &d[digit as usize]);
        }

        acc
    }

    extern {
        fn GFp_nistz256_add(r: *mut Limb/*[COMMON_OPS.num_limbs]*/,
                            a: *const Limb/*[COMMON_OPS.num_limbs]*/,
                            b: *const Limb/*[COMMON_OPS.num_limbs]*/);
        fn GFp_nistz256_mul_mont(r: *mut Limb/*[COMMON_OPS.num_limbs]*/,
                                 a: *const Limb/*[COMMON_OPS.num_limbs]*/,
                                 b: *const Limb/*[COMMON_OPS.num_limbs]*/);
        fn GFp_nistz256_sqr_mont(r: *mut Limb/*[COMMON_OPS.num_limbs]*/,
                                 a: *const Limb/*[COMMON_OPS.num_limbs]*/);

        fn GFp_nistz256_point_add(r: *mut Limb/*[3][COMMON_OPS.num_limbs]*/,
                                  a: *const Limb/*[3][COMMON_OPS.num_limbs]*/,
                                  b: *const Limb/*[3][COMMON_OPS.num_limbs]*/);
        fn GFp_nistz256_point_mul(r: *mut Limb/*[3][COMMON_OPS.num_limbs]*/,
                                  p_scalar: *const Limb/*[COMMON_OPS.num_limbs]*/,
                                  p_x: *const Limb/*[COMMON_OPS.num_limbs]*/,
                                  p_y: *const Limb/*[COMMON_OPS.num_limbs]*/);
        fn GFp_nistz256_point_mul_base(r: *mut Limb/*[3][COMMON_OPS.num_limbs]*/,
                                       g_scalar: *const Limb/*[COMMON_OPS.num_limbs]*/);

        fn GFp_p256_scalar_mul_mont(r: *mut Limb/*[COMMON_OPS.num_limbs]*/,
                                    a: *const Limb/*[COMMON_OPS.num_limbs]*/,
                                    b: *const Limb/*[COMMON_OPS.num_limbs]*/);
        fn GFp_p256_scalar_sqr_mont(r: *mut Limb/*[COMMON_OPS.num_limbs]*/,
                                    a: *const Limb/*[COMMON_OPS.num_limbs]*/);
        fn GFp_p256_scalar_sqr_rep_mont(r: *mut Limb/*[COMMON_OPS.num_limbs]*/,
                                        a: *const Limb/*[COMMON_OPS.num_limbs]*/,
                                        rep: c::int);
    }

    #[cfg(feature = "internal_benches")]
    mod internal_benches {
        use super::*;
        use super::super::internal_benches::*;

        bench_curve!(&[
            Scalar {
                limbs: LIMBS_1,
                m: PhantomData,
                encoding: PhantomData,
            },
            Scalar {
                limbs: LIMBS_ALTERNATING_10,
                m: PhantomData,
                encoding: PhantomData,
            },
            Scalar { // n - 1
                limbs: p256_limbs![0xffffffff, 0x00000000, 0xffffffff, 0xffffffff,
                                   0xbce6faad, 0xa7179e84, 0xf3b9cac2,
                                   0xfc632551 - 1],
                m: PhantomData,
                encoding: PhantomData,
            },
        ]);
    }

# Help

## Keyboard Shortcuts

?
  Show this help dialog
S
  Focus the search field
⇤
  Move up in search results
⇥
  Move down in search results
⏎
  Go to active search result
+
  Collapse/expand all sections

## Search Tricks

Prefix searches with a type followed by a colon (e.g. `fn:`) to restrict the search to a given type.

Accepted types are: `fn`, `mod`, `struct`, `enum`, `trait`, `type`, `macro`, and `const`.

Search functions by type signature (e.g. `vec -> usize` or `* -> vec`)