ring/ec/suite_b/ops/
p256.rs

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1// Copyright 2016-2023 Brian Smith.
2//
3// Permission to use, copy, modify, and/or distribute this software for any
4// purpose with or without fee is hereby granted, provided that the above
5// copyright notice and this permission notice appear in all copies.
6//
7// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
8// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
10// SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
11// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
12// OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
13// CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
14
15use super::{
16    elem::{binary_op, binary_op_assign},
17    elem_sqr_mul, elem_sqr_mul_acc, PublicModulus, *,
18};
19
20pub(super) const NUM_LIMBS: usize = 256 / LIMB_BITS;
21
22pub static COMMON_OPS: CommonOps = CommonOps {
23    num_limbs: elem::NumLimbs::P256,
24
25    q: PublicModulus {
26        p: limbs_from_hex("ffffffff00000001000000000000000000000000ffffffffffffffffffffffff"),
27        rr: PublicElem::from_hex("4fffffffdfffffffffffffffefffffffbffffffff0000000000000003"),
28    },
29    n: PublicElem::from_hex("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551"),
30
31    a: PublicElem::from_hex("fffffffc00000004000000000000000000000003fffffffffffffffffffffffc"),
32    b: PublicElem::from_hex("dc30061d04874834e5a220abf7212ed6acf005cd78843090d89cdf6229c4bddf"),
33
34    elem_mul_mont: p256_mul_mont,
35    elem_sqr_mont: p256_sqr_mont,
36};
37
38#[cfg(test)]
39pub(super) static GENERATOR: (PublicElem<R>, PublicElem<R>) = (
40    PublicElem::from_hex("18905f76a53755c679fb732b7762251075ba95fc5fedb60179e730d418a9143c"),
41    PublicElem::from_hex("8571ff1825885d85d2e88688dd21f3258b4ab8e4ba19e45cddf25357ce95560a"),
42);
43
44pub static PRIVATE_KEY_OPS: PrivateKeyOps = PrivateKeyOps {
45    common: &COMMON_OPS,
46    elem_inv_squared: p256_elem_inv_squared,
47    point_mul_base_impl: p256_point_mul_base_impl,
48    point_mul_impl: p256_point_mul,
49    point_add_jacobian_impl: p256_point_add,
50};
51
52fn p256_elem_inv_squared(q: &Modulus<Q>, a: &Elem<R>) -> Elem<R> {
53    // Calculate a**-2 (mod q) == a**(q - 3) (mod q)
54    //
55    // The exponent (q - 3) is:
56    //
57    //    0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
58
59    #[inline]
60    fn sqr_mul(q: &Modulus<Q>, a: &Elem<R>, squarings: LeakyWord, b: &Elem<R>) -> Elem<R> {
61        elem_sqr_mul(&COMMON_OPS, a, squarings, b, q.cpu())
62    }
63
64    #[inline]
65    fn sqr_mul_acc(q: &Modulus<Q>, a: &mut Elem<R>, squarings: LeakyWord, b: &Elem<R>) {
66        elem_sqr_mul_acc(&COMMON_OPS, a, squarings, b, q.cpu())
67    }
68
69    let b_1 = &a;
70    let b_11 = sqr_mul(q, b_1, 1, b_1);
71    let b_111 = sqr_mul(q, &b_11, 1, b_1);
72    let f_11 = sqr_mul(q, &b_111, 3, &b_111);
73    let fff = sqr_mul(q, &f_11, 6, &f_11);
74    let fff_111 = sqr_mul(q, &fff, 3, &b_111);
75    let fffffff_11 = sqr_mul(q, &fff_111, 15, &fff_111);
76    let ffffffff = sqr_mul(q, &fffffff_11, 2, &b_11);
77
78    // ffffffff00000001
79    let mut acc = sqr_mul(q, &ffffffff, 31 + 1, b_1);
80
81    // ffffffff00000001000000000000000000000000ffffffff
82    sqr_mul_acc(q, &mut acc, 96 + 32, &ffffffff);
83
84    // ffffffff00000001000000000000000000000000ffffffffffffffff
85    sqr_mul_acc(q, &mut acc, 32, &ffffffff);
86
87    // ffffffff00000001000000000000000000000000fffffffffffffffffffffff_11
88    sqr_mul_acc(q, &mut acc, 30, &fffffff_11);
89
90    // ffffffff00000001000000000000000000000000fffffffffffffffffffffffc
91    q.elem_square(&mut acc);
92    q.elem_square(&mut acc);
93
94    acc
95}
96
97fn p256_point_mul_base_impl(g_scalar: &Scalar, _cpu: cpu::Features) -> Point {
98    prefixed_extern! {
99        fn p256_point_mul_base(
100            r: *mut Limb,          // [3][COMMON_OPS.num_limbs]
101            g_scalar: *const Limb, // [COMMON_OPS.num_limbs]
102        );
103    }
104
105    let mut r = Point::new_at_infinity();
106    unsafe {
107        p256_point_mul_base(r.xyz.as_mut_ptr(), g_scalar.limbs.as_ptr());
108    }
109    r
110}
111
112pub static PUBLIC_KEY_OPS: PublicKeyOps = PublicKeyOps {
113    common: &COMMON_OPS,
114};
115
116pub static SCALAR_OPS: ScalarOps = ScalarOps {
117    common: &COMMON_OPS,
118    scalar_mul_mont: p256_scalar_mul_mont,
119};
120
121pub static PUBLIC_SCALAR_OPS: PublicScalarOps = PublicScalarOps {
122    scalar_ops: &SCALAR_OPS,
123    public_key_ops: &PUBLIC_KEY_OPS,
124
125    #[cfg(any(
126        all(target_arch = "aarch64", target_endian = "little"),
127        target_arch = "x86_64"
128    ))]
129    twin_mul: twin_mul_nistz256,
130
131    #[cfg(not(any(
132        all(target_arch = "aarch64", target_endian = "little"),
133        target_arch = "x86_64"
134    )))]
135    twin_mul: |g_scalar, p_scalar, p_xy, cpu| {
136        twin_mul_inefficient(&PRIVATE_KEY_OPS, g_scalar, p_scalar, p_xy, cpu)
137    },
138
139    q_minus_n: PublicElem::from_hex("4319055358e8617b0c46353d039cdaae"),
140
141    // TODO: Use an optimized variable-time implementation.
142    scalar_inv_to_mont_vartime: |s, cpu| PRIVATE_SCALAR_OPS.scalar_inv_to_mont(s, cpu),
143};
144
145#[cfg(any(
146    all(target_arch = "aarch64", target_endian = "little"),
147    target_arch = "x86_64"
148))]
149fn twin_mul_nistz256(
150    g_scalar: &Scalar,
151    p_scalar: &Scalar,
152    p_xy: &(Elem<R>, Elem<R>),
153    cpu: cpu::Features,
154) -> Point {
155    let scaled_g = point_mul_base_vartime(g_scalar, cpu);
156    let scaled_p = PRIVATE_KEY_OPS.point_mul(p_scalar, p_xy, cpu::features());
157    PRIVATE_KEY_OPS.point_sum(&scaled_g, &scaled_p, cpu)
158}
159
160#[cfg(any(
161    all(target_arch = "aarch64", target_endian = "little"),
162    target_arch = "x86_64"
163))]
164fn point_mul_base_vartime(g_scalar: &Scalar, _cpu: cpu::Features) -> Point {
165    prefixed_extern! {
166        fn p256_point_mul_base_vartime(r: *mut Limb,          // [3][COMMON_OPS.num_limbs]
167                                       g_scalar: *const Limb, // [COMMON_OPS.num_limbs]
168        );
169    }
170    let mut scaled_g = Point::new_at_infinity();
171    unsafe {
172        p256_point_mul_base_vartime(scaled_g.xyz.as_mut_ptr(), g_scalar.limbs.as_ptr());
173    }
174    scaled_g
175}
176
177pub static PRIVATE_SCALAR_OPS: PrivateScalarOps = PrivateScalarOps {
178    scalar_ops: &SCALAR_OPS,
179
180    oneRR_mod_n: PublicScalar::from_hex(
181        "66e12d94f3d956202845b2392b6bec594699799c49bd6fa683244c95be79eea2",
182    ),
183    scalar_inv_to_mont: p256_scalar_inv_to_mont,
184};
185
186#[allow(clippy::just_underscores_and_digits)]
187fn p256_scalar_inv_to_mont(a: Scalar<R>, _cpu: cpu::Features) -> Scalar<R> {
188    // Calculate the modular inverse of scalar |a| using Fermat's Little
189    // Theorem:
190    //
191    //    a**-1 (mod n) == a**(n - 2) (mod n)
192    //
193    // The exponent (n - 2) is:
194    //
195    //    0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254f
196
197    #[inline]
198    fn mul(a: &Scalar<R>, b: &Scalar<R>) -> Scalar<R> {
199        binary_op(p256_scalar_mul_mont, a, b)
200    }
201
202    #[inline]
203    fn sqr(a: &Scalar<R>) -> Scalar<R> {
204        let mut tmp = Scalar::zero();
205        unsafe { p256_scalar_sqr_rep_mont(tmp.limbs.as_mut_ptr(), a.limbs.as_ptr(), 1) }
206        tmp
207    }
208
209    // Returns (`a` squared `squarings` times) * `b`.
210    fn sqr_mul(a: &Scalar<R>, squarings: LeakyWord, b: &Scalar<R>) -> Scalar<R> {
211        debug_assert!(squarings >= 1);
212        let mut tmp = Scalar::zero();
213        unsafe { p256_scalar_sqr_rep_mont(tmp.limbs.as_mut_ptr(), a.limbs.as_ptr(), squarings) }
214        mul(&tmp, b)
215    }
216
217    // Sets `acc` = (`acc` squared `squarings` times) * `b`.
218    fn sqr_mul_acc(acc: &mut Scalar<R>, squarings: LeakyWord, b: &Scalar<R>) {
219        debug_assert!(squarings >= 1);
220        unsafe { p256_scalar_sqr_rep_mont(acc.limbs.as_mut_ptr(), acc.limbs.as_ptr(), squarings) }
221        binary_op_assign(p256_scalar_mul_mont, acc, b);
222    }
223
224    let _1 = &a;
225
226    let _10 = sqr(_1); // 2
227    let _100 = sqr(&_10); // 4
228    let _101 = mul(&_100, _1); // 5
229    let _111 = mul(&_101, &_10); // 7
230
231    let _1000 = sqr(&_100); // 8
232    let _10000 = sqr(&_1000); // 16
233    let _100000 = sqr(&_10000); // 32
234
235    let _100111 = mul(&_111, &_100000); // 39 = 7 + 32
236    let _101011 = mul(&_100, &_100111); // 43 = 4 + 39
237    let _101111 = mul(&_100, &_101011); // 47 = 4 + 39
238    let _1001111 = mul(&_100000, &_101111); // 79 = 32 + 47
239    let _86 = sqr(&_101011); // 86 = 43 * 2
240    let _1011011 = mul(&_101, &_86); // 91 = 5 + 86
241    let _92 = mul(_1, &_1011011); // 92 = 1 + 91
242    let _1100011 = mul(&_111, &_92); // 99 = 7 + 92
243    let _10111111 = mul(&_92, &_1100011); // 191 = 92 + 99
244    let _11011111 = mul(&_100000, &_10111111); // 223 = 32 + 191
245
246    let ff = mul(&_100000, &_11011111); // 255 = 32 + 223
247    let ffff = sqr_mul(&ff, 0 + 8, &ff);
248    let ffffffff = sqr_mul(&ffff, 0 + 16, &ffff);
249
250    // ffffffff00000000ffffffff
251    let mut acc = sqr_mul(&ffffffff, 32 + 32, &ffffffff);
252
253    // ffffffff00000000ffffffffffffffff
254    sqr_mul_acc(&mut acc, 0 + 32, &ffffffff);
255
256    // The rest of the exponent, in binary, is:
257    //
258    //    1011110011100110111110101010110110100111000101111001111010000100
259    //    1111001110111001110010101100001011111100011000110010010101001111
260
261    sqr_mul_acc(&mut acc, 6, &_101111);
262    sqr_mul_acc(&mut acc, 2 + 3, &_111);
263    sqr_mul_acc(&mut acc, 2 + 8, &_11011111);
264    sqr_mul_acc(&mut acc, 1 + 3, &_101);
265    sqr_mul_acc(&mut acc, 1 + 7, &_1011011);
266    sqr_mul_acc(&mut acc, 1 + 6, &_100111);
267    sqr_mul_acc(&mut acc, 3 + 6, &_101111);
268    sqr_mul_acc(&mut acc, 2 + 3, &_111);
269    sqr_mul_acc(&mut acc, 3, &_101);
270    sqr_mul_acc(&mut acc, 4 + 7, &_1001111);
271    sqr_mul_acc(&mut acc, 2 + 3, &_111);
272    sqr_mul_acc(&mut acc, 1 + 3, &_111);
273    sqr_mul_acc(&mut acc, 2 + 3, &_111);
274    sqr_mul_acc(&mut acc, 2 + 6, &_101011);
275    sqr_mul_acc(&mut acc, 4 + 8, &_10111111);
276    sqr_mul_acc(&mut acc, 3 + 7, &_1100011);
277    sqr_mul_acc(&mut acc, 2 + 1, _1);
278    sqr_mul_acc(&mut acc, 2 + 3, &_101);
279    sqr_mul_acc(&mut acc, 1 + 7, &_1001111);
280
281    acc
282}
283
284prefixed_extern! {
285    pub(super) fn p256_mul_mont(
286        r: *mut Limb,   // [COMMON_OPS.num_limbs]
287        a: *const Limb, // [COMMON_OPS.num_limbs]
288        b: *const Limb, // [COMMON_OPS.num_limbs]
289    );
290    pub(super) fn p256_sqr_mont(
291        r: *mut Limb,   // [COMMON_OPS.num_limbs]
292        a: *const Limb, // [COMMON_OPS.num_limbs]
293    );
294
295    fn p256_point_add(
296        r: *mut Limb,   // [3][COMMON_OPS.num_limbs]
297        a: *const Limb, // [3][COMMON_OPS.num_limbs]
298        b: *const Limb, // [3][COMMON_OPS.num_limbs]
299    );
300    fn p256_point_mul(
301        r: *mut Limb,          // [3][COMMON_OPS.num_limbs]
302        p_scalar: *const Limb, // [COMMON_OPS.num_limbs]
303        p_x: *const Limb,      // [COMMON_OPS.num_limbs]
304        p_y: *const Limb,      // [COMMON_OPS.num_limbs]
305    );
306
307    fn p256_scalar_mul_mont(
308        r: *mut Limb,   // [COMMON_OPS.num_limbs]
309        a: *const Limb, // [COMMON_OPS.num_limbs]
310        b: *const Limb, // [COMMON_OPS.num_limbs]
311    );
312    fn p256_scalar_sqr_rep_mont(
313        r: *mut Limb,   // [COMMON_OPS.num_limbs]
314        a: *const Limb, // [COMMON_OPS.num_limbs]
315        rep: LeakyWord,
316    );
317}
318
319#[cfg(test)]
320mod tests {
321    #[cfg(any(
322        all(target_arch = "aarch64", target_endian = "little"),
323        target_arch = "x86_64"
324    ))]
325    #[test]
326    fn p256_point_mul_base_vartime_test() {
327        use super::{super::tests::point_mul_base_tests, *};
328        point_mul_base_tests(
329            &PRIVATE_KEY_OPS,
330            point_mul_base_vartime,
331            test_vector_file!("p256_point_mul_base_tests.txt"),
332        );
333    }
334}
ring/ec/suite_b/ops/p256.rs

ring/ec/suite_b/ops/
p256.rs
