ring/ec/
suite_b.rs

1// Copyright 2016 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 AUTHORS DISCLAIM ALL WARRANTIES
8// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS 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
15//! Elliptic curve operations on P-256 & P-384.
16
17use self::ops::*;
18use crate::{arithmetic::montgomery::*, cpu, ec, error, io::der, limb::LimbMask, pkcs8};
19
20// NIST SP 800-56A Step 3: "If q is an odd prime p, verify that
21// yQ**2 = xQ**3 + axQ + b in GF(p), where the arithmetic is performed modulo
22// p."
23//
24// That is, verify that (x, y) is on the curve, which is true iif:
25//
26//     y**2 == x**3 + a*x + b (mod q)
27//
28// Or, equivalently, but more efficiently:
29//
30//     y**2 == (x**2 + a)*x + b  (mod q)
31//
32fn verify_affine_point_is_on_the_curve(
33    ops: &CommonOps,
34    (x, y): (&Elem<R>, &Elem<R>),
35) -> Result<(), error::Unspecified> {
36    verify_affine_point_is_on_the_curve_scaled(ops, (x, y), &ops.a, &ops.b)
37}
38
39// Use `verify_affine_point_is_on_the_curve` instead of this function whenever
40// the affine coordinates are available or will become available. This function
41// should only be used then the affine coordinates are never calculated. See
42// the notes for `verify_affine_point_is_on_the_curve_scaled`.
43//
44// The value `z**2` is returned on success because it is useful for ECDSA
45// verification.
46//
47// This function also verifies that the point is not at infinity.
48fn verify_jacobian_point_is_on_the_curve(
49    ops: &CommonOps,
50    p: &Point,
51) -> Result<Elem<R>, error::Unspecified> {
52    let z = ops.point_z(p);
53
54    // Verify that the point is not at infinity.
55    ops.elem_verify_is_not_zero(&z)?;
56
57    let x = ops.point_x(p);
58    let y = ops.point_y(p);
59
60    // We are given Jacobian coordinates (x, y, z). So, we have:
61    //
62    //    (x/z**2, y/z**3) == (x', y'),
63    //
64    // where (x', y') are the affine coordinates. The curve equation is:
65    //
66    //     y'**2  ==  x'**3 + a*x' + b  ==  (x'**2 + a)*x' + b
67    //
68    // Substituting our Jacobian coordinates, we get:
69    //
70    //    /   y  \**2       /  /   x  \**2       \   /   x  \
71    //    | ---- |      ==  |  | ---- |    +  a  | * | ---- |  +  b
72    //    \ z**3 /          \  \ z**2 /          /   \ z**2 /
73    //
74    // Simplify:
75    //
76    //            y**2      / x**2       \     x
77    //            ----  ==  | ----  +  a | * ----  +  b
78    //            z**6      \ z**4       /   z**2
79    //
80    // Multiply both sides by z**6:
81    //
82    //     z**6             / x**2       \   z**6
83    //     ---- * y**2  ==  | ----  +  a | * ---- * x  +  (z**6) * b
84    //     z**6             \ z**4       /   z**2
85    //
86    // Simplify:
87    //
88    //                      / x**2       \
89    //            y**2  ==  | ----  +  a | * z**4 * x  +  (z**6) * b
90    //                      \ z**4       /
91    //
92    // Distribute z**4:
93    //
94    //                      / z**4                     \
95    //            y**2  ==  | ---- * x**2  +  z**4 * a | * x  +  (z**6) * b
96    //                      \ z**4                     /
97    //
98    // Simplify:
99    //
100    //            y**2  ==  (x**2  +  z**4 * a) * x  +  (z**6) * b
101    //
102    let z2 = ops.elem_squared(&z);
103    let z4 = ops.elem_squared(&z2);
104    let z4_a = ops.elem_product(&z4, &ops.a);
105    let z6 = ops.elem_product(&z4, &z2);
106    let z6_b = ops.elem_product(&z6, &ops.b);
107    verify_affine_point_is_on_the_curve_scaled(ops, (&x, &y), &z4_a, &z6_b)?;
108    Ok(z2)
109}
110
111// Handles the common logic of point-is-on-the-curve checks for both affine and
112// Jacobian cases.
113//
114// When doing the check that the point is on the curve after a computation,
115// to avoid fault attacks or mitigate potential bugs, it is better for security
116// to use `verify_affine_point_is_on_the_curve` on the affine coordinates,
117// because it provides some protection against faults that occur in the
118// computation of the inverse of `z`. See the paper and presentation "Fault
119// Attacks on Projective-to-Affine Coordinates Conversion" by Diana Maimuţ,
120// Cédric Murdica, David Naccache, Mehdi Tibouchi. That presentation concluded
121// simply "Check the validity of the result after conversion to affine
122// coordinates." (It seems like a good idea to verify that
123// z_inv * z == 1 mod q too).
124//
125// In the case of affine coordinates (x, y), `a_scaled` and `b_scaled` are
126// `a` and `b`, respectively. In the case of Jacobian coordinates (x, y, z),
127// the computation and comparison is the same, except `a_scaled` and `b_scaled`
128// are (z**4 * a) and (z**6 * b), respectively. Thus, performance is another
129// reason to prefer doing the check on the affine coordinates, as Jacobian
130// computation requires 3 extra multiplications and 2 extra squarings.
131//
132// An example of a fault attack that isn't mitigated by a point-on-the-curve
133// check after multiplication is given in "Sign Change Fault Attacks On
134// Elliptic Curve Cryptosystems" by Johannes Blömer, Martin Otto, and
135// Jean-Pierre Seifert.
136fn verify_affine_point_is_on_the_curve_scaled(
137    ops: &CommonOps,
138    (x, y): (&Elem<R>, &Elem<R>),
139    a_scaled: &Elem<R>,
140    b_scaled: &Elem<R>,
141) -> Result<(), error::Unspecified> {
142    let lhs = ops.elem_squared(y);
143
144    let mut rhs = ops.elem_squared(x);
145    ops.elem_add(&mut rhs, a_scaled);
146    ops.elem_mul(&mut rhs, x);
147    ops.elem_add(&mut rhs, b_scaled);
148
149    if ops.elems_are_equal(&lhs, &rhs) != LimbMask::True {
150        return Err(error::Unspecified);
151    }
152
153    Ok(())
154}
155
156pub(crate) fn key_pair_from_pkcs8(
157    curve: &'static ec::Curve,
158    template: &pkcs8::Template,
159    input: untrusted::Input,
160    cpu_features: cpu::Features,
161) -> Result<ec::KeyPair, error::KeyRejected> {
162    let (ec_private_key, _) = pkcs8::unwrap_key(template, pkcs8::Version::V1Only, input)?;
163    let (private_key, public_key) =
164        ec_private_key.read_all(error::KeyRejected::invalid_encoding(), |input| {
165            // https://tools.ietf.org/html/rfc5915#section-3
166            der::nested(
167                input,
168                der::Tag::Sequence,
169                error::KeyRejected::invalid_encoding(),
170                |input| key_pair_from_pkcs8_(template, input),
171            )
172        })?;
173    key_pair_from_bytes(curve, private_key, public_key, cpu_features)
174}
175
176fn key_pair_from_pkcs8_<'a>(
177    template: &pkcs8::Template,
178    input: &mut untrusted::Reader<'a>,
179) -> Result<(untrusted::Input<'a>, untrusted::Input<'a>), error::KeyRejected> {
180    let version = der::small_nonnegative_integer(input)
181        .map_err(|error::Unspecified| error::KeyRejected::invalid_encoding())?;
182    if version != 1 {
183        return Err(error::KeyRejected::version_not_supported());
184    }
185
186    let private_key = der::expect_tag_and_get_value(input, der::Tag::OctetString)
187        .map_err(|error::Unspecified| error::KeyRejected::invalid_encoding())?;
188
189    // [0] parameters (optional).
190    if input.peek(u8::from(der::Tag::ContextSpecificConstructed0)) {
191        let actual_alg_id =
192            der::expect_tag_and_get_value(input, der::Tag::ContextSpecificConstructed0)
193                .map_err(|error::Unspecified| error::KeyRejected::invalid_encoding())?;
194        if actual_alg_id.as_slice_less_safe() != template.curve_oid().as_slice_less_safe() {
195            return Err(error::KeyRejected::wrong_algorithm());
196        }
197    }
198
199    // [1] publicKey. The RFC says it is optional, but we require it
200    // to be present.
201    let public_key = der::nested(
202        input,
203        der::Tag::ContextSpecificConstructed1,
204        error::Unspecified,
205        der::bit_string_with_no_unused_bits,
206    )
207    .map_err(|error::Unspecified| error::KeyRejected::invalid_encoding())?;
208
209    Ok((private_key, public_key))
210}
211
212pub(crate) fn key_pair_from_bytes(
213    curve: &'static ec::Curve,
214    private_key_bytes: untrusted::Input,
215    public_key_bytes: untrusted::Input,
216    cpu_features: cpu::Features,
217) -> Result<ec::KeyPair, error::KeyRejected> {
218    let seed = ec::Seed::from_bytes(curve, private_key_bytes, cpu_features)
219        .map_err(|error::Unspecified| error::KeyRejected::invalid_component())?;
220
221    let r = ec::KeyPair::derive(seed)
222        .map_err(|error::Unspecified| error::KeyRejected::unexpected_error())?;
223    if public_key_bytes.as_slice_less_safe() != r.public_key().as_ref() {
224        return Err(error::KeyRejected::inconsistent_components());
225    }
226
227    Ok(r)
228}
229
230pub mod curve;
231
232pub mod ecdh;
233
234pub mod ecdsa;
235
236mod ops;
237
238mod private_key;
239mod public_key;
ring/ec/suite_b.rs

ring/ec/
suite_b.rs
