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    // 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.

    //! Elliptic curve operations on P-256 & P-384.

    use arithmetic::montgomery::*;
    use {der, ec, error, pkcs8};
    use self::ops::*;
    use untrusted;

    // NIST SP 800-56A Step 3: "If q is an odd prime p, verify that
    // yQ**2 = xQ**3 + axQ + b in GF(p), where the arithmetic is performed modulo
    // p."
    //
    // That is, verify that (x, y) is on the curve, which is true iif:
    //
    //     y**2 == x**3 + a*x + b (mod q)
    //
    // Or, equivalently, but more efficiently:
    //
    //     y**2 == (x**2 + a)*x + b  (mod q)
    //
    fn verify_affine_point_is_on_the_curve(
            ops: &CommonOps, (x, y): (&Elem<R>, &Elem<R>))
            -> Result<(), error::Unspecified> {
        verify_affine_point_is_on_the_curve_scaled(ops, (x, y), &ops.a, &ops.b)
    }

    // Use `verify_affine_point_is_on_the_curve` instead of this function whenever
    // the affine coordinates are available or will become available. This function
    // should only be used then the affine coordinates are never calculated. See
    // the notes for `verify_affine_point_is_on_the_curve_scaled`.
    //
    // The value `z**2` is returned on success because it is useful for ECDSA
    // verification.
    //
    // This function also verifies that the point is not at infinity.
    fn verify_jacobian_point_is_on_the_curve(ops: &CommonOps, p: &Point)
                                             -> Result<Elem<R>, error::Unspecified> {
        let z = ops.point_z(p);

        // Verify that the point is not at infinity.
        ops.elem_verify_is_not_zero(&z)?;

        let x = ops.point_x(p);
        let y = ops.point_y(p);

        // We are given Jacobian coordinates (x, y, z). So, we have:
        //
        //    (x/z**2, y/z**3) == (x', y'),
        //
        // where (x', y') are the affine coordinates. The curve equation is:
        //
        //     y'**2  ==  x'**3 + a*x' + b  ==  (x'**2 + a)*x' + b
        //
        // Substituting our Jacobian coordinates, we get:
        //
        //    /   y  \**2       /  /   x  \**2       \   /   x  \
        //    | ---- |      ==  |  | ---- |    +  a  | * | ---- |  +  b
        //    \ z**3 /          \  \ z**2 /          /   \ z**2 /
        //
        // Simplify:
        //
        //            y**2      / x**2       \     x
        //            ----  ==  | ----  +  a | * ----  +  b
        //            z**6      \ z**4       /   z**2
        //
        // Multiply both sides by z**6:
        //
        //     z**6             / x**2       \   z**6
        //     ---- * y**2  ==  | ----  +  a | * ---- * x  +  (z**6) * b
        //     z**6             \ z**4       /   z**2
        //
        // Simplify:
        //
        //                      / x**2       \
        //            y**2  ==  | ----  +  a | * z**4 * x  +  (z**6) * b
        //                      \ z**4       /
        //
        // Distribute z**4:
        //
        //                      / z**4                     \
        //            y**2  ==  | ---- * x**2  +  z**4 * a | * x  +  (z**6) * b
        //                      \ z**4                     /
        //
        // Simplify:
        //
        //            y**2  ==  (x**2  +  z**4 * a) * x  +  (z**6) * b
        //
        let z2 = ops.elem_squared(&z);
        let z4 = ops.elem_squared(&z2);
        let z4_a = ops.elem_product(&z4, &ops.a);
        let z6 = ops.elem_product(&z4, &z2);
        let z6_b = ops.elem_product(&z6, &ops.b);
        verify_affine_point_is_on_the_curve_scaled(ops, (&x, &y), &z4_a, &z6_b)?;
        Ok(z2)
    }

    // Handles the common logic of point-is-on-the-curve checks for both affine and
    // Jacobian cases.
    //
    // When doing the check that the point is on the curve after a computation,
    // to avoid fault attacks or mitigate potential bugs, it is better for security
    // to use `verify_affine_point_is_on_the_curve` on the affine coordinates,
    // because it provides some protection against faults that occur in the
    // computation of the inverse of `z`. See the paper and presentation "Fault
    // Attacks on Projective-to-Affine Coordinates Conversion" by Diana Maimuţ,
    // Cédric Murdica, David Naccache, Mehdi Tibouchi. That presentation concluded
    // simply "Check the validity of the result after conversion to affine
    // coordinates." (It seems like a good idea to verify that
    // z_inv * z == 1 mod q too).
    //
    // In the case of affine coordinates (x, y), `a_scaled` and `b_scaled` are
    // `a` and `b`, respectively. In the case of Jacobian coordinates (x, y, z),
    // the computation and comparison is the same, except `a_scaled` and `b_scaled`
    // are (z**4 * a) and (z**6 * b), respectively. Thus, performance is another
    // reason to prefer doing the check on the affine coordinates, as Jacobian
    // computation requires 3 extra multiplications and 2 extra squarings.
    //
    // An example of a fault attack that isn't mitigated by a point-on-the-curve
    // check after multiplication is given in "Sign Change Fault Attacks On
    // Elliptic Curve Cryptosystems" by Johannes Blömer, Martin Otto, and
    // Jean-Pierre Seifert.
    fn verify_affine_point_is_on_the_curve_scaled(
            ops: &CommonOps, (x, y): (&Elem<R>, &Elem<R>), a_scaled: &Elem<R>,
            b_scaled: &Elem<R>) -> Result<(), error::Unspecified> {
        let lhs = ops.elem_squared(y);

        let mut rhs = ops.elem_squared(x);
        ops.elem_add(&mut rhs, a_scaled);
        ops.elem_mul(&mut rhs, x);
        ops.elem_add(&mut rhs, b_scaled);

        if !ops.elems_are_equal(&lhs, &rhs) {
            return Err(error::Unspecified);
        }

        Ok(())
    }

    pub fn key_pair_from_pkcs8(curve: &ec::Curve, template: &pkcs8::Template,
                               input: untrusted::Input)
                               -> Result<ec::KeyPair, error::Unspecified> {
        let (ec_private_key, _) =
            pkcs8::unwrap_key(template, pkcs8::Version::V1Only, input)?;
        let (private_key, public_key) = ec_private_key.read_all(
            error::Unspecified, |input| {
                // https://tools.ietf.org/html/rfc5915#section-3
                der::nested(input, der::Tag::Sequence, error::Unspecified, |input| {
                    let version = der::small_nonnegative_integer(input)?;
                    if version != 1 {
                        return Err(error::Unspecified);
                    }

                    let private_key =
                        der::expect_tag_and_get_value(input, der::Tag::OctetString)?;

                    // [0] parameters (optional).
                    if input.peek(der::Tag::ContextSpecificConstructed0 as u8) {
                        let actual_alg_id = der::expect_tag_and_get_value(
                            input, der::Tag::ContextSpecificConstructed0)?;
                        if actual_alg_id != template.curve_oid() {
                            return Err(error::Unspecified);
                        }
                    }

                    // [1] publicKey. The RFC says it is optional, but we require it
                    // to be present.
                    let public_key = der::nested(
                        input, der::Tag::ContextSpecificConstructed1,
                        error::Unspecified, der::bit_string_with_no_unused_bits)?;

                    Ok((private_key, public_key))
                })
            })?;
        key_pair_from_bytes(curve, private_key, public_key)
    }

    pub fn key_pair_from_bytes(curve: &ec::Curve,
                               private_key_bytes: untrusted::Input,
                               public_key_bytes: untrusted::Input)
                               -> Result<ec::KeyPair, error::Unspecified> {
        let private_key = ec::PrivateKey::from_bytes(curve, private_key_bytes)?;

        let mut public_key_check = [0; ec::PUBLIC_KEY_MAX_LEN];
        { // Borrow `public_key_check`.
            let public_key_check = &mut public_key_check[..curve.public_key_len];
            (curve.public_from_private)(public_key_check, &private_key)?;
            if public_key_bytes != &*public_key_check {
                return Err(error::Unspecified);
            }
        }

        Ok(ec::KeyPair {
            private_key: private_key,
            public_key: public_key_check,
        })
    }

    pub mod curve;
    pub mod ecdsa;
    pub mod ecdh;

    #[macro_use]
    #[path = "ops/ops.rs"]
    mod ops;

    mod private_key;
    mod public_key;

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