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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. //! Functionality shared by operations on private keys (ECC keygen and //! ECDSA signing). use super::{ops::*, verify_affine_point_is_on_the_curve}; use crate::{ arithmetic::montgomery::R, ec, error, limb::{self, LIMB_BYTES}, rand, }; /// Generates a random scalar in the range [1, n). pub fn random_scalar( ops: &PrivateKeyOps, rng: &dyn rand::SecureRandom, ) -> Result<Scalar, error::Unspecified> { let num_limbs = ops.common.num_limbs; let mut bytes = [0; ec::SCALAR_MAX_BYTES]; let bytes = &mut bytes[..(num_limbs * LIMB_BYTES)]; generate_private_scalar_bytes(ops, rng, bytes)?; scalar_from_big_endian_bytes(ops, bytes) } pub fn generate_private_scalar_bytes( ops: &PrivateKeyOps, rng: &dyn rand::SecureRandom, out: &mut [u8], ) -> Result<(), error::Unspecified> { // [NSA Suite B Implementer's Guide to ECDSA] Appendix A.1.2, and // [NSA Suite B Implementer's Guide to NIST SP 800-56A] Appendix B.2, // "Key Pair Generation by Testing Candidates". // // [NSA Suite B Implementer's Guide to ECDSA]: doc/ecdsa.pdf. // [NSA Suite B Implementer's Guide to NIST SP 800-56A]: doc/ecdh.pdf. // TODO: The NSA guide also suggests, in appendix B.1, another mechanism // that would avoid the need to use `rng.fill()` more than once. It works // by generating an extra 64 bits of random bytes and then reducing the // output (mod n). Supposedly, this removes enough of the bias towards // small values from the modular reduction, but it isn't obvious that it is // sufficient. TODO: Figure out what we can do to mitigate the bias issue // and switch to the other mechanism. let candidate = out; // XXX: The value 100 was chosen to match OpenSSL due to uncertainty of // what specific value would be better, but it seems bad to try 100 times. for _ in 0..100 { // NSA Guide Steps 1, 2, and 3. // // Since we calculate the length ourselves, it is pointless to check // it, since we can only check it by doing the same calculation. // NSA Guide Step 4. // // The requirement that the random number generator has the // requested security strength is delegated to `rng`. rng.fill(candidate)?; // NSA Guide Steps 5, 6, and 7. if check_scalar_big_endian_bytes(ops, candidate).is_err() { continue; } // NSA Guide Step 8 is done in `public_from_private()`. // NSA Guide Step 9. return Ok(()); } Err(error::Unspecified) } // The underlying X25519 and Ed25519 code uses an [u8; 32] to store the private // key. To make the ECDH and ECDSA code similar to that, we also store the // private key that way, which means we have to convert it to a Scalar whenever // we need to use it. #[inline] pub fn private_key_as_scalar(ops: &PrivateKeyOps, private_key: &ec::Seed) -> Scalar { // This cannot fail because we know the private key is valid. scalar_from_big_endian_bytes(ops, private_key.bytes_less_safe()).unwrap() } pub fn check_scalar_big_endian_bytes( ops: &PrivateKeyOps, bytes: &[u8], ) -> Result<(), error::Unspecified> { debug_assert_eq!(bytes.len(), ops.common.num_limbs * LIMB_BYTES); scalar_from_big_endian_bytes(ops, bytes).map(|_| ()) } // Parses a fixed-length (zero-padded) big-endian-encoded scalar in the range // [1, n). This is constant-time with respect to the actual value *only if* the // value is actually in range. In other words, this won't leak anything about a // valid value, but it might leak small amounts of information about an invalid // value (which constraint it failed). pub fn scalar_from_big_endian_bytes( ops: &PrivateKeyOps, bytes: &[u8], ) -> Result<Scalar, error::Unspecified> { // [NSA Suite B Implementer's Guide to ECDSA] Appendix A.1.2, and // [NSA Suite B Implementer's Guide to NIST SP 800-56A] Appendix B.2, // "Key Pair Generation by Testing Candidates". // // [NSA Suite B Implementer's Guide to ECDSA]: doc/ecdsa.pdf. // [NSA Suite B Implementer's Guide to NIST SP 800-56A]: doc/ecdh.pdf. // // Steps 5, 6, and 7. // // XXX: The NSA guide says that we should verify that the random scalar is // in the range [0, n - 1) and then add one to it so that it is in the range // [1, n). Instead, we verify that the scalar is in the range [1, n). This // way, we avoid needing to compute or store the value (n - 1), we avoid the // need to implement a function to add one to a scalar, and we avoid needing // to convert the scalar back into an array of bytes. scalar_parse_big_endian_fixed_consttime(ops.common, untrusted::Input::from(bytes)) } pub fn public_from_private( ops: &PrivateKeyOps, public_out: &mut [u8], my_private_key: &ec::Seed, ) -> Result<(), error::Unspecified> { let elem_and_scalar_bytes = ops.common.num_limbs * LIMB_BYTES; debug_assert_eq!(public_out.len(), 1 + (2 * elem_and_scalar_bytes)); let my_private_key = private_key_as_scalar(ops, my_private_key); let my_public_key = ops.point_mul_base(&my_private_key); public_out[0] = 4; // Uncompressed encoding. let (x_out, y_out) = (&mut public_out[1..]).split_at_mut(elem_and_scalar_bytes); // `big_endian_affine_from_jacobian` verifies that the point is not at // infinity and is on the curve. big_endian_affine_from_jacobian(ops, Some(x_out), Some(y_out), &my_public_key) } pub fn affine_from_jacobian( ops: &PrivateKeyOps, p: &Point, ) -> Result<(Elem<R>, Elem<R>), error::Unspecified> { let z = ops.common.point_z(p); // Since we restrict our private key to the range [1, n), the curve has // prime order, and we verify that the peer's point is on the curve, // there's no way that the result can be at infinity. But, use `assert!` // instead of `debug_assert!` anyway assert!(ops.common.elem_verify_is_not_zero(&z).is_ok()); let x = ops.common.point_x(p); let y = ops.common.point_y(p); let zz_inv = ops.elem_inverse_squared(&z); let x_aff = ops.common.elem_product(&x, &zz_inv); // `y_aff` is needed to validate the point is on the curve. It is also // needed in the non-ECDH case where we need to output it. let y_aff = { let zzzz_inv = ops.common.elem_squared(&zz_inv); let zzz_inv = ops.common.elem_product(&z, &zzzz_inv); ops.common.elem_product(&y, &zzz_inv) }; // If we validated our inputs correctly and then computed (x, y, z), then // (x, y, z) will be on the curve. See // `verify_affine_point_is_on_the_curve_scaled` for the motivation. verify_affine_point_is_on_the_curve(ops.common, (&x_aff, &y_aff))?; Ok((x_aff, y_aff)) } pub fn big_endian_affine_from_jacobian( ops: &PrivateKeyOps, x_out: Option<&mut [u8]>, y_out: Option<&mut [u8]>, p: &Point, ) -> Result<(), error::Unspecified> { let (x_aff, y_aff) = affine_from_jacobian(ops, p)?; let num_limbs = ops.common.num_limbs; if let Some(x_out) = x_out { let x = ops.common.elem_unencoded(&x_aff); limb::big_endian_from_limbs(&x.limbs[..num_limbs], x_out); } if let Some(y_out) = y_out { let y = ops.common.elem_unencoded(&y_aff); limb::big_endian_from_limbs(&y.limbs[..num_limbs], y_out); } Ok(()) }