use ed448_goldilocks::curve::MontgomeryPoint;
use ed448_goldilocks::Scalar;
use rand_core::{CryptoRng, RngCore};
impl From<[u8; 56]> for PublicKey {
fn from(arr: [u8; 56]) -> PublicKey {
let point = MontgomeryPoint(arr);
PublicKey(point)
}
}
impl From<[u8; 56]> for Secret {
fn from(arr: [u8; 56]) -> Secret {
let mut secret = Secret(arr);
secret.clamp();
secret
}
}
impl From<&Secret> for PublicKey {
fn from(secret: &Secret) -> PublicKey {
let point = MontgomeryPoint::generator().mul(&Scalar::from_bytes(secret.0));
PublicKey(point)
}
}
pub struct PublicKey(MontgomeryPoint);
pub struct Secret([u8; 56]);
pub type SharedSecret = PublicKey;
impl PublicKey {
pub fn from_bytes(bytes: &[u8]) -> Option<PublicKey> {
if bytes.len() != 56 {
return None;
}
let public_key = PublicKey::from(slice_to_array(bytes));
if public_key.0.is_low_order() {
return None;
}
Some(public_key)
}
pub fn as_bytes(&self) -> &[u8; 56] {
self.0.as_bytes()
}
}
impl Secret {
pub fn new<T>(csprng: &mut T) -> Self
where
T: RngCore + CryptoRng,
{
let mut bytes = [0u8; 56];
csprng.fill_bytes(&mut bytes);
Secret::from(bytes)
}
fn clamp(&mut self) {
self.0[0] &= 252;
self.0[55] |= 128;
}
pub fn as_diffie_hellman(&self, public_key: &PublicKey) -> Option<SharedSecret> {
if public_key.0.is_low_order() {
return None;
}
let shared_key = public_key.0.mul(&Scalar::from_bytes(self.0));
Some(PublicKey(shared_key))
}
pub fn to_diffie_hellman(self, public_key: &PublicKey) -> Option<SharedSecret> {
self.as_diffie_hellman(public_key)
}
pub fn from_bytes(bytes: &[u8]) -> Option<Secret> {
if bytes.len() != 56 {
return None;
}
let secret = Secret::from(slice_to_array(bytes));
Some(secret)
}
pub fn as_bytes(&self) -> &[u8; 56] {
&self.0
}
}
fn slice_to_array(bytes: &[u8]) -> [u8; 56] {
let mut array: [u8; 56] = [0; 56];
array.copy_from_slice(&bytes);
array
}
pub fn x448(point_bytes: [u8; 56], scalar_bytes: [u8; 56]) -> Option<[u8; 56]> {
let point = PublicKey::from_bytes(&point_bytes)?;
let scalar = Scalar::from_bytes(scalar_bytes);
Some(point.0.mul(&scalar).0)
}
#[cfg(test)]
mod test {
use super::*;
use rand_core::OsRng;
#[test]
fn test_low_order() {
const LOW_A: MontgomeryPoint = MontgomeryPoint([
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
]);
const LOW_B: MontgomeryPoint = MontgomeryPoint([
0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
]);
const LOW_C: MontgomeryPoint = MontgomeryPoint([
0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
]);
let bad_key_a = PublicKey(LOW_A);
let checked_bad_key_a = PublicKey::from_bytes(&LOW_A.0);
assert!(checked_bad_key_a.is_none());
let bad_key_b = PublicKey(LOW_B);
let checked_bad_key_b = PublicKey::from_bytes(&LOW_B.0);
assert!(checked_bad_key_b.is_none());
let bad_key_c = PublicKey(LOW_C);
let checked_bad_key_c = PublicKey::from_bytes(&LOW_C.0);
assert!(checked_bad_key_c.is_none());
let bob_priv = Secret::new(&mut OsRng);
let shared_bob = bob_priv.as_diffie_hellman(&bad_key_a);
assert!(shared_bob.is_none());
let shared_bob = bob_priv.as_diffie_hellman(&bad_key_b);
assert!(shared_bob.is_none());
let shared_bob = bob_priv.as_diffie_hellman(&bad_key_c);
assert!(shared_bob.is_none());
}
#[test]
fn test_random_dh() {
let alice_priv = Secret::new(&mut OsRng);
let alice_pub = PublicKey::from(&alice_priv);
let bob_priv = Secret::new(&mut OsRng);
let bob_pub = PublicKey::from(&bob_priv);
let low_order = alice_pub.0.is_low_order() || bob_pub.0.is_low_order();
assert!(low_order == false);
let shared_alice = alice_priv.as_diffie_hellman(&bob_pub).unwrap();
let shared_bob = bob_priv.as_diffie_hellman(&alice_pub).unwrap();
assert_eq!(shared_alice.as_bytes()[..], shared_bob.as_bytes()[..]);
}
#[test]
fn test_rfc_test_vectors_alice_bob() {
let alice_priv = Secret::from_bytes(&[
0x9a, 0x8f, 0x49, 0x25, 0xd1, 0x51, 0x9f, 0x57, 0x75, 0xcf, 0x46, 0xb0, 0x4b, 0x58,
0x0, 0xd4, 0xee, 0x9e, 0xe8, 0xba, 0xe8, 0xbc, 0x55, 0x65, 0xd4, 0x98, 0xc2, 0x8d,
0xd9, 0xc9, 0xba, 0xf5, 0x74, 0xa9, 0x41, 0x97, 0x44, 0x89, 0x73, 0x91, 0x0, 0x63,
0x82, 0xa6, 0xf1, 0x27, 0xab, 0x1d, 0x9a, 0xc2, 0xd8, 0xc0, 0xa5, 0x98, 0x72, 0x6b,
])
.unwrap();
let got_alice_pub = PublicKey::from(&alice_priv);
let expected_alice_pub = [
0x9b, 0x8, 0xf7, 0xcc, 0x31, 0xb7, 0xe3, 0xe6, 0x7d, 0x22, 0xd5, 0xae, 0xa1, 0x21, 0x7,
0x4a, 0x27, 0x3b, 0xd2, 0xb8, 0x3d, 0xe0, 0x9c, 0x63, 0xfa, 0xa7, 0x3d, 0x2c, 0x22,
0xc5, 0xd9, 0xbb, 0xc8, 0x36, 0x64, 0x72, 0x41, 0xd9, 0x53, 0xd4, 0xc, 0x5b, 0x12,
0xda, 0x88, 0x12, 0xd, 0x53, 0x17, 0x7f, 0x80, 0xe5, 0x32, 0xc4, 0x1f, 0xa0,
];
assert_eq!(got_alice_pub.as_bytes()[..], expected_alice_pub[..]);
let bob_priv = Secret::from_bytes(&[
0x1c, 0x30, 0x6a, 0x7a, 0xc2, 0xa0, 0xe2, 0xe0, 0x99, 0xb, 0x29, 0x44, 0x70, 0xcb,
0xa3, 0x39, 0xe6, 0x45, 0x37, 0x72, 0xb0, 0x75, 0x81, 0x1d, 0x8f, 0xad, 0xd, 0x1d,
0x69, 0x27, 0xc1, 0x20, 0xbb, 0x5e, 0xe8, 0x97, 0x2b, 0xd, 0x3e, 0x21, 0x37, 0x4c,
0x9c, 0x92, 0x1b, 0x9, 0xd1, 0xb0, 0x36, 0x6f, 0x10, 0xb6, 0x51, 0x73, 0x99, 0x2d,
])
.unwrap();
let got_bob_pub = PublicKey::from(&bob_priv);
let expected_bob_pub = [
0x3e, 0xb7, 0xa8, 0x29, 0xb0, 0xcd, 0x20, 0xf5, 0xbc, 0xfc, 0xb, 0x59, 0x9b, 0x6f,
0xec, 0xcf, 0x6d, 0xa4, 0x62, 0x71, 0x7, 0xbd, 0xb0, 0xd4, 0xf3, 0x45, 0xb4, 0x30,
0x27, 0xd8, 0xb9, 0x72, 0xfc, 0x3e, 0x34, 0xfb, 0x42, 0x32, 0xa1, 0x3c, 0xa7, 0x6,
0xdc, 0xb5, 0x7a, 0xec, 0x3d, 0xae, 0x7, 0xbd, 0xc1, 0xc6, 0x7b, 0xf3, 0x36, 0x9,
];
assert_eq!(got_bob_pub.as_bytes()[..], expected_bob_pub[..]);
let bob_shared = bob_priv.to_diffie_hellman(&got_alice_pub).unwrap();
let alice_shared = alice_priv.to_diffie_hellman(&got_bob_pub).unwrap();
assert_eq!(bob_shared.as_bytes()[..], alice_shared.as_bytes()[..]);
let expected_shared = [
0x7, 0xff, 0xf4, 0x18, 0x1a, 0xc6, 0xcc, 0x95, 0xec, 0x1c, 0x16, 0xa9, 0x4a, 0xf, 0x74,
0xd1, 0x2d, 0xa2, 0x32, 0xce, 0x40, 0xa7, 0x75, 0x52, 0x28, 0x1d, 0x28, 0x2b, 0xb6,
0xc, 0xb, 0x56, 0xfd, 0x24, 0x64, 0xc3, 0x35, 0x54, 0x39, 0x36, 0x52, 0x1c, 0x24, 0x40,
0x30, 0x85, 0xd5, 0x9a, 0x44, 0x9a, 0x50, 0x37, 0x51, 0x4a, 0x87, 0x9d,
];
assert_eq!(bob_shared.as_bytes()[..], expected_shared[..]);
}
#[test]
fn test_rfc_test_vectors_fixed() {
struct Test {
secret: [u8; 56],
point: [u8; 56],
expected: [u8; 56],
};
let test_vectors = vec![
Test {
secret: [
0x3d, 0x26, 0x2f, 0xdd, 0xf9, 0xec, 0x8e, 0x88, 0x49, 0x52, 0x66, 0xfe, 0xa1,
0x9a, 0x34, 0xd2, 0x88, 0x82, 0xac, 0xef, 0x4, 0x51, 0x4, 0xd0, 0xd1, 0xaa,
0xe1, 0x21, 0x70, 0xa, 0x77, 0x9c, 0x98, 0x4c, 0x24, 0xf8, 0xcd, 0xd7, 0x8f,
0xbf, 0xf4, 0x49, 0x43, 0xeb, 0xa3, 0x68, 0xf5, 0x4b, 0x29, 0x25, 0x9a, 0x4f,
0x1c, 0x60, 0xa, 0xd3,
],
point: [
0x6, 0xfc, 0xe6, 0x40, 0xfa, 0x34, 0x87, 0xbf, 0xda, 0x5f, 0x6c, 0xf2, 0xd5,
0x26, 0x3f, 0x8a, 0xad, 0x88, 0x33, 0x4c, 0xbd, 0x7, 0x43, 0x7f, 0x2, 0xf, 0x8,
0xf9, 0x81, 0x4d, 0xc0, 0x31, 0xdd, 0xbd, 0xc3, 0x8c, 0x19, 0xc6, 0xda, 0x25,
0x83, 0xfa, 0x54, 0x29, 0xdb, 0x94, 0xad, 0xa1, 0x8a, 0xa7, 0xa7, 0xfb, 0x4e,
0xf8, 0xa0, 0x86,
],
expected: [
0xce, 0x3e, 0x4f, 0xf9, 0x5a, 0x60, 0xdc, 0x66, 0x97, 0xda, 0x1d, 0xb1, 0xd8,
0x5e, 0x6a, 0xfb, 0xdf, 0x79, 0xb5, 0xa, 0x24, 0x12, 0xd7, 0x54, 0x6d, 0x5f,
0x23, 0x9f, 0xe1, 0x4f, 0xba, 0xad, 0xeb, 0x44, 0x5f, 0xc6, 0x6a, 0x1, 0xb0,
0x77, 0x9d, 0x98, 0x22, 0x39, 0x61, 0x11, 0x1e, 0x21, 0x76, 0x62, 0x82, 0xf7,
0x3d, 0xd9, 0x6b, 0x6f,
],
},
Test {
secret: [
0x20, 0x3d, 0x49, 0x44, 0x28, 0xb8, 0x39, 0x93, 0x52, 0x66, 0x5d, 0xdc, 0xa4,
0x2f, 0x9d, 0xe8, 0xfe, 0xf6, 0x0, 0x90, 0x8e, 0xd, 0x46, 0x1c, 0xb0, 0x21,
0xf8, 0xc5, 0x38, 0x34, 0x5d, 0xd7, 0x7c, 0x3e, 0x48, 0x6, 0xe2, 0x5f, 0x46,
0xd3, 0x31, 0x5c, 0x44, 0xe0, 0xa5, 0xb4, 0x37, 0x12, 0x82, 0xdd, 0x2c, 0x8d,
0x5b, 0xe3, 0x9, 0x5f,
],
point: [
0xf, 0xbc, 0xc2, 0xf9, 0x93, 0xcd, 0x56, 0xd3, 0x30, 0x5b, 0xb, 0x7d, 0x9e,
0x55, 0xd4, 0xc1, 0xa8, 0xfb, 0x5d, 0xbb, 0x52, 0xf8, 0xe9, 0xa1, 0xe9, 0xb6,
0x20, 0x1b, 0x16, 0x5d, 0x1, 0x58, 0x94, 0xe5, 0x6c, 0x4d, 0x35, 0x70, 0xbe,
0xe5, 0x2f, 0xe2, 0x5, 0xe2, 0x8a, 0x78, 0xb9, 0x1c, 0xdf, 0xbd, 0xe7, 0x1c,
0xe8, 0xd1, 0x57, 0xdb,
],
expected: [
0x88, 0x4a, 0x2, 0x57, 0x62, 0x39, 0xff, 0x7a, 0x2f, 0x2f, 0x63, 0xb2, 0xdb,
0x6a, 0x9f, 0xf3, 0x70, 0x47, 0xac, 0x13, 0x56, 0x8e, 0x1e, 0x30, 0xfe, 0x63,
0xc4, 0xa7, 0xad, 0x1b, 0x3e, 0xe3, 0xa5, 0x70, 0xd, 0xf3, 0x43, 0x21, 0xd6,
0x20, 0x77, 0xe6, 0x36, 0x33, 0xc5, 0x75, 0xc1, 0xc9, 0x54, 0x51, 0x4e, 0x99,
0xda, 0x7c, 0x17, 0x9d,
],
},
];
for vector in test_vectors {
let public_key = PublicKey::from_bytes(&vector.point).unwrap();
let secret = Secret::from_bytes(&vector.secret).unwrap();
let got = secret.as_diffie_hellman(&public_key).unwrap();
assert_eq!(got.as_bytes()[..], vector.expected[..])
}
}
fn swap(secret: &mut [u8; 56], public_key: &mut [u8; 56], result: &[u8; 56]) {
*public_key = *secret;
*secret = *result;
}
#[test]
#[ignore]
fn test_rfc_test_vectors_iteration() {
let one_iter = [
0x3f, 0x48, 0x2c, 0x8a, 0x9f, 0x19, 0xb0, 0x1e, 0x6c, 0x46, 0xee, 0x97, 0x11, 0xd9,
0xdc, 0x14, 0xfd, 0x4b, 0xf6, 0x7a, 0xf3, 0x7, 0x65, 0xc2, 0xae, 0x2b, 0x84, 0x6a,
0x4d, 0x23, 0xa8, 0xcd, 0xd, 0xb8, 0x97, 0x8, 0x62, 0x39, 0x49, 0x2c, 0xaf, 0x35, 0xb,
0x51, 0xf8, 0x33, 0x86, 0x8b, 0x9b, 0xc2, 0xb3, 0xbc, 0xa9, 0xcf, 0x41, 0x13,
];
let one_k_iter = [
0xaa, 0x3b, 0x47, 0x49, 0xd5, 0x5b, 0x9d, 0xaf, 0x1e, 0x5b, 0x0, 0x28, 0x88, 0x26,
0xc4, 0x67, 0x27, 0x4c, 0xe3, 0xeb, 0xbd, 0xd5, 0xc1, 0x7b, 0x97, 0x5e, 0x9, 0xd4,
0xaf, 0x6c, 0x67, 0xcf, 0x10, 0xd0, 0x87, 0x20, 0x2d, 0xb8, 0x82, 0x86, 0xe2, 0xb7,
0x9f, 0xce, 0xea, 0x3e, 0xc3, 0x53, 0xef, 0x54, 0xfa, 0xa2, 0x6e, 0x21, 0x9f, 0x38,
];
let one_mil_iter = [
0x7, 0x7f, 0x45, 0x36, 0x81, 0xca, 0xca, 0x36, 0x93, 0x19, 0x84, 0x20, 0xbb, 0xe5,
0x15, 0xca, 0xe0, 0x0, 0x24, 0x72, 0x51, 0x9b, 0x3e, 0x67, 0x66, 0x1a, 0x7e, 0x89,
0xca, 0xb9, 0x46, 0x95, 0xc8, 0xf4, 0xbc, 0xd6, 0x6e, 0x61, 0xb9, 0xb9, 0xc9, 0x46,
0xda, 0x8d, 0x52, 0x4d, 0xe3, 0xd6, 0x9b, 0xd9, 0xd9, 0xd6, 0x6b, 0x99, 0x7e, 0x37,
];
let mut point = MontgomeryPoint::generator().0;
let mut scalar = MontgomeryPoint::generator().0;
let mut result = [0u8; 56];
for _ in 1..=1 {
result = x448(point, scalar).unwrap();
swap(&mut scalar, &mut point, &result);
}
assert_eq!(&result[..], &one_iter[..]);
for _ in 1..=999 {
result = x448(point, scalar).unwrap();
swap(&mut scalar, &mut point, &result);
}
assert_eq!(&result[..], &one_k_iter[..]);
for _ in 1..=999_000 {
result = x448(point, scalar).unwrap();
swap(&mut scalar, &mut point, &result);
}
assert_eq!(&result[..], &one_mil_iter[..]);
}
}