diff --git a/Cargo.lock b/Cargo.lock index 1d10878..e84eb25 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -154,7 +154,7 @@ dependencies = [ [[package]] name = "raycrypt" -version = "0.1.0" +version = "0.3.0" dependencies = [ "benchmark-simple", "cfg-if", diff --git a/Cargo.toml b/Cargo.toml index e5b71d9..6849a07 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -1,6 +1,6 @@ [package] name = "raycrypt" -version = "0.2.0" +version = "0.3.0" edition = "2021" license = "MIT" description = "Encrypt at the speed of light" diff --git a/src/ecc.rs b/src/ecc.rs index af33b95..20149bb 100644 --- a/src/ecc.rs +++ b/src/ecc.rs @@ -1,4 +1,3 @@ -pub mod ed25519; pub(crate) mod field; pub(crate) mod ge; pub mod x25519; diff --git a/src/ecc/ed25519.rs b/src/ecc/ed25519.rs deleted file mode 100644 index c2d2df2..0000000 --- a/src/ecc/ed25519.rs +++ /dev/null @@ -1,225 +0,0 @@ -// adapted from the rust-crypto ed25519 implementation - -use crate::ecc::ge::{ge_scalarmult_base, sc_muladd, sc_reduce, GeP2, GeP3}; -use crate::ecc::InvalidKey; -use crate::utils::const_time_eq; -use getrandom::getrandom; -use sha2::{Digest, Sha512}; - -fn check_s_lt_l(s: &[u8]) -> bool { - static L: [u8; 32] = [ - 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, - 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00, 0x10, - ]; - let mut c: u8 = 0; - let mut n: u8 = 1; - - for i in (0..32).rev() { - c |= ((((s[i] as i32) - (L[i] as i32)) >> 8) as u8) & n; - n &= ((((s[i] ^ L[i]) as i32) - 1) >> 8) as u8; - } - - c != 0 -} - -/// A class to sign keys -pub struct SigningKey { - az: [u8; 64], - public: [u8; 32], -} - -impl SigningKey { - /// A constructor to generate a secret key from a 64-byte secret key - pub fn from(secret: &[u8]) -> Result { - if secret.len() != 64 { - return Err(InvalidKey); - } - - let az: [u8; 64] = { - let mut hasher = Sha512::new(); - hasher.update(&secret[0..32]); - let mut hash_output: [u8; 64] = hasher.finalize().into(); - hash_output[0] &= 248; - hash_output[31] &= 63; - hash_output[31] |= 64; - hash_output - }; - - Ok(SigningKey { - az, - public: secret[32..64].try_into().unwrap(), - }) - } - - /// A constructor to generate a secret key from a 32-byte seed - pub fn from_seed(seed: &[u8]) -> Result { - if seed.len() != 32 { - return Err(InvalidKey); - } - - let mut secret: [u8; 64] = { - let mut hasher = Sha512::new(); - hasher.update(seed); - let mut hash_output: [u8; 64] = hasher.finalize().into(); - hash_output[0] &= 248; - hash_output[31] &= 63; - hash_output[31] |= 64; - hash_output - }; - - let a = ge_scalarmult_base(&secret[0..32]); - let public_key = a.to_bytes(); - - secret[0..32].copy_from_slice(seed); - secret[32..64].copy_from_slice(&public_key); - - SigningKey::from(&secret) - } - - /// A constructor that randomly generates a secret key - pub fn generate() -> Result { - let mut seed = [0u8; 32]; - let result = getrandom(&mut seed); - - if result.is_err() { - return Err(InvalidKey); - } - - let mut secret: [u8; 64] = { - let mut hasher = Sha512::new(); - hasher.update(&seed); - let mut hash_output: [u8; 64] = hasher.finalize().into(); - hash_output[0] &= 248; - hash_output[31] &= 63; - hash_output[31] |= 64; - hash_output - }; - - let a = ge_scalarmult_base(&secret[0..32]); - let public_key = a.to_bytes(); - for (dest, src) in (&mut secret[32..64]).iter_mut().zip(public_key.iter()) { - *dest = *src; - } - for (dest, src) in (&mut secret[0..32]).iter_mut().zip(seed.iter()) { - *dest = *src; - } - - let mut secret: [u8; 64] = { - let mut hasher = Sha512::new(); - hasher.update(&seed); - let mut hash_output: [u8; 64] = hasher.finalize().into(); - hash_output[0] &= 248; - hash_output[31] &= 63; - hash_output[31] |= 64; - hash_output - }; - - let a = ge_scalarmult_base(&secret[0..32]); - let public_key = a.to_bytes(); - for (dest, src) in (&mut secret[32..64]).iter_mut().zip(public_key.iter()) { - *dest = *src; - } - for (dest, src) in (&mut secret[0..32]).iter_mut().zip(seed.iter()) { - *dest = *src; - } - - SigningKey::from(&secret) - } - - /// Returns the public key for verifying - pub fn public_key(&self) -> VerifyingKey { - VerifyingKey::from(&self.public).unwrap() - } - - /// Returns the public key for verifying - pub fn verifier(&self) -> VerifyingKey { - VerifyingKey::from(&self.public).unwrap() - } - - /// Signs messages - pub fn sign(&self, msg: &[u8]) -> [u8; 64] { - let nonce = { - let mut hasher = Sha512::new(); - hasher.update(&self.az[32..64]); - hasher.update(msg); - let mut hash_output: [u8; 64] = hasher.finalize().into(); - sc_reduce(&mut hash_output[0..64]); - hash_output - }; - - let mut signature: [u8; 64] = [0; 64]; - let r: GeP3 = ge_scalarmult_base(&nonce[0..32]); - signature[0..32].copy_from_slice(&r.to_bytes()); - signature[32..64].copy_from_slice(&self.public); - - { - let mut hasher = Sha512::new(); - hasher.update(signature.as_ref()); - hasher.update(msg); - let mut hram: [u8; 64] = hasher.finalize().into(); - sc_reduce(&mut hram); - sc_muladd( - &mut signature[32..64], - &hram[0..32], - &self.az[0..32], - &nonce[0..32], - ); - } - - signature - } -} - -/// A class to verify messages signed with the corresponding secret key -pub struct VerifyingKey { - public: [u8; 32], -} - -impl VerifyingKey { - /// Constructs a verifier from a public key - pub fn from(public_key: &[u8]) -> Result { - if public_key.len() != 32 { - return Err(InvalidKey); - } - Ok(VerifyingKey { - public: public_key.try_into().unwrap(), - }) - } - - pub fn verify(&self, message: &[u8], signature: &[u8]) -> bool { - if signature.len() != 64 { - return false; - } - - if !check_s_lt_l(&signature[32..64]) { - return false; - } - - let a = match GeP3::from_bytes_negate_vartime(&self.public) { - Some(g) => g, - None => { - return false; - } - }; - let mut d = 0; - for pk_byte in self.public.iter() { - d |= *pk_byte; - } - if d == 0 { - return false; - } - - let mut hasher = Sha512::new(); - hasher.update(&signature[0..32]); - hasher.update(&self.public); - hasher.update(message); - let mut hash: [u8; 64] = hasher.finalize().into(); - sc_reduce(&mut hash); - - let r = GeP2::double_scalarmult_vartime(hash.as_ref(), a, &signature[32..64]); - let rcheck = r.to_bytes(); - - const_time_eq(rcheck.as_ref(), &signature[0..32]) - } -} diff --git a/src/ecc/ge.rs b/src/ecc/ge.rs deleted file mode 100644 index b58ad0e..0000000 --- a/src/ecc/ge.rs +++ /dev/null @@ -1,6341 +0,0 @@ -// adapted from the rust-crypto ed25519 implementation - -use crate::utils::const_time_eq as fixed_time_eq; -use std::cmp::min; -use std::ops::{Add, Mul, Sub}; - -#[derive(Clone, Copy)] -pub struct Fe(pub [i32; 10]); - -impl Add for Fe { - type Output = Fe; - - /* - h = f + g - Can overlap h with f or g. - - Preconditions: - |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - - Postconditions: - |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - */ - fn add(self, _rhs: Fe) -> Fe { - let Fe(f) = self; - let Fe(g) = _rhs; - - let f0 = f[0]; - let f1 = f[1]; - let f2 = f[2]; - let f3 = f[3]; - let f4 = f[4]; - let f5 = f[5]; - let f6 = f[6]; - let f7 = f[7]; - let f8 = f[8]; - let f9 = f[9]; - let g0 = g[0]; - let g1 = g[1]; - let g2 = g[2]; - let g3 = g[3]; - let g4 = g[4]; - let g5 = g[5]; - let g6 = g[6]; - let g7 = g[7]; - let g8 = g[8]; - let g9 = g[9]; - let h0 = f0 + g0; - let h1 = f1 + g1; - let h2 = f2 + g2; - let h3 = f3 + g3; - let h4 = f4 + g4; - let h5 = f5 + g5; - let h6 = f6 + g6; - let h7 = f7 + g7; - let h8 = f8 + g8; - let h9 = f9 + g9; - Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9]) - } -} - -impl Sub for Fe { - type Output = Fe; - - /* - h = f - g - Can overlap h with f or g. - - Preconditions: - |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - - Postconditions: - |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - */ - fn sub(self, _rhs: Fe) -> Fe { - let Fe(f) = self; - let Fe(g) = _rhs; - - let f0 = f[0]; - let f1 = f[1]; - let f2 = f[2]; - let f3 = f[3]; - let f4 = f[4]; - let f5 = f[5]; - let f6 = f[6]; - let f7 = f[7]; - let f8 = f[8]; - let f9 = f[9]; - let g0 = g[0]; - let g1 = g[1]; - let g2 = g[2]; - let g3 = g[3]; - let g4 = g[4]; - let g5 = g[5]; - let g6 = g[6]; - let g7 = g[7]; - let g8 = g[8]; - let g9 = g[9]; - let h0 = f0 - g0; - let h1 = f1 - g1; - let h2 = f2 - g2; - let h3 = f3 - g3; - let h4 = f4 - g4; - let h5 = f5 - g5; - let h6 = f6 - g6; - let h7 = f7 - g7; - let h8 = f8 - g8; - let h9 = f9 - g9; - Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9]) - } -} - -impl Mul for Fe { - type Output = Fe; - - /* - h = f * g - Can overlap h with f or g. - - Preconditions: - |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - - Postconditions: - |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - */ - - /* - Notes on implementation strategy: - - Using schoolbook multiplication. - Karatsuba would save a little in some cost models. - - Most multiplications by 2 and 19 are 32-bit precomputations; - cheaper than 64-bit postcomputations. - - There is one remaining multiplication by 19 in the carry chain; - one *19 precomputation can be merged into this, - but the resulting data flow is considerably less clean. - - There are 12 carries below. - 10 of them are 2-way parallelizable and vectorizable. - Can get away with 11 carries, but then data flow is much deeper. - - With tighter constraints on inputs can squeeze carries into int32. - */ - - fn mul(self, _rhs: Fe) -> Fe { - let Fe(f) = self; - let Fe(g) = _rhs; - let f0 = f[0]; - let f1 = f[1]; - let f2 = f[2]; - let f3 = f[3]; - let f4 = f[4]; - let f5 = f[5]; - let f6 = f[6]; - let f7 = f[7]; - let f8 = f[8]; - let f9 = f[9]; - let g0 = g[0]; - let g1 = g[1]; - let g2 = g[2]; - let g3 = g[3]; - let g4 = g[4]; - let g5 = g[5]; - let g6 = g[6]; - let g7 = g[7]; - let g8 = g[8]; - let g9 = g[9]; - let g1_19 = 19 * g1; /* 1.4*2^29 */ - let g2_19 = 19 * g2; /* 1.4*2^30; still ok */ - let g3_19 = 19 * g3; - let g4_19 = 19 * g4; - let g5_19 = 19 * g5; - let g6_19 = 19 * g6; - let g7_19 = 19 * g7; - let g8_19 = 19 * g8; - let g9_19 = 19 * g9; - let f1_2 = 2 * f1; - let f3_2 = 2 * f3; - let f5_2 = 2 * f5; - let f7_2 = 2 * f7; - let f9_2 = 2 * f9; - let f0g0 = (f0 as i64) * (g0 as i64); - let f0g1 = (f0 as i64) * (g1 as i64); - let f0g2 = (f0 as i64) * (g2 as i64); - let f0g3 = (f0 as i64) * (g3 as i64); - let f0g4 = (f0 as i64) * (g4 as i64); - let f0g5 = (f0 as i64) * (g5 as i64); - let f0g6 = (f0 as i64) * (g6 as i64); - let f0g7 = (f0 as i64) * (g7 as i64); - let f0g8 = (f0 as i64) * (g8 as i64); - let f0g9 = (f0 as i64) * (g9 as i64); - let f1g0 = (f1 as i64) * (g0 as i64); - let f1g1_2 = (f1_2 as i64) * (g1 as i64); - let f1g2 = (f1 as i64) * (g2 as i64); - let f1g3_2 = (f1_2 as i64) * (g3 as i64); - let f1g4 = (f1 as i64) * (g4 as i64); - let f1g5_2 = (f1_2 as i64) * (g5 as i64); - let f1g6 = (f1 as i64) * (g6 as i64); - let f1g7_2 = (f1_2 as i64) * (g7 as i64); - let f1g8 = (f1 as i64) * (g8 as i64); - let f1g9_38 = (f1_2 as i64) * (g9_19 as i64); - let f2g0 = (f2 as i64) * (g0 as i64); - let f2g1 = (f2 as i64) * (g1 as i64); - let f2g2 = (f2 as i64) * (g2 as i64); - let f2g3 = (f2 as i64) * (g3 as i64); - let f2g4 = (f2 as i64) * (g4 as i64); - let f2g5 = (f2 as i64) * (g5 as i64); - let f2g6 = (f2 as i64) * (g6 as i64); - let f2g7 = (f2 as i64) * (g7 as i64); - let f2g8_19 = (f2 as i64) * (g8_19 as i64); - let f2g9_19 = (f2 as i64) * (g9_19 as i64); - let f3g0 = (f3 as i64) * (g0 as i64); - let f3g1_2 = (f3_2 as i64) * (g1 as i64); - let f3g2 = (f3 as i64) * (g2 as i64); - let f3g3_2 = (f3_2 as i64) * (g3 as i64); - let f3g4 = (f3 as i64) * (g4 as i64); - let f3g5_2 = (f3_2 as i64) * (g5 as i64); - let f3g6 = (f3 as i64) * (g6 as i64); - let f3g7_38 = (f3_2 as i64) * (g7_19 as i64); - let f3g8_19 = (f3 as i64) * (g8_19 as i64); - let f3g9_38 = (f3_2 as i64) * (g9_19 as i64); - let f4g0 = (f4 as i64) * (g0 as i64); - let f4g1 = (f4 as i64) * (g1 as i64); - let f4g2 = (f4 as i64) * (g2 as i64); - let f4g3 = (f4 as i64) * (g3 as i64); - let f4g4 = (f4 as i64) * (g4 as i64); - let f4g5 = (f4 as i64) * (g5 as i64); - let f4g6_19 = (f4 as i64) * (g6_19 as i64); - let f4g7_19 = (f4 as i64) * (g7_19 as i64); - let f4g8_19 = (f4 as i64) * (g8_19 as i64); - let f4g9_19 = (f4 as i64) * (g9_19 as i64); - let f5g0 = (f5 as i64) * (g0 as i64); - let f5g1_2 = (f5_2 as i64) * (g1 as i64); - let f5g2 = (f5 as i64) * (g2 as i64); - let f5g3_2 = (f5_2 as i64) * (g3 as i64); - let f5g4 = (f5 as i64) * (g4 as i64); - let f5g5_38 = (f5_2 as i64) * (g5_19 as i64); - let f5g6_19 = (f5 as i64) * (g6_19 as i64); - let f5g7_38 = (f5_2 as i64) * (g7_19 as i64); - let f5g8_19 = (f5 as i64) * (g8_19 as i64); - let f5g9_38 = (f5_2 as i64) * (g9_19 as i64); - let f6g0 = (f6 as i64) * (g0 as i64); - let f6g1 = (f6 as i64) * (g1 as i64); - let f6g2 = (f6 as i64) * (g2 as i64); - let f6g3 = (f6 as i64) * (g3 as i64); - let f6g4_19 = (f6 as i64) * (g4_19 as i64); - let f6g5_19 = (f6 as i64) * (g5_19 as i64); - let f6g6_19 = (f6 as i64) * (g6_19 as i64); - let f6g7_19 = (f6 as i64) * (g7_19 as i64); - let f6g8_19 = (f6 as i64) * (g8_19 as i64); - let f6g9_19 = (f6 as i64) * (g9_19 as i64); - let f7g0 = (f7 as i64) * (g0 as i64); - let f7g1_2 = (f7_2 as i64) * (g1 as i64); - let f7g2 = (f7 as i64) * (g2 as i64); - let f7g3_38 = (f7_2 as i64) * (g3_19 as i64); - let f7g4_19 = (f7 as i64) * (g4_19 as i64); - let f7g5_38 = (f7_2 as i64) * (g5_19 as i64); - let f7g6_19 = (f7 as i64) * (g6_19 as i64); - let f7g7_38 = (f7_2 as i64) * (g7_19 as i64); - let f7g8_19 = (f7 as i64) * (g8_19 as i64); - let f7g9_38 = (f7_2 as i64) * (g9_19 as i64); - let f8g0 = (f8 as i64) * (g0 as i64); - let f8g1 = (f8 as i64) * (g1 as i64); - let f8g2_19 = (f8 as i64) * (g2_19 as i64); - let f8g3_19 = (f8 as i64) * (g3_19 as i64); - let f8g4_19 = (f8 as i64) * (g4_19 as i64); - let f8g5_19 = (f8 as i64) * (g5_19 as i64); - let f8g6_19 = (f8 as i64) * (g6_19 as i64); - let f8g7_19 = (f8 as i64) * (g7_19 as i64); - let f8g8_19 = (f8 as i64) * (g8_19 as i64); - let f8g9_19 = (f8 as i64) * (g9_19 as i64); - let f9g0 = (f9 as i64) * (g0 as i64); - let f9g1_38 = (f9_2 as i64) * (g1_19 as i64); - let f9g2_19 = (f9 as i64) * (g2_19 as i64); - let f9g3_38 = (f9_2 as i64) * (g3_19 as i64); - let f9g4_19 = (f9 as i64) * (g4_19 as i64); - let f9g5_38 = (f9_2 as i64) * (g5_19 as i64); - let f9g6_19 = (f9 as i64) * (g6_19 as i64); - let f9g7_38 = (f9_2 as i64) * (g7_19 as i64); - let f9g8_19 = (f9 as i64) * (g8_19 as i64); - let f9g9_38 = (f9_2 as i64) * (g9_19 as i64); - let mut h0 = f0g0 - + f1g9_38 - + f2g8_19 - + f3g7_38 - + f4g6_19 - + f5g5_38 - + f6g4_19 - + f7g3_38 - + f8g2_19 - + f9g1_38; - let mut h1 = f0g1 - + f1g0 - + f2g9_19 - + f3g8_19 - + f4g7_19 - + f5g6_19 - + f6g5_19 - + f7g4_19 - + f8g3_19 - + f9g2_19; - let mut h2 = f0g2 - + f1g1_2 - + f2g0 - + f3g9_38 - + f4g8_19 - + f5g7_38 - + f6g6_19 - + f7g5_38 - + f8g4_19 - + f9g3_38; - let mut h3 = - f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; - let mut h4 = - f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; - let mut h5 = - f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; - let mut h6 = - f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; - let mut h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; - let mut h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; - let mut h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0; - let mut carry0; - let carry1; - let carry2; - let carry3; - let mut carry4; - let carry5; - let carry6; - let carry7; - let carry8; - let carry9; - - /* - |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38)) - i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8 - |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19)) - i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9 - */ - - carry0 = (h0 + (1 << 25)) >> 26; - h1 += carry0; - h0 -= carry0 << 26; - carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - /* |h0| <= 2^25 */ - /* |h4| <= 2^25 */ - /* |h1| <= 1.51*2^58 */ - /* |h5| <= 1.51*2^58 */ - - carry1 = (h1 + (1 << 24)) >> 25; - h2 += carry1; - h1 -= carry1 << 25; - carry5 = (h5 + (1 << 24)) >> 25; - h6 += carry5; - h5 -= carry5 << 25; - /* |h1| <= 2^24; from now on fits into int32 */ - /* |h5| <= 2^24; from now on fits into int32 */ - /* |h2| <= 1.21*2^59 */ - /* |h6| <= 1.21*2^59 */ - - carry2 = (h2 + (1 << 25)) >> 26; - h3 += carry2; - h2 -= carry2 << 26; - carry6 = (h6 + (1 << 25)) >> 26; - h7 += carry6; - h6 -= carry6 << 26; - /* |h2| <= 2^25; from now on fits into int32 unchanged */ - /* |h6| <= 2^25; from now on fits into int32 unchanged */ - /* |h3| <= 1.51*2^58 */ - /* |h7| <= 1.51*2^58 */ - - carry3 = (h3 + (1 << 24)) >> 25; - h4 += carry3; - h3 -= carry3 << 25; - carry7 = (h7 + (1 << 24)) >> 25; - h8 += carry7; - h7 -= carry7 << 25; - /* |h3| <= 2^24; from now on fits into int32 unchanged */ - /* |h7| <= 2^24; from now on fits into int32 unchanged */ - /* |h4| <= 1.52*2^33 */ - /* |h8| <= 1.52*2^33 */ - - carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - carry8 = (h8 + (1 << 25)) >> 26; - h9 += carry8; - h8 -= carry8 << 26; - /* |h4| <= 2^25; from now on fits into int32 unchanged */ - /* |h8| <= 2^25; from now on fits into int32 unchanged */ - /* |h5| <= 1.01*2^24 */ - /* |h9| <= 1.51*2^58 */ - - carry9 = (h9 + (1 << 24)) >> 25; - h0 += carry9 * 19; - h9 -= carry9 << 25; - /* |h9| <= 2^24; from now on fits into int32 unchanged */ - /* |h0| <= 1.8*2^37 */ - - carry0 = (h0 + (1 << 25)) >> 26; - h1 += carry0; - h0 -= carry0 << 26; - /* |h0| <= 2^25; from now on fits into int32 unchanged */ - /* |h1| <= 1.01*2^24 */ - - Fe([ - h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32, h5 as i32, h6 as i32, h7 as i32, - h8 as i32, h9 as i32, - ]) - } -} - -impl Fe { - pub fn from_bytes(s: &[u8]) -> Fe { - let mut h0 = load_4i(&s[0..4]); - let mut h1 = load_3i(&s[4..7]) << 6; - let mut h2 = load_3i(&s[7..10]) << 5; - let mut h3 = load_3i(&s[10..13]) << 3; - let mut h4 = load_3i(&s[13..16]) << 2; - let mut h5 = load_4i(&s[16..20]); - let mut h6 = load_3i(&s[20..23]) << 7; - let mut h7 = load_3i(&s[23..26]) << 5; - let mut h8 = load_3i(&s[26..29]) << 4; - let mut h9 = (load_3i(&s[29..32]) & 8388607) << 2; - - let carry9 = (h9 + (1 << 24)) >> 25; - h0 += carry9 * 19; - h9 -= carry9 << 25; - let carry1 = (h1 + (1 << 24)) >> 25; - h2 += carry1; - h1 -= carry1 << 25; - let carry3 = (h3 + (1 << 24)) >> 25; - h4 += carry3; - h3 -= carry3 << 25; - let carry5 = (h5 + (1 << 24)) >> 25; - h6 += carry5; - h5 -= carry5 << 25; - let carry7 = (h7 + (1 << 24)) >> 25; - h8 += carry7; - h7 -= carry7 << 25; - - let carry0 = (h0 + (1 << 25)) >> 26; - h1 += carry0; - h0 -= carry0 << 26; - let carry2 = (h2 + (1 << 25)) >> 26; - h3 += carry2; - h2 -= carry2 << 26; - let carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - let carry6 = (h6 + (1 << 25)) >> 26; - h7 += carry6; - h6 -= carry6 << 26; - let carry8 = (h8 + (1 << 25)) >> 26; - h9 += carry8; - h8 -= carry8 << 26; - - Fe([ - h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32, h5 as i32, h6 as i32, h7 as i32, - h8 as i32, h9 as i32, - ]) - } - - /* - Preconditions: - |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - - Write p=2^255-19; q=floor(h/p). - Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). - - Proof: - Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. - Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4. - - Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). - Then 0 [u8; 32] { - let &Fe(es) = self; - let mut h0 = es[0]; - let mut h1 = es[1]; - let mut h2 = es[2]; - let mut h3 = es[3]; - let mut h4 = es[4]; - let mut h5 = es[5]; - let mut h6 = es[6]; - let mut h7 = es[7]; - let mut h8 = es[8]; - let mut h9 = es[9]; - let mut q; - - q = (19 * h9 + (1 << 24)) >> 25; - q = (h0 + q) >> 26; - q = (h1 + q) >> 25; - q = (h2 + q) >> 26; - q = (h3 + q) >> 25; - q = (h4 + q) >> 26; - q = (h5 + q) >> 25; - q = (h6 + q) >> 26; - q = (h7 + q) >> 25; - q = (h8 + q) >> 26; - q = (h9 + q) >> 25; - - /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ - h0 += 19 * q; - /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ - - let carry0 = h0 >> 26; - h1 += carry0; - h0 -= carry0 << 26; - let carry1 = h1 >> 25; - h2 += carry1; - h1 -= carry1 << 25; - let carry2 = h2 >> 26; - h3 += carry2; - h2 -= carry2 << 26; - let carry3 = h3 >> 25; - h4 += carry3; - h3 -= carry3 << 25; - let carry4 = h4 >> 26; - h5 += carry4; - h4 -= carry4 << 26; - let carry5 = h5 >> 25; - h6 += carry5; - h5 -= carry5 << 25; - let carry6 = h6 >> 26; - h7 += carry6; - h6 -= carry6 << 26; - let carry7 = h7 >> 25; - h8 += carry7; - h7 -= carry7 << 25; - let carry8 = h8 >> 26; - h9 += carry8; - h8 -= carry8 << 26; - let carry9 = h9 >> 25; - h9 -= carry9 << 25; - /* h10 = carry9 */ - - /* - Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. - Have h0+...+2^230 h9 between 0 and 2^255-1; - evidently 2^255 h10-2^255 q = 0. - Goal: Output h0+...+2^230 h9. - */ - [ - (h0 >> 0) as u8, - (h0 >> 8) as u8, - (h0 >> 16) as u8, - ((h0 >> 24) | (h1 << 2)) as u8, - (h1 >> 6) as u8, - (h1 >> 14) as u8, - ((h1 >> 22) | (h2 << 3)) as u8, - (h2 >> 5) as u8, - (h2 >> 13) as u8, - ((h2 >> 21) | (h3 << 5)) as u8, - (h3 >> 3) as u8, - (h3 >> 11) as u8, - ((h3 >> 19) | (h4 << 6)) as u8, - (h4 >> 2) as u8, - (h4 >> 10) as u8, - (h4 >> 18) as u8, - (h5 >> 0) as u8, - (h5 >> 8) as u8, - (h5 >> 16) as u8, - ((h5 >> 24) | (h6 << 1)) as u8, - (h6 >> 7) as u8, - (h6 >> 15) as u8, - ((h6 >> 23) | (h7 << 3)) as u8, - (h7 >> 5) as u8, - (h7 >> 13) as u8, - ((h7 >> 21) | (h8 << 4)) as u8, - (h8 >> 4) as u8, - (h8 >> 12) as u8, - ((h8 >> 20) | (h9 << 6)) as u8, - (h9 >> 2) as u8, - (h9 >> 10) as u8, - (h9 >> 18) as u8, - ] - } - - pub fn maybe_swap_with(&mut self, other: &mut Fe, do_swap: i32) { - let &mut Fe(f) = self; - let &mut Fe(g) = other; - let f0 = f[0]; - let f1 = f[1]; - let f2 = f[2]; - let f3 = f[3]; - let f4 = f[4]; - let f5 = f[5]; - let f6 = f[6]; - let f7 = f[7]; - let f8 = f[8]; - let f9 = f[9]; - let g0 = g[0]; - let g1 = g[1]; - let g2 = g[2]; - let g3 = g[3]; - let g4 = g[4]; - let g5 = g[5]; - let g6 = g[6]; - let g7 = g[7]; - let g8 = g[8]; - let g9 = g[9]; - let mut x0 = f0 ^ g0; - let mut x1 = f1 ^ g1; - let mut x2 = f2 ^ g2; - let mut x3 = f3 ^ g3; - let mut x4 = f4 ^ g4; - let mut x5 = f5 ^ g5; - let mut x6 = f6 ^ g6; - let mut x7 = f7 ^ g7; - let mut x8 = f8 ^ g8; - let mut x9 = f9 ^ g9; - let b = -do_swap; - x0 &= b; - x1 &= b; - x2 &= b; - x3 &= b; - x4 &= b; - x5 &= b; - x6 &= b; - x7 &= b; - x8 &= b; - x9 &= b; - *self = Fe([ - f0 ^ x0, - f1 ^ x1, - f2 ^ x2, - f3 ^ x3, - f4 ^ x4, - f5 ^ x5, - f6 ^ x6, - f7 ^ x7, - f8 ^ x8, - f9 ^ x9, - ]); - *other = Fe([ - g0 ^ x0, - g1 ^ x1, - g2 ^ x2, - g3 ^ x3, - g4 ^ x4, - g5 ^ x5, - g6 ^ x6, - g7 ^ x7, - g8 ^ x8, - g9 ^ x9, - ]); - } - - pub fn maybe_set(&mut self, other: &Fe, do_swap: i32) { - let &mut Fe(f) = self; - let &Fe(g) = other; - let f0 = f[0]; - let f1 = f[1]; - let f2 = f[2]; - let f3 = f[3]; - let f4 = f[4]; - let f5 = f[5]; - let f6 = f[6]; - let f7 = f[7]; - let f8 = f[8]; - let f9 = f[9]; - let g0 = g[0]; - let g1 = g[1]; - let g2 = g[2]; - let g3 = g[3]; - let g4 = g[4]; - let g5 = g[5]; - let g6 = g[6]; - let g7 = g[7]; - let g8 = g[8]; - let g9 = g[9]; - let mut x0 = f0 ^ g0; - let mut x1 = f1 ^ g1; - let mut x2 = f2 ^ g2; - let mut x3 = f3 ^ g3; - let mut x4 = f4 ^ g4; - let mut x5 = f5 ^ g5; - let mut x6 = f6 ^ g6; - let mut x7 = f7 ^ g7; - let mut x8 = f8 ^ g8; - let mut x9 = f9 ^ g9; - let b = -do_swap; - x0 &= b; - x1 &= b; - x2 &= b; - x3 &= b; - x4 &= b; - x5 &= b; - x6 &= b; - x7 &= b; - x8 &= b; - x9 &= b; - *self = Fe([ - f0 ^ x0, - f1 ^ x1, - f2 ^ x2, - f3 ^ x3, - f4 ^ x4, - f5 ^ x5, - f6 ^ x6, - f7 ^ x7, - f8 ^ x8, - f9 ^ x9, - ]); - } - - /* - h = f * 121666 - Can overlap h with f. - - Preconditions: - |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - - Postconditions: - |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - */ - - fn mul_121666(&self) -> Fe { - let &Fe(f) = self; - - let mut h0 = (f[0] as i64) * 121666; - let mut h1 = (f[1] as i64) * 121666; - let mut h2 = (f[2] as i64) * 121666; - let mut h3 = (f[3] as i64) * 121666; - let mut h4 = (f[4] as i64) * 121666; - let mut h5 = (f[5] as i64) * 121666; - let mut h6 = (f[6] as i64) * 121666; - let mut h7 = (f[7] as i64) * 121666; - let mut h8 = (f[8] as i64) * 121666; - let mut h9 = (f[9] as i64) * 121666; - - let carry9 = (h9 + (1 << 24)) >> 25; - h0 += carry9 * 19; - h9 -= carry9 << 25; - let carry1 = (h1 + (1 << 24)) >> 25; - h2 += carry1; - h1 -= carry1 << 25; - let carry3 = (h3 + (1 << 24)) >> 25; - h4 += carry3; - h3 -= carry3 << 25; - let carry5 = (h5 + (1 << 24)) >> 25; - h6 += carry5; - h5 -= carry5 << 25; - let carry7 = (h7 + (1 << 24)) >> 25; - h8 += carry7; - h7 -= carry7 << 25; - - let carry0 = (h0 + (1 << 25)) >> 26; - h1 += carry0; - h0 -= carry0 << 26; - let carry2 = (h2 + (1 << 25)) >> 26; - h3 += carry2; - h2 -= carry2 << 26; - let carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - let carry6 = (h6 + (1 << 25)) >> 26; - h7 += carry6; - h6 -= carry6 << 26; - let carry8 = (h8 + (1 << 25)) >> 26; - h9 += carry8; - h8 -= carry8 << 26; - - Fe([ - h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32, h5 as i32, h6 as i32, h7 as i32, - h8 as i32, h9 as i32, - ]) - } - - /* - h = f * f - Can overlap h with f. - - Preconditions: - |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - - Postconditions: - |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - */ - - /* - See fe_mul.c for discussion of implementation strategy. - */ - fn square(&self) -> Fe { - let &Fe(f) = self; - - let f0 = f[0]; - let f1 = f[1]; - let f2 = f[2]; - let f3 = f[3]; - let f4 = f[4]; - let f5 = f[5]; - let f6 = f[6]; - let f7 = f[7]; - let f8 = f[8]; - let f9 = f[9]; - let f0_2 = 2 * f0; - let f1_2 = 2 * f1; - let f2_2 = 2 * f2; - let f3_2 = 2 * f3; - let f4_2 = 2 * f4; - let f5_2 = 2 * f5; - let f6_2 = 2 * f6; - let f7_2 = 2 * f7; - let f5_38 = 38 * f5; /* 1.31*2^30 */ - let f6_19 = 19 * f6; /* 1.31*2^30 */ - let f7_38 = 38 * f7; /* 1.31*2^30 */ - let f8_19 = 19 * f8; /* 1.31*2^30 */ - let f9_38 = 38 * f9; /* 1.31*2^30 */ - let f0f0 = (f0 as i64) * (f0 as i64); - let f0f1_2 = (f0_2 as i64) * (f1 as i64); - let f0f2_2 = (f0_2 as i64) * (f2 as i64); - let f0f3_2 = (f0_2 as i64) * (f3 as i64); - let f0f4_2 = (f0_2 as i64) * (f4 as i64); - let f0f5_2 = (f0_2 as i64) * (f5 as i64); - let f0f6_2 = (f0_2 as i64) * (f6 as i64); - let f0f7_2 = (f0_2 as i64) * (f7 as i64); - let f0f8_2 = (f0_2 as i64) * (f8 as i64); - let f0f9_2 = (f0_2 as i64) * (f9 as i64); - let f1f1_2 = (f1_2 as i64) * (f1 as i64); - let f1f2_2 = (f1_2 as i64) * (f2 as i64); - let f1f3_4 = (f1_2 as i64) * (f3_2 as i64); - let f1f4_2 = (f1_2 as i64) * (f4 as i64); - let f1f5_4 = (f1_2 as i64) * (f5_2 as i64); - let f1f6_2 = (f1_2 as i64) * (f6 as i64); - let f1f7_4 = (f1_2 as i64) * (f7_2 as i64); - let f1f8_2 = (f1_2 as i64) * (f8 as i64); - let f1f9_76 = (f1_2 as i64) * (f9_38 as i64); - let f2f2 = (f2 as i64) * (f2 as i64); - let f2f3_2 = (f2_2 as i64) * (f3 as i64); - let f2f4_2 = (f2_2 as i64) * (f4 as i64); - let f2f5_2 = (f2_2 as i64) * (f5 as i64); - let f2f6_2 = (f2_2 as i64) * (f6 as i64); - let f2f7_2 = (f2_2 as i64) * (f7 as i64); - let f2f8_38 = (f2_2 as i64) * (f8_19 as i64); - let f2f9_38 = (f2 as i64) * (f9_38 as i64); - let f3f3_2 = (f3_2 as i64) * (f3 as i64); - let f3f4_2 = (f3_2 as i64) * (f4 as i64); - let f3f5_4 = (f3_2 as i64) * (f5_2 as i64); - let f3f6_2 = (f3_2 as i64) * (f6 as i64); - let f3f7_76 = (f3_2 as i64) * (f7_38 as i64); - let f3f8_38 = (f3_2 as i64) * (f8_19 as i64); - let f3f9_76 = (f3_2 as i64) * (f9_38 as i64); - let f4f4 = (f4 as i64) * (f4 as i64); - let f4f5_2 = (f4_2 as i64) * (f5 as i64); - let f4f6_38 = (f4_2 as i64) * (f6_19 as i64); - let f4f7_38 = (f4 as i64) * (f7_38 as i64); - let f4f8_38 = (f4_2 as i64) * (f8_19 as i64); - let f4f9_38 = (f4 as i64) * (f9_38 as i64); - let f5f5_38 = (f5 as i64) * (f5_38 as i64); - let f5f6_38 = (f5_2 as i64) * (f6_19 as i64); - let f5f7_76 = (f5_2 as i64) * (f7_38 as i64); - let f5f8_38 = (f5_2 as i64) * (f8_19 as i64); - let f5f9_76 = (f5_2 as i64) * (f9_38 as i64); - let f6f6_19 = (f6 as i64) * (f6_19 as i64); - let f6f7_38 = (f6 as i64) * (f7_38 as i64); - let f6f8_38 = (f6_2 as i64) * (f8_19 as i64); - let f6f9_38 = (f6 as i64) * (f9_38 as i64); - let f7f7_38 = (f7 as i64) * (f7_38 as i64); - let f7f8_38 = (f7_2 as i64) * (f8_19 as i64); - let f7f9_76 = (f7_2 as i64) * (f9_38 as i64); - let f8f8_19 = (f8 as i64) * (f8_19 as i64); - let f8f9_38 = (f8 as i64) * (f9_38 as i64); - let f9f9_38 = (f9 as i64) * (f9_38 as i64); - let mut h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; - let mut h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; - let mut h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; - let mut h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; - let mut h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; - let mut h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; - let mut h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; - let mut h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; - let mut h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; - let mut h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; - - let carry0 = (h0 + (1 << 25)) >> 26; - h1 += carry0; - h0 -= carry0 << 26; - let carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - - let carry1 = (h1 + (1 << 24)) >> 25; - h2 += carry1; - h1 -= carry1 << 25; - let carry5 = (h5 + (1 << 24)) >> 25; - h6 += carry5; - h5 -= carry5 << 25; - - let carry2 = (h2 + (1 << 25)) >> 26; - h3 += carry2; - h2 -= carry2 << 26; - let carry6 = (h6 + (1 << 25)) >> 26; - h7 += carry6; - h6 -= carry6 << 26; - - let carry3 = (h3 + (1 << 24)) >> 25; - h4 += carry3; - h3 -= carry3 << 25; - let carry7 = (h7 + (1 << 24)) >> 25; - h8 += carry7; - h7 -= carry7 << 25; - - let carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - let carry8 = (h8 + (1 << 25)) >> 26; - h9 += carry8; - h8 -= carry8 << 26; - - let carry9 = (h9 + (1 << 24)) >> 25; - h0 += carry9 * 19; - h9 -= carry9 << 25; - - let carrya = (h0 + (1 << 25)) >> 26; - h1 += carrya; - h0 -= carrya << 26; - - Fe([ - h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32, h5 as i32, h6 as i32, h7 as i32, - h8 as i32, h9 as i32, - ]) - } - - fn square_and_double(&self) -> Fe { - let &Fe(f) = self; - - let f0 = f[0]; - let f1 = f[1]; - let f2 = f[2]; - let f3 = f[3]; - let f4 = f[4]; - let f5 = f[5]; - let f6 = f[6]; - let f7 = f[7]; - let f8 = f[8]; - let f9 = f[9]; - let f0_2 = 2 * f0; - let f1_2 = 2 * f1; - let f2_2 = 2 * f2; - let f3_2 = 2 * f3; - let f4_2 = 2 * f4; - let f5_2 = 2 * f5; - let f6_2 = 2 * f6; - let f7_2 = 2 * f7; - let f5_38 = 38 * f5; /* 1.959375*2^30 */ - let f6_19 = 19 * f6; /* 1.959375*2^30 */ - let f7_38 = 38 * f7; /* 1.959375*2^30 */ - let f8_19 = 19 * f8; /* 1.959375*2^30 */ - let f9_38 = 38 * f9; /* 1.959375*2^30 */ - let f0f0 = (f0 as i64) * (f0 as i64); - let f0f1_2 = (f0_2 as i64) * (f1 as i64); - let f0f2_2 = (f0_2 as i64) * (f2 as i64); - let f0f3_2 = (f0_2 as i64) * (f3 as i64); - let f0f4_2 = (f0_2 as i64) * (f4 as i64); - let f0f5_2 = (f0_2 as i64) * (f5 as i64); - let f0f6_2 = (f0_2 as i64) * (f6 as i64); - let f0f7_2 = (f0_2 as i64) * (f7 as i64); - let f0f8_2 = (f0_2 as i64) * (f8 as i64); - let f0f9_2 = (f0_2 as i64) * (f9 as i64); - let f1f1_2 = (f1_2 as i64) * (f1 as i64); - let f1f2_2 = (f1_2 as i64) * (f2 as i64); - let f1f3_4 = (f1_2 as i64) * (f3_2 as i64); - let f1f4_2 = (f1_2 as i64) * (f4 as i64); - let f1f5_4 = (f1_2 as i64) * (f5_2 as i64); - let f1f6_2 = (f1_2 as i64) * (f6 as i64); - let f1f7_4 = (f1_2 as i64) * (f7_2 as i64); - let f1f8_2 = (f1_2 as i64) * (f8 as i64); - let f1f9_76 = (f1_2 as i64) * (f9_38 as i64); - let f2f2 = (f2 as i64) * (f2 as i64); - let f2f3_2 = (f2_2 as i64) * (f3 as i64); - let f2f4_2 = (f2_2 as i64) * (f4 as i64); - let f2f5_2 = (f2_2 as i64) * (f5 as i64); - let f2f6_2 = (f2_2 as i64) * (f6 as i64); - let f2f7_2 = (f2_2 as i64) * (f7 as i64); - let f2f8_38 = (f2_2 as i64) * (f8_19 as i64); - let f2f9_38 = (f2 as i64) * (f9_38 as i64); - let f3f3_2 = (f3_2 as i64) * (f3 as i64); - let f3f4_2 = (f3_2 as i64) * (f4 as i64); - let f3f5_4 = (f3_2 as i64) * (f5_2 as i64); - let f3f6_2 = (f3_2 as i64) * (f6 as i64); - let f3f7_76 = (f3_2 as i64) * (f7_38 as i64); - let f3f8_38 = (f3_2 as i64) * (f8_19 as i64); - let f3f9_76 = (f3_2 as i64) * (f9_38 as i64); - let f4f4 = (f4 as i64) * (f4 as i64); - let f4f5_2 = (f4_2 as i64) * (f5 as i64); - let f4f6_38 = (f4_2 as i64) * (f6_19 as i64); - let f4f7_38 = (f4 as i64) * (f7_38 as i64); - let f4f8_38 = (f4_2 as i64) * (f8_19 as i64); - let f4f9_38 = (f4 as i64) * (f9_38 as i64); - let f5f5_38 = (f5 as i64) * (f5_38 as i64); - let f5f6_38 = (f5_2 as i64) * (f6_19 as i64); - let f5f7_76 = (f5_2 as i64) * (f7_38 as i64); - let f5f8_38 = (f5_2 as i64) * (f8_19 as i64); - let f5f9_76 = (f5_2 as i64) * (f9_38 as i64); - let f6f6_19 = (f6 as i64) * (f6_19 as i64); - let f6f7_38 = (f6 as i64) * (f7_38 as i64); - let f6f8_38 = (f6_2 as i64) * (f8_19 as i64); - let f6f9_38 = (f6 as i64) * (f9_38 as i64); - let f7f7_38 = (f7 as i64) * (f7_38 as i64); - let f7f8_38 = (f7_2 as i64) * (f8_19 as i64); - let f7f9_76 = (f7_2 as i64) * (f9_38 as i64); - let f8f8_19 = (f8 as i64) * (f8_19 as i64); - let f8f9_38 = (f8 as i64) * (f9_38 as i64); - let f9f9_38 = (f9 as i64) * (f9_38 as i64); - let mut h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; - let mut h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; - let mut h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; - let mut h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; - let mut h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; - let mut h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; - let mut h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; - let mut h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; - let mut h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; - let mut h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; - let mut carry0: i64; - let carry1: i64; - let carry2: i64; - let carry3: i64; - let mut carry4: i64; - let carry5: i64; - let carry6: i64; - let carry7: i64; - let carry8: i64; - let carry9: i64; - - h0 += h0; - h1 += h1; - h2 += h2; - h3 += h3; - h4 += h4; - h5 += h5; - h6 += h6; - h7 += h7; - h8 += h8; - h9 += h9; - - carry0 = (h0 + (1 << 25)) >> 26; - h1 += carry0; - h0 -= carry0 << 26; - carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - - carry1 = (h1 + (1 << 24)) >> 25; - h2 += carry1; - h1 -= carry1 << 25; - carry5 = (h5 + (1 << 24)) >> 25; - h6 += carry5; - h5 -= carry5 << 25; - - carry2 = (h2 + (1 << 25)) >> 26; - h3 += carry2; - h2 -= carry2 << 26; - carry6 = (h6 + (1 << 25)) >> 26; - h7 += carry6; - h6 -= carry6 << 26; - - carry3 = (h3 + (1 << 24)) >> 25; - h4 += carry3; - h3 -= carry3 << 25; - carry7 = (h7 + (1 << 24)) >> 25; - h8 += carry7; - h7 -= carry7 << 25; - - carry4 = (h4 + (1 << 25)) >> 26; - h5 += carry4; - h4 -= carry4 << 26; - carry8 = (h8 + (1 << 25)) >> 26; - h9 += carry8; - h8 -= carry8 << 26; - - carry9 = (h9 + (1 << 24)) >> 25; - h0 += carry9 * 19; - h9 -= carry9 << 25; - - carry0 = (h0 + (1 << 25)) >> 26; - h1 += carry0; - h0 -= carry0 << 26; - - Fe([ - h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32, h5 as i32, h6 as i32, h7 as i32, - h8 as i32, h9 as i32, - ]) - } - - pub fn invert(&self) -> Fe { - let z1 = *self; - - /* qhasm: z2 = z1^2^1 */ - let z2 = z1.square(); - /* qhasm: z8 = z2^2^2 */ - let z8 = z2.square().square(); - /* qhasm: z9 = z1*z8 */ - let z9 = z1 * z8; - - /* qhasm: z11 = z2*z9 */ - let z11 = z2 * z9; - - /* qhasm: z22 = z11^2^1 */ - let z22 = z11.square(); - - /* qhasm: z_5_0 = z9*z22 */ - let z_5_0 = z9 * z22; - - /* qhasm: z_10_5 = z_5_0^2^5 */ - let z_10_5 = (0..5).fold(z_5_0, |z_5_n, _| z_5_n.square()); - - /* qhasm: z_10_0 = z_10_5*z_5_0 */ - let z_10_0 = z_10_5 * z_5_0; - - /* qhasm: z_20_10 = z_10_0^2^10 */ - let z_20_10 = (0..10).fold(z_10_0, |x, _| x.square()); - - /* qhasm: z_20_0 = z_20_10*z_10_0 */ - let z_20_0 = z_20_10 * z_10_0; - - /* qhasm: z_40_20 = z_20_0^2^20 */ - let z_40_20 = (0..20).fold(z_20_0, |x, _| x.square()); - - /* qhasm: z_40_0 = z_40_20*z_20_0 */ - let z_40_0 = z_40_20 * z_20_0; - - /* qhasm: z_50_10 = z_40_0^2^10 */ - let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square()); - - /* qhasm: z_50_0 = z_50_10*z_10_0 */ - let z_50_0 = z_50_10 * z_10_0; - - /* qhasm: z_100_50 = z_50_0^2^50 */ - let z_100_50 = (0..50).fold(z_50_0, |x, _| x.square()); - - /* qhasm: z_100_0 = z_100_50*z_50_0 */ - let z_100_0 = z_100_50 * z_50_0; - - /* qhasm: z_200_100 = z_100_0^2^100 */ - let z_200_100 = (0..100).fold(z_100_0, |x, _| x.square()); - - /* qhasm: z_200_0 = z_200_100*z_100_0 */ - /* asm 1: fe_mul(>z_200_0=fe#3,z_200_0=t2,z_255_21=fe#12,z_255_21=out, bool { - let bs = self.to_bytes(); - let zero = [0; 32]; - !fixed_time_eq(bs.as_ref(), zero.as_ref()) - } - - fn is_negative(&self) -> bool { - (self.to_bytes()[0] & 1) != 0 - } - - fn neg(&self) -> Fe { - let &Fe(f) = self; - Fe([ - -f[0], -f[1], -f[2], -f[3], -f[4], -f[5], -f[6], -f[7], -f[8], -f[9], - ]) - } - - fn pow25523(&self) -> Fe { - let z2 = self.square(); - let z8 = (0..2).fold(z2, |x, _| x.square()); - let z9 = *self * z8; - let z11 = z2 * z9; - let z22 = z11.square(); - let z_5_0 = z9 * z22; - let z_10_5 = (0..5).fold(z_5_0, |x, _| x.square()); - let z_10_0 = z_10_5 * z_5_0; - let z_20_10 = (0..10).fold(z_10_0, |x, _| x.square()); - let z_20_0 = z_20_10 * z_10_0; - let z_40_20 = (0..20).fold(z_20_0, |x, _| x.square()); - let z_40_0 = z_40_20 * z_20_0; - let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square()); - let z_50_0 = z_50_10 * z_10_0; - let z_100_50 = (0..50).fold(z_50_0, |x, _| x.square()); - let z_100_0 = z_100_50 * z_50_0; - let z_200_100 = (0..100).fold(z_100_0, |x, _| x.square()); - let z_200_0 = z_200_100 * z_100_0; - let z_250_50 = (0..50).fold(z_200_0, |x, _| x.square()); - let z_250_0 = z_250_50 * z_50_0; - let z_252_2 = (0..2).fold(z_250_0, |x, _| x.square()); - let z_252_3 = z_252_2 * *self; - - z_252_3 - } -} - -static FE_ZERO: Fe = Fe([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]); -static FE_ONE: Fe = Fe([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]); -static FE_SQRTM1: Fe = Fe([ - -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482, -]); -static FE_D: Fe = Fe([ - -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, - -12055116, -]); -static FE_D2: Fe = Fe([ - -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, - 9444199, -]); - -fn load_4u(s: &[u8]) -> u64 { - (s[0] as u64) | ((s[1] as u64) << 8) | ((s[2] as u64) << 16) | ((s[3] as u64) << 24) -} -fn load_4i(s: &[u8]) -> i64 { - load_4u(s) as i64 -} -fn load_3u(s: &[u8]) -> u64 { - (s[0] as u64) | ((s[1] as u64) << 8) | ((s[2] as u64) << 16) -} -fn load_3i(s: &[u8]) -> i64 { - load_3u(s) as i64 -} - -#[derive(Clone, Copy)] -pub struct GeP2 { - x: Fe, - y: Fe, - z: Fe, -} - -#[derive(Clone, Copy)] -pub struct GeP3 { - x: Fe, - y: Fe, - z: Fe, - t: Fe, -} - -#[derive(Clone, Copy)] -pub struct GeP1P1 { - x: Fe, - y: Fe, - z: Fe, - t: Fe, -} - -#[derive(Clone, Copy)] -pub struct GePrecomp { - y_plus_x: Fe, - y_minus_x: Fe, - xy2d: Fe, -} - -#[derive(Clone, Copy)] -pub struct GeCached { - y_plus_x: Fe, - y_minus_x: Fe, - z: Fe, - t2d: Fe, -} - -impl GeP1P1 { - fn to_p2(&self) -> GeP2 { - GeP2 { - x: self.x * self.t, - y: self.y * self.z, - z: self.z * self.t, - } - } - - fn to_p3(&self) -> GeP3 { - GeP3 { - x: self.x * self.t, - y: self.y * self.z, - z: self.z * self.t, - t: self.x * self.y, - } - } -} - -impl GeP2 { - fn zero() -> GeP2 { - GeP2 { - x: FE_ZERO, - y: FE_ONE, - z: FE_ONE, - } - } - - pub fn to_bytes(&self) -> [u8; 32] { - let recip = self.z.invert(); - let x = self.x * recip; - let y = self.y * recip; - let mut bs = y.to_bytes(); - bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7; - bs - } - - fn dbl(&self) -> GeP1P1 { - let xx = self.x.square(); - let yy = self.y.square(); - let b = self.z.square_and_double(); - let a = self.x + self.y; - let aa = a.square(); - let y3 = yy + xx; - let z3 = yy - xx; - let x3 = aa - y3; - let t3 = b - z3; - - GeP1P1 { - x: x3, - y: y3, - z: z3, - t: t3, - } - } - - fn slide(a: &[u8]) -> [i8; 256] { - let mut r = [0i8; 256]; - for i in 0..256 { - r[i] = (1 & (a[i >> 3] >> (i & 7))) as i8; - } - for i in 0..256 { - if r[i] != 0 { - for b in 1..min(7, 256 - i) { - if r[i + b] != 0 { - if r[i] + (r[i + b] << b) <= 15 { - r[i] += r[i + b] << b; - r[i + b] = 0; - } else if r[i] - (r[i + b] << b) >= -15 { - r[i] -= r[i + b] << b; - for k in i + b..256 { - if r[k] == 0 { - r[k] = 1; - break; - } - r[k] = 0; - } - } else { - break; - } - } - } - } - } - - r - } - - /* - r = a * A + b * B - where a = a[0]+256*a[1]+...+256^31 a[31]. - and b = b[0]+256*b[1]+...+256^31 b[31]. - B is the Ed25519 base point (x,4/5) with x positive. - */ - pub fn double_scalarmult_vartime(a_scalar: &[u8], a_point: GeP3, b_scalar: &[u8]) -> GeP2 { - let aslide = GeP2::slide(a_scalar); - let bslide = GeP2::slide(b_scalar); - - let mut ai = [GeCached { - y_plus_x: FE_ZERO, - y_minus_x: FE_ZERO, - z: FE_ZERO, - t2d: FE_ZERO, - }; 8]; /* A,3A,5A,7A,9A,11A,13A,15A */ - ai[0] = a_point.to_cached(); - let a2 = a_point.dbl().to_p3(); - ai[1] = (a2 + ai[0]).to_p3().to_cached(); - ai[2] = (a2 + ai[1]).to_p3().to_cached(); - ai[3] = (a2 + ai[2]).to_p3().to_cached(); - ai[4] = (a2 + ai[3]).to_p3().to_cached(); - ai[5] = (a2 + ai[4]).to_p3().to_cached(); - ai[6] = (a2 + ai[5]).to_p3().to_cached(); - ai[7] = (a2 + ai[6]).to_p3().to_cached(); - - let mut r = GeP2::zero(); - - let mut i: usize = 255; - loop { - if aslide[i] != 0 || bslide[i] != 0 { - break; - } - if i == 0 { - return r; - } - i -= 1; - } - - loop { - let mut t = r.dbl(); - if aslide[i] > 0 { - t = t.to_p3() + ai[(aslide[i] / 2) as usize]; - } else if aslide[i] < 0 { - t = t.to_p3() - ai[(-aslide[i] / 2) as usize]; - } - - if bslide[i] > 0 { - t = t.to_p3() + BI[(bslide[i] / 2) as usize]; - } else if bslide[i] < 0 { - t = t.to_p3() - BI[(-bslide[i] / 2) as usize]; - } - - r = t.to_p2(); - - if i == 0 { - return r; - } - i -= 1; - } - } -} - -impl GeP3 { - pub fn from_bytes_negate_vartime(s: &[u8]) -> Option { - let y = Fe::from_bytes(s); - let z = FE_ONE; - let y_squared = y.square(); - let u = y_squared - FE_ONE; - let v = (y_squared * FE_D) + FE_ONE; - let v_raise_3 = v.square() * v; - let v_raise_7 = v_raise_3.square() * v; - let uv7 = v_raise_7 * u; // Is this commutative? u comes second in the code, but not in the notation... - - let mut x = uv7.pow25523() * v_raise_3 * u; - - let vxx = x.square() * v; - let check = vxx - u; - if check.is_nonzero() { - let check2 = vxx + u; - if check2.is_nonzero() { - return None; - } - x = x * FE_SQRTM1; - } - - if x.is_negative() == ((s[31] >> 7) != 0) { - x = x.neg(); - } - - let t = x * y; - - Some(GeP3 { - x: x, - y: y, - z: z, - t: t, - }) - } - - fn to_p2(&self) -> GeP2 { - GeP2 { - x: self.x, - y: self.y, - z: self.z, - } - } - - fn to_cached(&self) -> GeCached { - GeCached { - y_plus_x: self.y + self.x, - y_minus_x: self.y - self.x, - z: self.z, - t2d: self.t * FE_D2, - } - } - - fn zero() -> GeP3 { - GeP3 { - x: FE_ZERO, - y: FE_ONE, - z: FE_ONE, - t: FE_ZERO, - } - } - - fn dbl(&self) -> GeP1P1 { - self.to_p2().dbl() - } - - pub fn to_bytes(&self) -> [u8; 32] { - let recip = self.z.invert(); - let x = self.x * recip; - let y = self.y * recip; - let mut bs = y.to_bytes(); - bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7; - bs - } -} - -impl Add for GeP3 { - type Output = GeP1P1; - - fn add(self, _rhs: GeCached) -> GeP1P1 { - let y1_plus_x1 = self.y + self.x; - let y1_minus_x1 = self.y - self.x; - let a = y1_plus_x1 * _rhs.y_plus_x; - let b = y1_minus_x1 * _rhs.y_minus_x; - let c = _rhs.t2d * self.t; - let zz = self.z * _rhs.z; - let d = zz + zz; - let x3 = a - b; - let y3 = a + b; - let z3 = d + c; - let t3 = d - c; - - GeP1P1 { - x: x3, - y: y3, - z: z3, - t: t3, - } - } -} - -impl Add for GeP3 { - type Output = GeP1P1; - - fn add(self, _rhs: GePrecomp) -> GeP1P1 { - let y1_plus_x1 = self.y + self.x; - let y1_minus_x1 = self.y - self.x; - let a = y1_plus_x1 * _rhs.y_plus_x; - let b = y1_minus_x1 * _rhs.y_minus_x; - let c = _rhs.xy2d * self.t; - let d = self.z + self.z; - let x3 = a - b; - let y3 = a + b; - let z3 = d + c; - let t3 = d - c; - - GeP1P1 { - x: x3, - y: y3, - z: z3, - t: t3, - } - } -} - -impl Sub for GeP3 { - type Output = GeP1P1; - - fn sub(self, _rhs: GeCached) -> GeP1P1 { - let y1_plus_x1 = self.y + self.x; - let y1_minus_x1 = self.y - self.x; - let a = y1_plus_x1 * _rhs.y_minus_x; - let b = y1_minus_x1 * _rhs.y_plus_x; - let c = _rhs.t2d * self.t; - let zz = self.z * _rhs.z; - let d = zz + zz; - let x3 = a - b; - let y3 = a + b; - let z3 = d - c; - let t3 = d + c; - - GeP1P1 { - x: x3, - y: y3, - z: z3, - t: t3, - } - } -} - -impl Sub for GeP3 { - type Output = GeP1P1; - - fn sub(self, _rhs: GePrecomp) -> GeP1P1 { - let y1_plus_x1 = self.y + self.x; - let y1_minus_x1 = self.y - self.x; - let a = y1_plus_x1 * _rhs.y_minus_x; - let b = y1_minus_x1 * _rhs.y_plus_x; - let c = _rhs.xy2d * self.t; - let d = self.z + self.z; - let x3 = a - b; - let y3 = a + b; - let z3 = d - c; - let t3 = d + c; - - GeP1P1 { - x: x3, - y: y3, - z: z3, - t: t3, - } - } -} - -fn equal(b: u8, c: u8) -> i32 { - let x = b ^ c; /* 0: yes; 1..255: no */ - let mut y = x as u32; /* 0: yes; 1..255: no */ - y = y.wrapping_sub(1); /* 4294967295: yes; 0..254: no */ - y >>= 31; /* 1: yes; 0: no */ - y as i32 -} - -impl GePrecomp { - fn zero() -> GePrecomp { - GePrecomp { - y_plus_x: FE_ONE, - y_minus_x: FE_ONE, - xy2d: FE_ZERO, - } - } - - pub fn maybe_set(&mut self, other: &GePrecomp, do_swap: i32) { - self.y_plus_x.maybe_set(&other.y_plus_x, do_swap); - self.y_minus_x.maybe_set(&other.y_minus_x, do_swap); - self.xy2d.maybe_set(&other.xy2d, do_swap); - } - - pub fn select(pos: usize, b: i8) -> GePrecomp { - let bnegative = (b as u8) >> 7; - let babs: u8 = (b - (((-(bnegative as i8)) & b) << 1)) as u8; - let mut t = GePrecomp::zero(); - t.maybe_set(&GE_PRECOMP_BASE[pos][0], equal(babs, 1)); - t.maybe_set(&GE_PRECOMP_BASE[pos][1], equal(babs, 2)); - t.maybe_set(&GE_PRECOMP_BASE[pos][2], equal(babs, 3)); - t.maybe_set(&GE_PRECOMP_BASE[pos][3], equal(babs, 4)); - t.maybe_set(&GE_PRECOMP_BASE[pos][4], equal(babs, 5)); - t.maybe_set(&GE_PRECOMP_BASE[pos][5], equal(babs, 6)); - t.maybe_set(&GE_PRECOMP_BASE[pos][6], equal(babs, 7)); - t.maybe_set(&GE_PRECOMP_BASE[pos][7], equal(babs, 8)); - let minus_t = GePrecomp { - y_plus_x: t.y_minus_x, - y_minus_x: t.y_plus_x, - xy2d: t.xy2d.neg(), - }; - t.maybe_set(&minus_t, bnegative as i32); - t - } -} - -/* -h = a * B -where a = a[0]+256*a[1]+...+256^31 a[31] -B is the Ed25519 base point (x,4/5) with x positive. - -Preconditions: - a[31] <= 127 -*/ -pub fn ge_scalarmult_base(a: &[u8]) -> GeP3 { - let mut es: [i8; 64] = [0; 64]; - let mut r: GeP1P1; - let mut s: GeP2; - let mut t: GePrecomp; - - for i in 0..32 { - es[2 * i + 0] = ((a[i] >> 0) & 15) as i8; - es[2 * i + 1] = ((a[i] >> 4) & 15) as i8; - } - /* each es[i] is between 0 and 15 */ - /* es[63] is between 0 and 7 */ - - let mut carry: i8 = 0; - for i in 0..63 { - es[i] += carry; - carry = es[i] + 8; - carry >>= 4; - es[i] -= carry << 4; - } - es[63] += carry; - /* each es[i] is between -8 and 8 */ - - let mut h = GeP3::zero(); - for i in (1..64).step_by(2) { - t = GePrecomp::select(i / 2, es[i]); - r = h + t; - h = r.to_p3(); - } - - r = h.dbl(); - s = r.to_p2(); - r = s.dbl(); - s = r.to_p2(); - r = s.dbl(); - s = r.to_p2(); - r = s.dbl(); - h = r.to_p3(); - - for i in (0..64).step_by(2) { - t = GePrecomp::select(i / 2, es[i]); - r = h + t; - h = r.to_p3(); - } - - h -} -/* -Input: - s[0]+256*s[1]+...+256^63*s[63] = s - -Output: - s[0]+256*s[1]+...+256^31*s[31] = s mod l - where l = 2^252 + 27742317777372353535851937790883648493. - Overwrites s in place. -*/ -pub fn sc_reduce(s: &mut [u8]) { - let mut s0: i64 = 2097151 & load_3i(s); - let mut s1: i64 = 2097151 & (load_4i(&s[2..6]) >> 5); - let mut s2: i64 = 2097151 & (load_3i(&s[5..8]) >> 2); - let mut s3: i64 = 2097151 & (load_4i(&s[7..11]) >> 7); - let mut s4: i64 = 2097151 & (load_4i(&s[10..14]) >> 4); - let mut s5: i64 = 2097151 & (load_3i(&s[13..16]) >> 1); - let mut s6: i64 = 2097151 & (load_4i(&s[15..19]) >> 6); - let mut s7: i64 = 2097151 & (load_3i(&s[18..21]) >> 3); - let mut s8: i64 = 2097151 & load_3i(&s[21..24]); - let mut s9: i64 = 2097151 & (load_4i(&s[23..27]) >> 5); - let mut s10: i64 = 2097151 & (load_3i(&s[26..29]) >> 2); - let mut s11: i64 = 2097151 & (load_4i(&s[28..32]) >> 7); - let mut s12: i64 = 2097151 & (load_4i(&s[31..35]) >> 4); - let mut s13: i64 = 2097151 & (load_3i(&s[34..37]) >> 1); - let mut s14: i64 = 2097151 & (load_4i(&s[36..40]) >> 6); - let mut s15: i64 = 2097151 & (load_3i(&s[39..42]) >> 3); - let mut s16: i64 = 2097151 & load_3i(&s[42..45]); - let mut s17: i64 = 2097151 & (load_4i(&s[44..48]) >> 5); - let s18: i64 = 2097151 & (load_3i(&s[47..50]) >> 2); - let s19: i64 = 2097151 & (load_4i(&s[49..53]) >> 7); - let s20: i64 = 2097151 & (load_4i(&s[52..56]) >> 4); - let s21: i64 = 2097151 & (load_3i(&s[55..58]) >> 1); - let s22: i64 = 2097151 & (load_4i(&s[57..61]) >> 6); - let s23: i64 = load_4i(&s[60..64]) >> 3; - let mut carry0: i64; - let mut carry1: i64; - let mut carry2: i64; - let mut carry3: i64; - let mut carry4: i64; - let mut carry5: i64; - let mut carry6: i64; - let mut carry7: i64; - let mut carry8: i64; - let mut carry9: i64; - let mut carry10: i64; - let mut carry11: i64; - let carry12: i64; - let carry13: i64; - let carry14: i64; - let carry15: i64; - let carry16: i64; - - s11 += s23 * 666643; - s12 += s23 * 470296; - s13 += s23 * 654183; - s14 -= s23 * 997805; - s15 += s23 * 136657; - s16 -= s23 * 683901; - - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; - - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; - - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; - - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; - - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 << 21; - carry12 = (s12 + (1 << 20)) >> 21; - s13 += carry12; - s12 -= carry12 << 21; - carry14 = (s14 + (1 << 20)) >> 21; - s15 += carry14; - s14 -= carry14 << 21; - carry16 = (s16 + (1 << 20)) >> 21; - s17 += carry16; - s16 -= carry16 << 21; - - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 << 21; - carry13 = (s13 + (1 << 20)) >> 21; - s14 += carry13; - s13 -= carry13 << 21; - carry15 = (s15 + (1 << 20)) >> 21; - s16 += carry15; - s15 -= carry15 << 21; - - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; - - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; - - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; - - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; - - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = (s0 + (1 << 20)) >> 21; - s1 += carry0; - s0 -= carry0 << 21; - carry2 = (s2 + (1 << 20)) >> 21; - s3 += carry2; - s2 -= carry2 << 21; - carry4 = (s4 + (1 << 20)) >> 21; - s5 += carry4; - s4 -= carry4 << 21; - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 << 21; - - carry1 = (s1 + (1 << 20)) >> 21; - s2 += carry1; - s1 -= carry1 << 21; - carry3 = (s3 + (1 << 20)) >> 21; - s4 += carry3; - s3 -= carry3 << 21; - carry5 = (s5 + (1 << 20)) >> 21; - s6 += carry5; - s5 -= carry5 << 21; - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; - s1 += carry0; - s0 -= carry0 << 21; - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 << 21; - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 << 21; - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 << 21; - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 << 21; - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 << 21; - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 << 21; - carry11 = s11 >> 21; - s12 += carry11; - s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - - carry0 = s0 >> 21; - s1 += carry0; - s0 -= carry0 << 21; - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 << 21; - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 << 21; - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 << 21; - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 << 21; - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 << 21; - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 << 21; - - s[0] = (s0 >> 0) as u8; - s[1] = (s0 >> 8) as u8; - s[2] = ((s0 >> 16) | (s1 << 5)) as u8; - s[3] = (s1 >> 3) as u8; - s[4] = (s1 >> 11) as u8; - s[5] = ((s1 >> 19) | (s2 << 2)) as u8; - s[6] = (s2 >> 6) as u8; - s[7] = ((s2 >> 14) | (s3 << 7)) as u8; - s[8] = (s3 >> 1) as u8; - s[9] = (s3 >> 9) as u8; - s[10] = ((s3 >> 17) | (s4 << 4)) as u8; - s[11] = (s4 >> 4) as u8; - s[12] = (s4 >> 12) as u8; - s[13] = ((s4 >> 20) | (s5 << 1)) as u8; - s[14] = (s5 >> 7) as u8; - s[15] = ((s5 >> 15) | (s6 << 6)) as u8; - s[16] = (s6 >> 2) as u8; - s[17] = (s6 >> 10) as u8; - s[18] = ((s6 >> 18) | (s7 << 3)) as u8; - s[19] = (s7 >> 5) as u8; - s[20] = (s7 >> 13) as u8; - s[21] = (s8 >> 0) as u8; - s[22] = (s8 >> 8) as u8; - s[23] = ((s8 >> 16) | (s9 << 5)) as u8; - s[24] = (s9 >> 3) as u8; - s[25] = (s9 >> 11) as u8; - s[26] = ((s9 >> 19) | (s10 << 2)) as u8; - s[27] = (s10 >> 6) as u8; - s[28] = ((s10 >> 14) | (s11 << 7)) as u8; - s[29] = (s11 >> 1) as u8; - s[30] = (s11 >> 9) as u8; - s[31] = (s11 >> 17) as u8; -} - -/* -Input: - a[0]+256*a[1]+...+256^31*a[31] = a - b[0]+256*b[1]+...+256^31*b[31] = b - c[0]+256*c[1]+...+256^31*c[31] = c - -Output: - s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l - where l = 2^252 + 27742317777372353535851937790883648493. -*/ -pub fn sc_muladd(s: &mut [u8], a: &[u8], b: &[u8], c: &[u8]) { - let a0 = 2097151 & load_3i(&a[0..3]); - let a1 = 2097151 & (load_4i(&a[2..6]) >> 5); - let a2 = 2097151 & (load_3i(&a[5..8]) >> 2); - let a3 = 2097151 & (load_4i(&a[7..11]) >> 7); - let a4 = 2097151 & (load_4i(&a[10..14]) >> 4); - let a5 = 2097151 & (load_3i(&a[13..16]) >> 1); - let a6 = 2097151 & (load_4i(&a[15..19]) >> 6); - let a7 = 2097151 & (load_3i(&a[18..21]) >> 3); - let a8 = 2097151 & load_3i(&a[21..24]); - let a9 = 2097151 & (load_4i(&a[23..27]) >> 5); - let a10 = 2097151 & (load_3i(&a[26..29]) >> 2); - let a11 = load_4i(&a[28..32]) >> 7; - let b0 = 2097151 & load_3i(&b[0..3]); - let b1 = 2097151 & (load_4i(&b[2..6]) >> 5); - let b2 = 2097151 & (load_3i(&b[5..8]) >> 2); - let b3 = 2097151 & (load_4i(&b[7..11]) >> 7); - let b4 = 2097151 & (load_4i(&b[10..14]) >> 4); - let b5 = 2097151 & (load_3i(&b[13..16]) >> 1); - let b6 = 2097151 & (load_4i(&b[15..19]) >> 6); - let b7 = 2097151 & (load_3i(&b[18..21]) >> 3); - let b8 = 2097151 & load_3i(&b[21..24]); - let b9 = 2097151 & (load_4i(&b[23..27]) >> 5); - let b10 = 2097151 & (load_3i(&b[26..29]) >> 2); - let b11 = load_4i(&b[28..32]) >> 7; - let c0 = 2097151 & load_3i(&c[0..3]); - let c1 = 2097151 & (load_4i(&c[2..6]) >> 5); - let c2 = 2097151 & (load_3i(&c[5..8]) >> 2); - let c3 = 2097151 & (load_4i(&c[7..11]) >> 7); - let c4 = 2097151 & (load_4i(&c[10..14]) >> 4); - let c5 = 2097151 & (load_3i(&c[13..16]) >> 1); - let c6 = 2097151 & (load_4i(&c[15..19]) >> 6); - let c7 = 2097151 & (load_3i(&c[18..21]) >> 3); - let c8 = 2097151 & load_3i(&c[21..24]); - let c9 = 2097151 & (load_4i(&c[23..27]) >> 5); - let c10 = 2097151 & (load_3i(&c[26..29]) >> 2); - let c11 = load_4i(&c[28..32]) >> 7; - let mut s0: i64; - let mut s1: i64; - let mut s2: i64; - let mut s3: i64; - let mut s4: i64; - let mut s5: i64; - let mut s6: i64; - let mut s7: i64; - let mut s8: i64; - let mut s9: i64; - let mut s10: i64; - let mut s11: i64; - let mut s12: i64; - let mut s13: i64; - let mut s14: i64; - let mut s15: i64; - let mut s16: i64; - let mut s17: i64; - let mut s18: i64; - let mut s19: i64; - let mut s20: i64; - let mut s21: i64; - let mut s22: i64; - let mut s23: i64; - let mut carry0: i64; - let mut carry1: i64; - let mut carry2: i64; - let mut carry3: i64; - let mut carry4: i64; - let mut carry5: i64; - let mut carry6: i64; - let mut carry7: i64; - let mut carry8: i64; - let mut carry9: i64; - let mut carry10: i64; - let mut carry11: i64; - let mut carry12: i64; - let mut carry13: i64; - let mut carry14: i64; - let mut carry15: i64; - let mut carry16: i64; - let carry17: i64; - let carry18: i64; - let carry19: i64; - let carry20: i64; - let carry21: i64; - let carry22: i64; - - s0 = c0 + a0 * b0; - s1 = c1 + a0 * b1 + a1 * b0; - s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; - s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; - s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; - s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; - s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; - s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; - s8 = c8 - + a0 * b8 - + a1 * b7 - + a2 * b6 - + a3 * b5 - + a4 * b4 - + a5 * b3 - + a6 * b2 - + a7 * b1 - + a8 * b0; - s9 = c9 - + a0 * b9 - + a1 * b8 - + a2 * b7 - + a3 * b6 - + a4 * b5 - + a5 * b4 - + a6 * b3 - + a7 * b2 - + a8 * b1 - + a9 * b0; - s10 = c10 - + a0 * b10 - + a1 * b9 - + a2 * b8 - + a3 * b7 - + a4 * b6 - + a5 * b5 - + a6 * b4 - + a7 * b3 - + a8 * b2 - + a9 * b1 - + a10 * b0; - s11 = c11 - + a0 * b11 - + a1 * b10 - + a2 * b9 - + a3 * b8 - + a4 * b7 - + a5 * b6 - + a6 * b5 - + a7 * b4 - + a8 * b3 - + a9 * b2 - + a10 * b1 - + a11 * b0; - s12 = a1 * b11 - + a2 * b10 - + a3 * b9 - + a4 * b8 - + a5 * b7 - + a6 * b6 - + a7 * b5 - + a8 * b4 - + a9 * b3 - + a10 * b2 - + a11 * b1; - s13 = a2 * b11 - + a3 * b10 - + a4 * b9 - + a5 * b8 - + a6 * b7 - + a7 * b6 - + a8 * b5 - + a9 * b4 - + a10 * b3 - + a11 * b2; - s14 = - a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; - s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; - s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; - s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; - s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; - s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; - s20 = a9 * b11 + a10 * b10 + a11 * b9; - s21 = a10 * b11 + a11 * b10; - s22 = a11 * b11; - s23 = 0; - - carry0 = (s0 + (1 << 20)) >> 21; - s1 += carry0; - s0 -= carry0 << 21; - carry2 = (s2 + (1 << 20)) >> 21; - s3 += carry2; - s2 -= carry2 << 21; - carry4 = (s4 + (1 << 20)) >> 21; - s5 += carry4; - s4 -= carry4 << 21; - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 << 21; - carry12 = (s12 + (1 << 20)) >> 21; - s13 += carry12; - s12 -= carry12 << 21; - carry14 = (s14 + (1 << 20)) >> 21; - s15 += carry14; - s14 -= carry14 << 21; - carry16 = (s16 + (1 << 20)) >> 21; - s17 += carry16; - s16 -= carry16 << 21; - carry18 = (s18 + (1 << 20)) >> 21; - s19 += carry18; - s18 -= carry18 << 21; - carry20 = (s20 + (1 << 20)) >> 21; - s21 += carry20; - s20 -= carry20 << 21; - carry22 = (s22 + (1 << 20)) >> 21; - s23 += carry22; - s22 -= carry22 << 21; - - carry1 = (s1 + (1 << 20)) >> 21; - s2 += carry1; - s1 -= carry1 << 21; - carry3 = (s3 + (1 << 20)) >> 21; - s4 += carry3; - s3 -= carry3 << 21; - carry5 = (s5 + (1 << 20)) >> 21; - s6 += carry5; - s5 -= carry5 << 21; - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 << 21; - carry13 = (s13 + (1 << 20)) >> 21; - s14 += carry13; - s13 -= carry13 << 21; - carry15 = (s15 + (1 << 20)) >> 21; - s16 += carry15; - s15 -= carry15 << 21; - carry17 = (s17 + (1 << 20)) >> 21; - s18 += carry17; - s17 -= carry17 << 21; - carry19 = (s19 + (1 << 20)) >> 21; - s20 += carry19; - s19 -= carry19 << 21; - carry21 = (s21 + (1 << 20)) >> 21; - s22 += carry21; - s21 -= carry21 << 21; - - s11 += s23 * 666643; - s12 += s23 * 470296; - s13 += s23 * 654183; - s14 -= s23 * 997805; - s15 += s23 * 136657; - s16 -= s23 * 683901; - - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; - - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; - - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; - - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; - - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 << 21; - carry12 = (s12 + (1 << 20)) >> 21; - s13 += carry12; - s12 -= carry12 << 21; - carry14 = (s14 + (1 << 20)) >> 21; - s15 += carry14; - s14 -= carry14 << 21; - carry16 = (s16 + (1 << 20)) >> 21; - s17 += carry16; - s16 -= carry16 << 21; - - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 << 21; - carry13 = (s13 + (1 << 20)) >> 21; - s14 += carry13; - s13 -= carry13 << 21; - carry15 = (s15 + (1 << 20)) >> 21; - s16 += carry15; - s15 -= carry15 << 21; - - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; - - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; - - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; - - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; - - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = (s0 + (1 << 20)) >> 21; - s1 += carry0; - s0 -= carry0 << 21; - carry2 = (s2 + (1 << 20)) >> 21; - s3 += carry2; - s2 -= carry2 << 21; - carry4 = (s4 + (1 << 20)) >> 21; - s5 += carry4; - s4 -= carry4 << 21; - carry6 = (s6 + (1 << 20)) >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry8 = (s8 + (1 << 20)) >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry10 = (s10 + (1 << 20)) >> 21; - s11 += carry10; - s10 -= carry10 << 21; - - carry1 = (s1 + (1 << 20)) >> 21; - s2 += carry1; - s1 -= carry1 << 21; - carry3 = (s3 + (1 << 20)) >> 21; - s4 += carry3; - s3 -= carry3 << 21; - carry5 = (s5 + (1 << 20)) >> 21; - s6 += carry5; - s5 -= carry5 << 21; - carry7 = (s7 + (1 << 20)) >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry9 = (s9 + (1 << 20)) >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry11 = (s11 + (1 << 20)) >> 21; - s12 += carry11; - s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; - s1 += carry0; - s0 -= carry0 << 21; - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 << 21; - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 << 21; - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 << 21; - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 << 21; - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 << 21; - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 << 21; - carry11 = s11 >> 21; - s12 += carry11; - s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - - carry0 = s0 >> 21; - s1 += carry0; - s0 -= carry0 << 21; - carry1 = s1 >> 21; - s2 += carry1; - s1 -= carry1 << 21; - carry2 = s2 >> 21; - s3 += carry2; - s2 -= carry2 << 21; - carry3 = s3 >> 21; - s4 += carry3; - s3 -= carry3 << 21; - carry4 = s4 >> 21; - s5 += carry4; - s4 -= carry4 << 21; - carry5 = s5 >> 21; - s6 += carry5; - s5 -= carry5 << 21; - carry6 = s6 >> 21; - s7 += carry6; - s6 -= carry6 << 21; - carry7 = s7 >> 21; - s8 += carry7; - s7 -= carry7 << 21; - carry8 = s8 >> 21; - s9 += carry8; - s8 -= carry8 << 21; - carry9 = s9 >> 21; - s10 += carry9; - s9 -= carry9 << 21; - carry10 = s10 >> 21; - s11 += carry10; - s10 -= carry10 << 21; - - s[0] = (s0 >> 0) as u8; - s[1] = (s0 >> 8) as u8; - s[2] = ((s0 >> 16) | (s1 << 5)) as u8; - s[3] = (s1 >> 3) as u8; - s[4] = (s1 >> 11) as u8; - s[5] = ((s1 >> 19) | (s2 << 2)) as u8; - s[6] = (s2 >> 6) as u8; - s[7] = ((s2 >> 14) | (s3 << 7)) as u8; - s[8] = (s3 >> 1) as u8; - s[9] = (s3 >> 9) as u8; - s[10] = ((s3 >> 17) | (s4 << 4)) as u8; - s[11] = (s4 >> 4) as u8; - s[12] = (s4 >> 12) as u8; - s[13] = ((s4 >> 20) | (s5 << 1)) as u8; - s[14] = (s5 >> 7) as u8; - s[15] = ((s5 >> 15) | (s6 << 6)) as u8; - s[16] = (s6 >> 2) as u8; - s[17] = (s6 >> 10) as u8; - s[18] = ((s6 >> 18) | (s7 << 3)) as u8; - s[19] = (s7 >> 5) as u8; - s[20] = (s7 >> 13) as u8; - s[21] = (s8 >> 0) as u8; - s[22] = (s8 >> 8) as u8; - s[23] = ((s8 >> 16) | (s9 << 5)) as u8; - s[24] = (s9 >> 3) as u8; - s[25] = (s9 >> 11) as u8; - s[26] = ((s9 >> 19) | (s10 << 2)) as u8; - s[27] = (s10 >> 6) as u8; - s[28] = ((s10 >> 14) | (s11 << 7)) as u8; - s[29] = (s11 >> 1) as u8; - s[30] = (s11 >> 9) as u8; - s[31] = (s11 >> 17) as u8; -} - -static BI: [GePrecomp; 8] = [ - GePrecomp { - y_plus_x: Fe([ - 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, - -6079156, 2047605, - ]), - y_minus_x: Fe([ - -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, - -15469378, - ]), - xy2d: Fe([ - -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, - -24514362, -4438546, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, - 28944400, -1550024, - ]), - y_minus_x: Fe([ - 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, - 7689662, 11199574, - ]), - xy2d: Fe([ - 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, - -17749093, -9920357, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, - -15438304, 10819380, - ]), - y_minus_x: Fe([ - 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, - -12668491, 5581306, - ]), - xy2d: Fe([ - 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, - -23678021, -15815942, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, - -15175766, - ]), - y_minus_x: Fe([ - -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, - 30598449, 7715701, - ]), - xy2d: Fe([ - 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, - -1409300, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, - -13062696, 13821877, - ]), - y_minus_x: Fe([ - -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, - 18853322, -14220951, - ]), - xy2d: Fe([ - 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, - 2207753, -3209784, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, - -31111463, -16132436, - ]), - y_minus_x: Fe([ - 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, - 6466918, - ]), - xy2d: Fe([ - 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, - -30714912, 16193877, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, - -18074513, 9256800, - ]), - y_minus_x: Fe([ - -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, - -19827198, 630305, - ]), - xy2d: Fe([ - -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, - -2449256, -14291300, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, - 25105118, -7894876, - ]), - y_minus_x: Fe([ - -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, - 2198790, -15804619, - ]), - xy2d: Fe([ - -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, - -32461234, -12290683, - ]), - }, -]; - -static GE_PRECOMP_BASE: [[GePrecomp; 8]; 32] = [ - [ - GePrecomp { - y_plus_x: Fe([ - 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, - -6079156, 2047605, - ]), - y_minus_x: Fe([ - -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, - 19500929, -15469378, - ]), - xy2d: Fe([ - -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, - -24514362, -4438546, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, - -3814571, -358445, -10211303, - ]), - y_minus_x: Fe([ - -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, - -26829678, -5319081, - ]), - xy2d: Fe([ - 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, - -15472047, -4166697, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, - 28944400, -1550024, - ]), - y_minus_x: Fe([ - 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, - 7689662, 11199574, - ]), - xy2d: Fe([ - 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, - -17749093, -9920357, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, - 3284568, -6276540, - ]), - y_minus_x: Fe([ - 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, - 13059162, 10374397, - ]), - xy2d: Fe([ - 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, - -641708, -101325, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, - -15438304, 10819380, - ]), - y_minus_x: Fe([ - 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, - -12668491, 5581306, - ]), - xy2d: Fe([ - 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, - -23678021, -15815942, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, - -9818940, -12085777, - ]), - y_minus_x: Fe([ - -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, - 1762328, 14866737, - ]), - xy2d: Fe([ - -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, - 27914454, 4383652, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, - -23952439, -15175766, - ]), - y_minus_x: Fe([ - -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, - 30598449, 7715701, - ]), - xy2d: Fe([ - 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, - 29794553, -1409300, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, - -33154098, 2381726, - ]), - y_minus_x: Fe([ - -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, - -32300832, 15351955, - ]), - xy2d: Fe([ - 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, - 29551813, 10109425, - ]), - }, - ], - [ - GePrecomp { - y_plus_x: Fe([ - -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, - 10092783, -4764171, - ]), - y_minus_x: Fe([ - 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, - -17810127, 12803510, - ]), - xy2d: Fe([ - 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, - 18016357, 4397660, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, - -17477504, 982639, - ]), - y_minus_x: Fe([ - 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, - -21047696, 9934963, - ]), - xy2d: Fe([ - 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, - -30123922, -10897950, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, - -13338309, 5500568, - ]), - y_minus_x: Fe([ - 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, - 10874051, 13524335, - ]), - xy2d: Fe([ - 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, - -22528059, 5376628, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, - 4535768, 1569007, - ]), - y_minus_x: Fe([ - -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, - 31848280, 12543772, - ]), - xy2d: Fe([ - -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, - 7718482, 14474653, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, - 24316168, -5253567, - ]), - y_minus_x: Fe([ - 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, - -20729456, 8321686, - ]), - xy2d: Fe([ - 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, - -9984458, 608372, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, - 27229399, 23887, - ]), - y_minus_x: Fe([ - -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, - -1633405, 16678954, - ]), - xy2d: Fe([ - -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, - -17169265, 4904953, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, - 2128236, -4326833, - ]), - y_minus_x: Fe([ - -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, - -6882542, -2986532, - ]), - xy2d: Fe([ - -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, - 15736322, 4143876, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, - 23527084, -16458268, - ]), - y_minus_x: Fe([ - 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, - -15188911, -14416214, - ]), - xy2d: Fe([ - 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, - -4774191, -16323038, - ]), - }, - ], - [ - GePrecomp { - y_plus_x: Fe([ - 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, - 7390890, 2759800, - ]), - y_minus_x: Fe([ - 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, - 1244380, -12919645, - ]), - xy2d: Fe([ - -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, - 15886429, 16489664, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, - -30606455, -712933, - ]), - y_minus_x: Fe([ - -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, - -30836462, 5113182, - ]), - xy2d: Fe([ - -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, - 13847711, 5387222, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, - -19600662, 10370991, - ]), - y_minus_x: Fe([ - 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, - 32232924, 16763880, - ]), - xy2d: Fe([ - 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, - 3140038, -16510092, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, - -28774454, 366295, - ]), - y_minus_x: Fe([ - 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, - 719605, 11671788, - ]), - xy2d: Fe([ - 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, - 27000813, -10195553, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, - 6750977, -14521026, - ]), - y_minus_x: Fe([ - 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, - 8169720, 16220347, - ]), - xy2d: Fe([ - -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, - -5990708, -14166033, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, - 2655861, 1738395, - ]), - y_minus_x: Fe([ - -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, - -19087449, -11005278, - ]), - xy2d: Fe([ - 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, - 10478196, 8544890, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, - 17789017, -3395995, - ]), - y_minus_x: Fe([ - -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, - 30460520, 1052596, - ]), - xy2d: Fe([ - -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, - 3179268, -9478891, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, - -16411740, 19072640, -9511060, - ]), - y_minus_x: Fe([ - 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, - 473099, 5040608, - ]), - xy2d: Fe([ - -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, - -19558642, -3131606, - ]), - }, - ], - [ - GePrecomp { - y_plus_x: Fe([ - 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, - -27868496, 11538389, - ]), - y_minus_x: Fe([ - -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, - -5676054, 5797016, - ]), - xy2d: Fe([ - -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, - -2369172, -5877341, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, - 15123619, 10811505, - ]), - y_minus_x: Fe([ - 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, - -28886779, -11974553, - ]), - xy2d: Fe([ - -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, - 4714547, -9600655, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, - -11745876, 12340220, - ]), - y_minus_x: Fe([ - 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, - 15370987, 9608631, - ]), - xy2d: Fe([ - -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, - -28210621, -8814099, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, - 20571223, 8420556, - ]), - y_minus_x: Fe([ - 14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, - 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-15233648, 5540521, - ]), - y_minus_x: Fe([ - -11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, - -16128528, -14962807, - ]), - xy2d: Fe([ - 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, - -11513277, -15205948, - ]), - }, - GePrecomp { - y_plus_x: Fe([ - 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, - -19179614, 5867134, - ]), - y_minus_x: Fe([ - -32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, - -29749703, -16108455, - ]), - xy2d: Fe([ - 27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, - -19526700, 7734629, - ]), - }, - ], - [ - GePrecomp { - y_plus_x: Fe([ - -8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, - 18549497, 15302069, - ]), - y_minus_x: Fe([ - -32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, - -8872242, 8424746, - ]), - xy2d: Fe([ - 24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, - 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let _ = getrandom::getrandom(&mut nonce); - let _ = getrandom::getrandom(&mut ad); + let _ = getrandom(&mut nonce); + let _ = getrandom(&mut ad); let mut output = aeads::aegis256::encrypt::<16>(&key, msg, &nonce, &ad); output.append(&mut nonce.to_vec());