// -*- mode: rust; -*- // // This file is part of curve25519-dalek. // Copyright (c) 2016-2021 isis agora lovecruft // Copyright (c) 2016-2019 Henry de Valence // See LICENSE for licensing information. // // Authors: // - Isis Agora Lovecruft // - Henry de Valence //! Field arithmetic modulo \\(p = 2\^{255} - 19\\). //! //! The `curve25519_dalek::field` module provides a type alias //! `curve25519_dalek::field::FieldElement` to a field element type //! defined in the `backend` module; either `FieldElement51` or //! `FieldElement2625`. //! //! Field operations defined in terms of machine //! operations, such as field multiplication or squaring, are defined in //! the backend implementation. //! //! Field operations defined in terms of other field operations, such as //! field inversion or square roots, are defined here. use core::cmp::{Eq, PartialEq}; use subtle::ConditionallySelectable; use subtle::ConditionallyNegatable; use subtle::Choice; use subtle::ConstantTimeEq; use constants; use backend; #[cfg(feature = "fiat_u32_backend")] pub use backend::serial::fiat_u32::field::*; #[cfg(feature = "fiat_u64_backend")] pub use backend::serial::fiat_u64::field::*; /// A `FieldElement` represents an element of the field /// \\( \mathbb Z / (2\^{255} - 19)\\). /// /// The `FieldElement` type is an alias for one of the platform-specific /// implementations. /// Using formally-verified field arithmetic from fiat-crypto #[cfg(feature = "fiat_u32_backend")] pub type FieldElement = backend::serial::fiat_u32::field::FieldElement2625; #[cfg(feature = "fiat_u64_backend")] pub type FieldElement = backend::serial::fiat_u64::field::FieldElement51; #[cfg(feature = "u64_backend")] pub use backend::serial::u64::field::*; /// A `FieldElement` represents an element of the field /// \\( \mathbb Z / (2\^{255} - 19)\\). /// /// The `FieldElement` type is an alias for one of the platform-specific /// implementations. #[cfg(feature = "u64_backend")] pub type FieldElement = backend::serial::u64::field::FieldElement51; #[cfg(feature = "u32_backend")] pub use backend::serial::u32::field::*; /// A `FieldElement` represents an element of the field /// \\( \mathbb Z / (2\^{255} - 19)\\). /// /// The `FieldElement` type is an alias for one of the platform-specific /// implementations. #[cfg(feature = "u32_backend")] pub type FieldElement = backend::serial::u32::field::FieldElement2625; impl Eq for FieldElement {} impl PartialEq for FieldElement { fn eq(&self, other: &FieldElement) -> bool { self.ct_eq(other).unwrap_u8() == 1u8 } } impl ConstantTimeEq for FieldElement { /// Test equality between two `FieldElement`s. Since the /// internal representation is not canonical, the field elements /// are normalized to wire format before comparison. fn ct_eq(&self, other: &FieldElement) -> Choice { self.to_bytes().ct_eq(&other.to_bytes()) } } impl FieldElement { /// Determine if this `FieldElement` is negative, in the sense /// used in the ed25519 paper: `x` is negative if the low bit is /// set. /// /// # Return /// /// If negative, return `Choice(1)`. Otherwise, return `Choice(0)`. pub fn is_negative(&self) -> Choice { let bytes = self.to_bytes(); (bytes[0] & 1).into() } /// Determine if this `FieldElement` is zero. /// /// # Return /// /// If zero, return `Choice(1)`. Otherwise, return `Choice(0)`. pub fn is_zero(&self) -> Choice { let zero = [0u8; 32]; let bytes = self.to_bytes(); bytes.ct_eq(&zero) } /// Compute (self^(2^250-1), self^11), used as a helper function /// within invert() and pow22523(). fn pow22501(&self) -> (FieldElement, FieldElement) { // Instead of managing which temporary variables are used // for what, we define as many as we need and leave stack // allocation to the compiler // // Each temporary variable t_i is of the form (self)^e_i. // Squaring t_i corresponds to multiplying e_i by 2, // so the pow2k function shifts e_i left by k places. // Multiplying t_i and t_j corresponds to adding e_i + e_j. // // Temporary t_i Nonzero bits of e_i // let t0 = self.square(); // 1 e_0 = 2^1 let t1 = t0.square().square(); // 3 e_1 = 2^3 let t2 = self * &t1; // 3,0 e_2 = 2^3 + 2^0 let t3 = &t0 * &t2; // 3,1,0 let t4 = t3.square(); // 4,2,1 let t5 = &t2 * &t4; // 4,3,2,1,0 let t6 = t5.pow2k(5); // 9,8,7,6,5 let t7 = &t6 * &t5; // 9,8,7,6,5,4,3,2,1,0 let t8 = t7.pow2k(10); // 19..10 let t9 = &t8 * &t7; // 19..0 let t10 = t9.pow2k(20); // 39..20 let t11 = &t10 * &t9; // 39..0 let t12 = t11.pow2k(10); // 49..10 let t13 = &t12 * &t7; // 49..0 let t14 = t13.pow2k(50); // 99..50 let t15 = &t14 * &t13; // 99..0 let t16 = t15.pow2k(100); // 199..100 let t17 = &t16 * &t15; // 199..0 let t18 = t17.pow2k(50); // 249..50 let t19 = &t18 * &t13; // 249..0 (t19, t3) } /// Given a slice of public `FieldElements`, replace each with its inverse. /// /// All input `FieldElements` **MUST** be nonzero. #[cfg(feature = "alloc")] pub fn batch_invert(inputs: &mut [FieldElement]) { // Montgomery’s Trick and Fast Implementation of Masked AES // Genelle, Prouff and Quisquater // Section 3.2 let n = inputs.len(); let mut scratch = vec![FieldElement::one(); n]; // Keep an accumulator of all of the previous products let mut acc = FieldElement::one(); // Pass through the input vector, recording the previous // products in the scratch space for (input, scratch) in inputs.iter().zip(scratch.iter_mut()) { *scratch = acc; acc = &acc * input; } // acc is nonzero iff all inputs are nonzero assert_eq!(acc.is_zero().unwrap_u8(), 0); // Compute the inverse of all products acc = acc.invert(); // Pass through the vector backwards to compute the inverses // in place for (input, scratch) in inputs.iter_mut().rev().zip(scratch.into_iter().rev()) { let tmp = &acc * input; *input = &acc * &scratch; acc = tmp; } } /// Given a nonzero field element, compute its inverse. /// /// The inverse is computed as self^(p-2), since /// x^(p-2)x = x^(p-1) = 1 (mod p). /// /// This function returns zero on input zero. pub fn invert(&self) -> FieldElement { // The bits of p-2 = 2^255 -19 -2 are 11010111111...11. // // nonzero bits of exponent let (t19, t3) = self.pow22501(); // t19: 249..0 ; t3: 3,1,0 let t20 = t19.pow2k(5); // 254..5 let t21 = &t20 * &t3; // 254..5,3,1,0 t21 } /// Raise this field element to the power (p-5)/8 = 2^252 -3. fn pow_p58(&self) -> FieldElement { // The bits of (p-5)/8 are 101111.....11. // // nonzero bits of exponent let (t19, _) = self.pow22501(); // 249..0 let t20 = t19.pow2k(2); // 251..2 let t21 = self * &t20; // 251..2,0 t21 } /// Given `FieldElements` `u` and `v`, compute either `sqrt(u/v)` /// or `sqrt(i*u/v)` in constant time. /// /// This function always returns the nonnegative square root. /// /// # Return /// /// - `(Choice(1), +sqrt(u/v)) ` if `v` is nonzero and `u/v` is square; /// - `(Choice(1), zero) ` if `u` is zero; /// - `(Choice(0), zero) ` if `v` is zero and `u` is nonzero; /// - `(Choice(0), +sqrt(i*u/v))` if `u/v` is nonsquare (so `i*u/v` is square). /// pub fn sqrt_ratio_i(u: &FieldElement, v: &FieldElement) -> (Choice, FieldElement) { // Using the same trick as in ed25519 decoding, we merge the // inversion, the square root, and the square test as follows. // // To compute sqrt(α), we can compute β = α^((p+3)/8). // Then β^2 = ±α, so multiplying β by sqrt(-1) if necessary // gives sqrt(α). // // To compute 1/sqrt(α), we observe that // 1/β = α^(p-1 - (p+3)/8) = α^((7p-11)/8) // = α^3 * (α^7)^((p-5)/8). // // We can therefore compute sqrt(u/v) = sqrt(u)/sqrt(v) // by first computing // r = u^((p+3)/8) v^(p-1-(p+3)/8) // = u u^((p-5)/8) v^3 (v^7)^((p-5)/8) // = (uv^3) (uv^7)^((p-5)/8). // // If v is nonzero and u/v is square, then r^2 = ±u/v, // so vr^2 = ±u. // If vr^2 = u, then sqrt(u/v) = r. // If vr^2 = -u, then sqrt(u/v) = r*sqrt(-1). // // If v is zero, r is also zero. let v3 = &v.square() * v; let v7 = &v3.square() * v; let mut r = &(u * &v3) * &(u * &v7).pow_p58(); let check = v * &r.square(); let i = &constants::SQRT_M1; let correct_sign_sqrt = check.ct_eq( u); let flipped_sign_sqrt = check.ct_eq( &(-u)); let flipped_sign_sqrt_i = check.ct_eq(&(&(-u)*i)); let r_prime = &constants::SQRT_M1 * &r; r.conditional_assign(&r_prime, flipped_sign_sqrt | flipped_sign_sqrt_i); // Choose the nonnegative square root. let r_is_negative = r.is_negative(); r.conditional_negate(r_is_negative); let was_nonzero_square = correct_sign_sqrt | flipped_sign_sqrt; (was_nonzero_square, r) } /// Attempt to compute `sqrt(1/self)` in constant time. /// /// Convenience wrapper around `sqrt_ratio_i`. /// /// This function always returns the nonnegative square root. /// /// # Return /// /// - `(Choice(1), +sqrt(1/self)) ` if `self` is a nonzero square; /// - `(Choice(0), zero) ` if `self` is zero; /// - `(Choice(0), +sqrt(i/self)) ` if `self` is a nonzero nonsquare; /// pub fn invsqrt(&self) -> (Choice, FieldElement) { FieldElement::sqrt_ratio_i(&FieldElement::one(), self) } } #[cfg(test)] extern crate rand; #[cfg(test)] mod test { use field::*; use subtle::ConditionallyNegatable; /// Random element a of GF(2^255-19), from Sage /// a = 1070314506888354081329385823235218444233221\ /// 2228051251926706380353716438957572 static A_BYTES: [u8; 32] = [ 0x04, 0xfe, 0xdf, 0x98, 0xa7, 0xfa, 0x0a, 0x68, 0x84, 0x92, 0xbd, 0x59, 0x08, 0x07, 0xa7, 0x03, 0x9e, 0xd1, 0xf6, 0xf2, 0xe1, 0xd9, 0xe2, 0xa4, 0xa4, 0x51, 0x47, 0x36, 0xf3, 0xc3, 0xa9, 0x17]; /// Byte representation of a**2 static ASQ_BYTES: [u8; 32] = [ 0x75, 0x97, 0x24, 0x9e, 0xe6, 0x06, 0xfe, 0xab, 0x24, 0x04, 0x56, 0x68, 0x07, 0x91, 0x2d, 0x5d, 0x0b, 0x0f, 0x3f, 0x1c, 0xb2, 0x6e, 0xf2, 0xe2, 0x63, 0x9c, 0x12, 0xba, 0x73, 0x0b, 0xe3, 0x62]; /// Byte representation of 1/a static AINV_BYTES: [u8; 32] = [0x96, 0x1b, 0xcd, 0x8d, 0x4d, 0x5e, 0xa2, 0x3a, 0xe9, 0x36, 0x37, 0x93, 0xdb, 0x7b, 0x4d, 0x70, 0xb8, 0x0d, 0xc0, 0x55, 0xd0, 0x4c, 0x1d, 0x7b, 0x90, 0x71, 0xd8, 0xe9, 0xb6, 0x18, 0xe6, 0x30]; /// Byte representation of a^((p-5)/8) static AP58_BYTES: [u8; 32] = [0x6a, 0x4f, 0x24, 0x89, 0x1f, 0x57, 0x60, 0x36, 0xd0, 0xbe, 0x12, 0x3c, 0x8f, 0xf5, 0xb1, 0x59, 0xe0, 0xf0, 0xb8, 0x1b, 0x20, 0xd2, 0xb5, 0x1f, 0x15, 0x21, 0xf9, 0xe3, 0xe1, 0x61, 0x21, 0x55]; #[test] fn a_mul_a_vs_a_squared_constant() { let a = FieldElement::from_bytes(&A_BYTES); let asq = FieldElement::from_bytes(&ASQ_BYTES); assert_eq!(asq, &a * &a); } #[test] fn a_square_vs_a_squared_constant() { let a = FieldElement::from_bytes(&A_BYTES); let asq = FieldElement::from_bytes(&ASQ_BYTES); assert_eq!(asq, a.square()); } #[test] fn a_square2_vs_a_squared_constant() { let a = FieldElement::from_bytes(&A_BYTES); let asq = FieldElement::from_bytes(&ASQ_BYTES); assert_eq!(a.square2(), &asq+&asq); } #[test] fn a_invert_vs_inverse_of_a_constant() { let a = FieldElement::from_bytes(&A_BYTES); let ainv = FieldElement::from_bytes(&AINV_BYTES); let should_be_inverse = a.invert(); assert_eq!(ainv, should_be_inverse); assert_eq!(FieldElement::one(), &a * &should_be_inverse); } #[test] fn batch_invert_a_matches_nonbatched() { let a = FieldElement::from_bytes(&A_BYTES); let ap58 = FieldElement::from_bytes(&AP58_BYTES); let asq = FieldElement::from_bytes(&ASQ_BYTES); let ainv = FieldElement::from_bytes(&AINV_BYTES); let a2 = &a + &a; let a_list = vec![a, ap58, asq, ainv, a2]; let mut ainv_list = a_list.clone(); FieldElement::batch_invert(&mut ainv_list[..]); for i in 0..5 { assert_eq!(a_list[i].invert(), ainv_list[i]); } } #[test] fn sqrt_ratio_behavior() { let zero = FieldElement::zero(); let one = FieldElement::one(); let i = constants::SQRT_M1; let two = &one + &one; // 2 is nonsquare mod p. let four = &two + &two; // 4 is square mod p. // 0/0 should return (1, 0) since u is 0 let (choice, sqrt) = FieldElement::sqrt_ratio_i(&zero, &zero); assert_eq!(choice.unwrap_u8(), 1); assert_eq!(sqrt, zero); assert_eq!(sqrt.is_negative().unwrap_u8(), 0); // 1/0 should return (0, 0) since v is 0, u is nonzero let (choice, sqrt) = FieldElement::sqrt_ratio_i(&one, &zero); assert_eq!(choice.unwrap_u8(), 0); assert_eq!(sqrt, zero); assert_eq!(sqrt.is_negative().unwrap_u8(), 0); // 2/1 is nonsquare, so we expect (0, sqrt(i*2)) let (choice, sqrt) = FieldElement::sqrt_ratio_i(&two, &one); assert_eq!(choice.unwrap_u8(), 0); assert_eq!(sqrt.square(), &two * &i); assert_eq!(sqrt.is_negative().unwrap_u8(), 0); // 4/1 is square, so we expect (1, sqrt(4)) let (choice, sqrt) = FieldElement::sqrt_ratio_i(&four, &one); assert_eq!(choice.unwrap_u8(), 1); assert_eq!(sqrt.square(), four); assert_eq!(sqrt.is_negative().unwrap_u8(), 0); // 1/4 is square, so we expect (1, 1/sqrt(4)) let (choice, sqrt) = FieldElement::sqrt_ratio_i(&one, &four); assert_eq!(choice.unwrap_u8(), 1); assert_eq!(&sqrt.square() * &four, one); assert_eq!(sqrt.is_negative().unwrap_u8(), 0); } #[test] fn a_p58_vs_ap58_constant() { let a = FieldElement::from_bytes(&A_BYTES); let ap58 = FieldElement::from_bytes(&AP58_BYTES); assert_eq!(ap58, a.pow_p58()); } #[test] fn equality() { let a = FieldElement::from_bytes(&A_BYTES); let ainv = FieldElement::from_bytes(&AINV_BYTES); assert!(a == a); assert!(a != ainv); } /// Notice that the last element has the high bit set, which /// should be ignored static B_BYTES: [u8;32] = [113, 191, 169, 143, 91, 234, 121, 15, 241, 131, 217, 36, 230, 101, 92, 234, 8, 208, 170, 251, 97, 127, 70, 210, 58, 23, 166, 87, 240, 169, 184, 178]; #[test] fn from_bytes_highbit_is_ignored() { let mut cleared_bytes = B_BYTES; cleared_bytes[31] &= 127u8; let with_highbit_set = FieldElement::from_bytes(&B_BYTES); let without_highbit_set = FieldElement::from_bytes(&cleared_bytes); assert_eq!(without_highbit_set, with_highbit_set); } #[test] fn conditional_negate() { let one = FieldElement::one(); let minus_one = FieldElement::minus_one(); let mut x = one; x.conditional_negate(Choice::from(1)); assert_eq!(x, minus_one); x.conditional_negate(Choice::from(0)); assert_eq!(x, minus_one); x.conditional_negate(Choice::from(1)); assert_eq!(x, one); } #[test] fn encoding_is_canonical() { // Encode 1 wrongly as 1 + (2^255 - 19) = 2^255 - 18 let one_encoded_wrongly_bytes: [u8;32] = [0xee, 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, 0xff, 0xff, 0xff, 0x7f]; // Decode to a field element let one = FieldElement::from_bytes(&one_encoded_wrongly_bytes); // .. then check that the encoding is correct let one_bytes = one.to_bytes(); assert_eq!(one_bytes[0], 1); for i in 1..32 { assert_eq!(one_bytes[i], 0); } } #[test] fn batch_invert_empty() { FieldElement::batch_invert(&mut []); } #[test] fn make_vectors() { // reminder to self: to create just this vector, run // cargo test field::test::make_vectors use std::fs::File; use std::io::prelude::*; use std::path::Path; use engine25519_as::*; use self::rand::Rng; fn write_helper(file: &mut File, elem: FieldElement) { let elem_bytes = elem.to_bytes(); let _ = file.write(&elem_bytes); /* for i in 0..elem_bytes.len()/4 { let word: u32 = elem_bytes.pread::(i).unwrap(); let _ = write!(file, "{:02x}", elem_bytes[i]); } let _ = write!(file, " ");*/ } fn write_test_header(file: &mut File, loading_address: u32, mcode: &[i32], num_src_regs: u32, reg_window: u32, num_tests: u32, ) { let mcode_len: u32 = mcode.len() as u32; let _ = file.write(&(0x5645_4354 as u32).to_le_bytes()); let _ = file.write(&( ((loading_address & 0xFFFF << 16) | (mcode_len & 0xFFFF) ) as u32) .to_le_bytes() ); // load address 0 + code length let _ = file.write(&( ((num_src_regs & 0x1F) << 27 // number of source registers per test | (reg_window & 0xF) << 23 // register window to use | (num_tests & 0x3F_FFFF) // number of tests ) as u32) .to_le_bytes() ); // 2 registers, window 0, 1 vector // the actual microcode for i in 0..mcode_len { let _ = file.write(&(mcode[i as usize] as u32).to_le_bytes()); } // pad with 0's to a 256-bit stride for _ in 0..(8 - ((3 + mcode_len) % 8)) { // 3 words for metadata + code length let _ = file.write(&[0,0,0,0]); // write out 32-bit words of 0 (as array of u8) } } let path = Path::new("test_vectors.bin"); let mut file = File::create(&path).unwrap(); // Metadata record format. Each test should have the following layout: // 0x0 0x56454354 "VECT" - indicates a valid vector set // 0x4 [31 load address 16] [15 length of code 0] // 0x8 [31 N registers to load 27] [26 W window 23] [22 X number of vectors sets 0] // 0xC [microcode] (variable length) // [ padding of 0x0 until 0x20 * align ] // 0x20*align [X test vectors] // Records can repeat; as long as "VECT" is found, the test framework will attemp to load and run the test // // End of records MUST end with a word that is NOT 0x56454354 // This is because the ROM read can "wrap around" and the test will run forever // We use 0xFFFF_FFFF to indicate this // // For each test, vectors are storted with the following convention: // Check result is always in r31 // N Registers loaded starting at r0 into window W fn test_add(mut file: &mut File) { // test addition. two input registers (r0, r1), one output register (r31). let num_src_regs = 2; let reg_window = 0; let num_tests = 5; // one manual test + 4 random vectors let loading_address = 0; // microcode loading address let mcode = assemble_engine25519!( start: add %2, %0, %1 trd %3, %2 sub %31, %2, %3 fin ); write_test_header(&mut file, loading_address, &mcode, num_src_regs, reg_window, num_tests); // test vectors // 1 plus -1 = 0 -> this works overflow path let a = FieldElement::one(); let b = FieldElement::minus_one(); let q = &a + &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // four random numbers for _ in 0..4 { let a = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let b = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let q = &a + &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); } } fn ref_fact(n: usize) -> FieldElement { let mut a = FieldElement::one(); let mut result = FieldElement::one(); for _ in 0..n { result = &result * &a; a = &a + &FieldElement::one(); } result } fn test_loop(mut file: &mut File) { // test addition. two input registers (r0, r1), one output register (r31). let num_src_regs = 1; let reg_window = 0; let num_tests = 5; // 5 sequential tests let loading_address = 0; // microcode loading address // compute a factorial using a loop // also tests psa/psb with constants // %0 is the argument, %31 is the result // %10 is the multiplicand for the factorial // %0 is re-used as the loop counter let mcode = assemble_engine25519!( start: psa %10, #1 psb %31, #1 loop: mul %31, %31, %10 add %10, %10, #1 sub %0, %0, #1 brz end, %0 brz loop, #0 end: fin ); write_test_header(&mut file, loading_address, &mcode, num_src_regs, reg_window, num_tests); // test vectors let mut n = FieldElement::one(); for i in 1..6 { write_helper(&mut file, n); n = &n + &FieldElement::one(); // mirror i's progression let q = ref_fact(i); write_helper(&mut file, q); } } fn test_cswap(mut file: &mut File) { // test cswap. three input registers: (r0, r1) to swap, (r2) to control swap, one output register (r31). let num_src_regs = 3; let reg_window = 15; let num_tests = 4; let loading_address = 0; // microcode loading address // psa is used to move %0 to %31 mostly to test that psa works let mcode = assemble_engine25519!( start: xor %30, %0, %1 msk %30, %2, %30 xor %0, %30, %0 xor %1, %30, %1 psa %31, %0 fin ); write_test_header(&mut file, loading_address, &mcode, num_src_regs, reg_window, num_tests); // test vectors for i in 0..4 { let a = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let b = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let swap: FieldElement; let q: FieldElement; if i % 2 == 0 { swap = FieldElement::zero(); q = a; } else { swap = FieldElement::one(); q = b; } write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, swap); write_helper(&mut file, q); } } fn test_mul(mut file: &mut File) { let extra_tests = 100; // vary this to add more random vectors at the end // test multiplier. two input registers: (r0, r1), one output register (r31). let num_src_regs = 2; let reg_window = 0; let num_tests = 22 + extra_tests; let loading_address = 0; // microcode loading address let mcode = assemble_engine25519!( start: mul %31, %1, %0 fin ); write_test_header(&mut file, loading_address, &mcode, num_src_regs, reg_window, num_tests); // 1: 1*1 - simple case let a = FieldElement::one(); let b = FieldElement::one(); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 2: 1*-1 - simple case let a = FieldElement::one(); let b = FieldElement::minus_one(); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 3 let a = FieldElement::from_bytes(&[ 0xEB, 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, 0xFF, 0xFF, 0xFF, 0x7f,]); let b = FieldElement::one(); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 4 let a = FieldElement::from_bytes(&[ 0xA4, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0x2A, ]); let b = FieldElement::from_bytes(&[ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 5 let a = FieldElement::from_bytes(&[ 0xED, 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, 0xFF, 0xFF, 0xFF, 0x7f, ]); let b = FieldElement::from_bytes(&[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 6 let a = FieldElement::from_bytes(&[ 0xF7, 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, 0xFF, 0xFF, 0xFF, 0x3f, ]); let b = FieldElement::from_bytes(&[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 7 let a = FieldElement::from_bytes(&[ 0xA5, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0x2A, ]); let b = FieldElement::from_bytes(&[ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 8 let a = FieldElement::from_bytes(&[ 0xA5, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0x2A, ]); let b = FieldElement::from_bytes(&[ 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 9: not normalized input! let a = FieldElement::from_bytes(&[ 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, 0xFF, 0xFF, 0xFF, 0xFF, 0x7f, ]); let b = FieldElement::from_bytes(&[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 10 let a = FieldElement::from_bytes(&[ 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, 0xFF, 0xFF, 0xFF, 0xFF, 0x3f, ]); let b = FieldElement::from_bytes(&[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 11 let a = FieldElement::from_bytes(&[ 0xF8, 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, 0xFF, 0xFF, 0xFF, 0x3f, ]); let b = FieldElement::from_bytes(&[ 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 12 let a = FieldElement::from_bytes(&[ 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x99, 0x19, ]); let b = FieldElement::from_bytes(&[ 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 13 let a = FieldElement::from_bytes(&[ 0x94, 0xc2, 0xf9, 0x3b, 0xb7, 0xe7, 0xe5, 0x78, 0x22, 0x23, 0x00, 0x14, 0x55, 0x41, 0x56, 0x05, 0xb0, 0xfe, 0x1d, 0x61, 0x0d, 0x0b, 0x08, 0xc9, 0x22, 0x3a, 0xc4, 0x55, 0xcd, 0xb0, 0x93, 0x52, ]); let b = FieldElement::from_bytes(&[ 0x17, 0x0c, 0x1e, 0x93, 0xea, 0x6e, 0x51, 0xc0, 0xcb, 0xf9, 0x48, 0xe7, 0x60, 0x36, 0x1f, 0xaf, 0x65, 0x8d, 0xf2, 0xe9, 0x36, 0xd2, 0x71, 0x00, 0x94, 0x56, 0x48, 0x55, 0x1c, 0xe9, 0x48, 0x1d, ]); let q = &a * &b; // 08 55 8c eb 97 70 ea b5 da c7 eb 83 d1 3a b3 a7 // 99 31 f4 be 87 3c 26 e9 1c d0 9c 82 08 da 5c 0d write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 14 let a = FieldElement::from_bytes(&[ 0x6d, 0xad, 0x72, 0xf8, 0x64, 0x1b, 0x8f, 0x43, 0xba, 0x50, 0xb5, 0x83, 0xe1, 0x5f, 0xd6, 0x43, 0x9b, 0xb2, 0xbc, 0x60, 0xae, 0x92, 0x3a, 0xdb, 0x05, 0x83, 0x4a, 0xd6, 0x19, 0x36, 0x95, 0x87, ]); let b = FieldElement::from_bytes(&[ 0xe4, 0x34, 0x15, 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, ]); let q = &a * &b; // 000002a6 bc74dd8d 2e43fe6f 23132ca5 d3e70179 c129465a 7c4d49cc ccf864a7 write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); // 0xa7, 0x64, 0xf8, 0xcc, 0xcc, 0x49, 0x4d, 0x7c, // 0x5a, 0x46, 0x29, 0xc1, 0x79, 0x01, 0xe7, 0xd3, // 0xa5, 0x2c, 0x13, 0x23, 0x6f, 0xfe, 0x43, 0x2e, // 0x8d, 0xdd, 0x74, 0xbc, 0xa6, 0x02, 0x00, 0x00, // 15-22 for _ in 0..(8+extra_tests) { let a = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let b = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let q = &a * &b; write_helper(&mut file, a); write_helper(&mut file, b); write_helper(&mut file, q); } } fn test_diff_add_and_double(mut file: &mut File) { use montgomery::ProjectivePoint; // test cswap. three input registers: (r0, r1) to swap, (r2) to control swap, one output register (r31). let num_src_regs = 5; let reg_window = 0; let num_tests = 8; let loading_address = 0; // microcode loading address let mcode = assemble_engine25519!( start: // test preamble psa %20, %0 psa %21, %1 psa %22, %2 psa %23, %3 psa %24, %4 // P.U in %20 // P.W in %21 // Q.U in %22 // Q.W in %23 // affine_PmQ in %24 // %30 is the TRD scratch register // %29 is the subtraction temporary value register // let t0 = &P.U + &P.W; add %0, %20, %21 trd %30, %0 sub %0, %0, %30 // let t1 = &P.U - &P.W; sub %21, #3, %21 // negate &P.W using #FIELDPRIME (#3) add %1, %20, %21 trd %30, %1 sub %1, %1, %30 // let t2 = &Q.U + &Q.W; add %2, %22, %23 trd %30, %2 sub %2, %2, %30 // let t3 = &Q.U - &Q.W; sub %23, #3, %23 add %3, %22, %23 trd %30, %3 sub %3, %3, %30 // let t4 = t0.square(); // (U_P + W_P)^2 = U_P^2 + 2 U_P W_P + W_P^2 mul %4, %0, %0 // let t5 = t1.square(); // (U_P - W_P)^2 = U_P^2 - 2 U_P W_P + W_P^2 mul %5, %1, %1 // let t6 = &t4 - &t5; // 4 U_P W_P sub %29, #3, %5 add %6, %4, %29 trd %30, %6 sub %6, %6, %30 // let t7 = &t0 * &t3; // (U_P + W_P) (U_Q - W_Q) = U_P U_Q + W_P U_Q - U_P W_Q - W_P W_Q mul %7, %0, %3 // let t8 = &t1 * &t2; // (U_P - W_P) (U_Q + W_Q) = U_P U_Q - W_P U_Q + U_P W_Q - W_P W_Q mul %8, %1, %2 // let t9 = &t7 + &t8; // 2 (U_P U_Q - W_P W_Q) add %9, %7, %8 trd %30, %9 sub %9, %9, %30 // let t10 = &t7 - &t8; // 2 (W_P U_Q - U_P W_Q) sub %29, #3, %8 add %10, %7, %29 trd %30, %10 sub %10, %10, %30 // let t11 = t9.square(); // 4 (U_P U_Q - W_P W_Q)^2 mul %11, %9, %9 // let t12 = t10.square(); // 4 (W_P U_Q - U_P W_Q)^2 mul %12, %10, %10 // let t13 = &APLUS2_OVER_FOUR * &t6; // (A + 2) U_P U_Q mul %13, #4, %6 // #4 is A+2/4 // let t14 = &t4 * &t5; // ((U_P + W_P)(U_P - W_P))^2 = (U_P^2 - W_P^2)^2 mul %14, %4, %5 // let t15 = &t13 + &t5; // (U_P - W_P)^2 + (A + 2) U_P W_P add %15, %13, %5 trd %30, %15 sub %15, %15, %30 // let t16 = &t6 * &t15; // 4 (U_P W_P) ((U_P - W_P)^2 + (A + 2) U_P W_P) mul %16, %6, %15 // let t17 = affine_PmQ * &t12; // U_D * 4 (W_P U_Q - U_P W_Q)^2 mul %17, %24, %12 // affine_PmQ loaded into %24 ///// these can be eliminated down the road, but included for 1:1 algorithm correspodence to reference in early testing // let t18 = t11; // W_D * 4 (U_P U_Q - W_P W_Q)^2 psa %18, %11 // P.U = t14; // U_{P'} = (U_P + W_P)^2 (U_P - W_P)^2 psa %20, %14 // P.W = t16; // W_{P'} = (4 U_P W_P) ((U_P - W_P)^2 + ((A + 2)/4) 4 U_P W_P) psa %21, %16 // Q.U = t18; // U_{Q'} = W_D * 4 (U_P U_Q - W_P W_Q)^2 psa %22, %18 // Q.W = t17; // W_{Q'} = U_D * 4 (W_P U_Q - U_P W_Q)^2 psa %23, %17 // test postamble -- sum together the points to create a single composite test output add %31, %20, %21 trd %30, %31 sub %31, %31, %30 add %31, %31, %22 trd %30, %31 sub %31, %31, %30 add %31, %31, %23 trd %30, %31 sub %31, %31, %30 // leave result in r31 fin // finish execution ); write_test_header(&mut file, loading_address, &mcode, num_src_regs, reg_window, num_tests); use montgomery::differential_add_and_double; // test vectors for _ in 0..8 { let pu = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let pw = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let qu = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let qw = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); let pmq = FieldElement::from_bytes(&rand::thread_rng().gen::<[u8; 32]>()); write_helper(&mut file, pu); write_helper(&mut file, pw); write_helper(&mut file, qu); write_helper(&mut file, qw); write_helper(&mut file, pmq); #[allow(non_snake_case)] let mut P: ProjectivePoint = ProjectivePoint{U:pu, W:pw}; #[allow(non_snake_case)] let mut Q: ProjectivePoint = ProjectivePoint{U:qu, W:qw}; differential_add_and_double(&mut P, &mut Q, &pmq); write_helper(&mut file, &(&P.U + &P.W) + &(&Q.U + &Q.W)); } } fn test_scalar_mul(mut file: &mut File) { use montgomery::ProjectivePoint; // test cswap. three input registers: (r0, r1) to swap, (r2) to control swap, one output register (r31). let num_src_regs = 7; let reg_window = 0; let num_tests = 1; let loading_address = 0; // microcode loading address let mcode = assemble_engine25519!( start: psa %25, %0 // x0.U psa %26, %1 // x0.W psa %27, %2 // x1.U psa %28, %3 // x1.W psa %24, %4 // affine point psa %31, %5 // scalar psa %19, %6 // the number 254 // P.U in %20 // P.W in %21 // Q.U in %22 // Q.W in %23 // affine_PmQ in %24 // %30 is the TRD scratch register and cswap dummy // %29 is the subtraction temporary value register and k_t // x0.U in %25 // x0.W in %26 // x1.U in %27 // x1.W in %28 // %19 is the loop counter, starts with 254 (if 0, loop runs exactly once) // %31 is the scalar // %18 is the swap variable psa %18, #0 // for i in (0..255).rev() mainloop: // let choice: u8 = (bits[i + 1] ^ bits[i]) as u8; // ProjectivePoint::conditional_swap(&mut x0, &mut x1, choice.into()); xbt %29, %31 // orignally[k_t = (k>>t) & 1] now[k_t = k[254]] shl %31, %31 // k = k<<1 xor %18, %18, %29 // swap ^= k_t // cswap x0.U (%25), x1.U (%27) xor %30, %25, %27 msk %30, %18, %30 xor %25, %30, %25 xor %27, %30, %27 // cswap x0.W (%26), x1.W (%28) xor %30, %26, %28 msk %30, %18, %30 xor %26, %30, %26 xor %28, %30, %28 psa %18, %29 // swap = k_t // differential_add_and_double(&mut x0, &mut x1, &affine_u); psa %20, %25 psa %21, %26 psa %22, %27 psa %23, %28 // affine_u is already in %24 // let t0 = &P.U + &P.W; add %0, %20, %21 trd %30, %0 sub %0, %0, %30 // let t1 = &P.U - &P.W; sub %21, #3, %21 // negate &P.W using #FIELDPRIME (#3) add %1, %20, %21 trd %30, %1 sub %1, %1, %30 // let t2 = &Q.U + &Q.W; add %2, %22, %23 trd %30, %2 sub %2, %2, %30 // let t3 = &Q.U - &Q.W; sub %23, #3, %23 add %3, %22, %23 trd %30, %3 sub %3, %3, %30 // let t4 = t0.square(); // (U_P + W_P)^2 = U_P^2 + 2 U_P W_P + W_P^2 mul %4, %0, %0 // let t5 = t1.square(); // (U_P - W_P)^2 = U_P^2 - 2 U_P W_P + W_P^2 mul %5, %1, %1 // let t6 = &t4 - &t5; // 4 U_P W_P sub %29, #3, %5 add %6, %4, %29 trd %30, %6 sub %6, %6, %30 // let t7 = &t0 * &t3; // (U_P + W_P) (U_Q - W_Q) = U_P U_Q + W_P U_Q - U_P W_Q - W_P W_Q mul %7, %0, %3 // let t8 = &t1 * &t2; // (U_P - W_P) (U_Q + W_Q) = U_P U_Q - W_P U_Q + U_P W_Q - W_P W_Q mul %8, %1, %2 // let t9 = &t7 + &t8; // 2 (U_P U_Q - W_P W_Q) add %9, %7, %8 trd %30, %9 sub %9, %9, %30 // let t10 = &t7 - &t8; // 2 (W_P U_Q - U_P W_Q) sub %29, #3, %8 add %10, %7, %29 trd %30, %10 sub %10, %10, %30 // let t11 = t9.square(); // 4 (U_P U_Q - W_P W_Q)^2 mul %11, %9, %9 // let t12 = t10.square(); // 4 (W_P U_Q - U_P W_Q)^2 mul %12, %10, %10 // let t13 = &APLUS2_OVER_FOUR * &t6; // (A + 2) U_P U_Q mul %13, #4, %6 // #4 is A+2/4 // let t14 = &t4 * &t5; // ((U_P + W_P)(U_P - W_P))^2 = (U_P^2 - W_P^2)^2 mul %14, %4, %5 // let t15 = &t13 + &t5; // (U_P - W_P)^2 + (A + 2) U_P W_P add %15, %13, %5 trd %30, %15 sub %15, %15, %30 // let t16 = &t6 * &t15; // 4 (U_P W_P) ((U_P - W_P)^2 + (A + 2) U_P W_P) mul %16, %6, %15 // let t17 = affine_PmQ * &t12; // U_D * 4 (W_P U_Q - U_P W_Q)^2 mul %17, %24, %12 // affine_PmQ loaded into %24 ///// these can be eliminated down the road, but included for 1:1 algorithm correspodence to reference in early testing // P.U = t14; // U_{P'} = (U_P + W_P)^2 (U_P - W_P)^2 psa %20, %14 // P.W = t16; // W_{P'} = (4 U_P W_P) ((U_P - W_P)^2 + ((A + 2)/4) 4 U_P W_P) psa %21, %16 // let t18 = t11; // W_D * 4 (U_P U_Q - W_P W_Q)^2 // Q.U = t18; // U_{Q'} = W_D * 4 (U_P U_Q - W_P W_Q)^2 psa %22, %11 // collapsed two to save a register // Q.W = t17; // W_{Q'} = U_D * 4 (W_P U_Q - U_P W_Q)^2 psa %23, %17 ///// 'return' arguments for next iteration, can be optimized out later psa %25, %20 psa %26, %21 psa %27, %22 psa %28, %23 brz end, %19 // if loop counter is 0, quit sub %19, %19, #1 // subtract one from the loop counter and run again brz mainloop, #0 // go back to the top end: // ProjectivePoint::conditional_swap(&mut x0, &mut x1, Choice::from(bits[0] as u8)); // cswap x0.U (%25), x1.U (%27) xor %30, %25, %27 msk %30, %18, %30 xor %25, %30, %25 xor %27, %30, %27 // cswap x0.W (%26), x1.W (%28) xor %30, %26, %28 msk %30, %18, %30 xor %26, %30, %26 xor %28, %30, %28 //// test post-amble // test postamble -- sum together the points to create a single composite test output add %31, %25, %26 trd %30, %31 sub %31, %31, %30 fin // finish execution ); write_test_header(&mut file, loading_address, &mcode, num_src_regs, reg_window, num_tests); use scalar::Scalar; use montgomery::MontgomeryPoint; use montgomery::differential_add_and_double; fn clamp_scalar(mut scalar: [u8; 32]) -> Scalar { scalar[0] &= 248; scalar[31] &= 127; scalar[31] |= 64; Scalar::from_bits(scalar) } let scalar: Scalar = clamp_scalar(rand::thread_rng().gen::<[u8; 32]>()); let mp: MontgomeryPoint = MontgomeryPoint {0: rand::thread_rng().gen::<[u8; 32]>() }; // Algorithm 8 of Costello-Smith 2017 let affine_u = FieldElement::from_bytes(&mp.0); let mut x0 = ProjectivePoint { U: FieldElement::one(), W: FieldElement::zero(), }; let mut x1 = ProjectivePoint { U: affine_u, W: FieldElement::one(), }; // test vectors input to test routine write_helper(&mut file, x0.U); write_helper(&mut file, x0.W); write_helper(&mut file, x1.U); write_helper(&mut file, x1.W); write_helper(&mut file, affine_u); file.write(&scalar.bytes).unwrap(); let number254 = FieldElement::from_bytes(&[ 254, 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, ]); write_helper(&mut file, number254); let bits: [i8; 256] = scalar.bits(); for i in (0..255).rev() { let choice: u8 = (bits[i + 1] ^ bits[i]) as u8; debug_assert!(choice == 0 || choice == 1); ProjectivePoint::conditional_swap(&mut x0, &mut x1, choice.into()); differential_add_and_double(&mut x0, &mut x1, &affine_u); } ProjectivePoint::conditional_swap(&mut x0, &mut x1, Choice::from(bits[0] as u8)); // result is in x0 // result vector write_helper(&mut file, &x0.U + &x0.W); } test_scalar_mul(&mut file); test_add(&mut file); test_loop(&mut file); test_cswap(&mut file); test_mul(&mut file); test_diff_add_and_double(&mut file); // end sequence let _ = file.write(&(0xFFFF_FFFF as u32).to_le_bytes()); } }