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Test MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY #738

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Merged
tarcieri merged 1 commit into from
Feb 3, 2023
Merged

Test MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY #738

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23 changes: 16 additions & 7 deletions k256/src/arithmetic/field.rs
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -522,6 +522,14 @@ mod tests {
}
}

/// t = (modulus - 1) >> S
const T: [u64; 4] = [
0xffffffff7ffffe17,
0xffffffffffffffff,
0xffffffffffffffff,
0x7fffffffffffffff,
];

#[test]
fn two_inv_constant() {
assert_eq!(
Expand All @@ -539,6 +547,14 @@ mod tests {
.normalize(),
FieldElement::ONE
);

// MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY
assert_eq!(
FieldElement::MULTIPLICATIVE_GENERATOR
.pow_vartime(&T)
.normalize(),
FieldElement::ROOT_OF_UNITY
)
}

#[test]
Expand All @@ -551,13 +567,6 @@ mod tests {

#[test]
fn delta_constant() {
const T: [u64; 4] = [
0xffffffff7ffffe17,
0xffffffffffffffff,
0xffffffffffffffff,
0x7fffffffffffffff,
];

// DELTA^{t} mod m == 1
assert_eq!(
FieldElement::DELTA.pow_vartime(&T).normalize(),
Expand Down
21 changes: 14 additions & 7 deletions k256/src/arithmetic/scalar.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -757,6 +757,14 @@ mod tests {
}
}

/// t = (modulus - 1) >> S
const T: [u64; 4] = [
0xeeff497a3340d905,
0xfaeabb739abd2280,
0xffffffffffffffff,
0x03ffffffffffffff,
];

#[test]
fn two_inv_constant() {
assert_eq!(Scalar::from(2u32) * Scalar::TWO_INV, Scalar::ONE);
Expand All @@ -769,6 +777,12 @@ mod tests {
Scalar::ROOT_OF_UNITY.pow_vartime(&[1u64 << Scalar::S, 0, 0, 0]),
Scalar::ONE
);

// MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY
assert_eq!(
Scalar::MULTIPLICATIVE_GENERATOR.pow_vartime(&T),
Scalar::ROOT_OF_UNITY
)
}

#[test]
Expand All @@ -781,13 +795,6 @@ mod tests {

#[test]
fn delta_constant() {
const T: [u64; 4] = [
0xeeff497a3340d905,
0xfaeabb739abd2280,
0xffffffffffffffff,
0x03ffffffffffffff,
];

// DELTA^{t} mod m == 1
assert_eq!(Scalar::DELTA.pow_vartime(&T), Scalar::ONE);
}
Expand Down
21 changes: 14 additions & 7 deletions p256/src/arithmetic/field.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -160,6 +160,14 @@ mod tests {
use elliptic_curve::{bigint::U256, ff::PrimeField};
use proptest::{num, prelude::*};

/// t = (modulus - 1) >> S
const T: [u64; 4] = [
0xffffffffffffffff,
0x000000007fffffff,
0x8000000000000000,
0x7fffffff80000000,
];

#[test]
fn two_inv_constant() {
assert_eq!(
Expand All @@ -175,6 +183,12 @@ mod tests {
FieldElement::ROOT_OF_UNITY.pow_vartime(&[1u64 << FieldElement::S, 0, 0, 0]),
FieldElement::ONE
);

// MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY
assert_eq!(
FieldElement::MULTIPLICATIVE_GENERATOR.pow_vartime(&T),
FieldElement::ROOT_OF_UNITY
)
}

#[test]
Expand All @@ -187,13 +201,6 @@ mod tests {

#[test]
fn delta_constant() {
const T: [u64; 4] = [
0xffffffffffffffff,
0x000000007fffffff,
0x8000000000000000,
0x7fffffff80000000,
];

// DELTA^{t} mod m == 1
assert_eq!(FieldElement::DELTA.pow_vartime(&T), FieldElement::ONE);
}
Expand Down
21 changes: 14 additions & 7 deletions p256/src/arithmetic/scalar.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -686,6 +686,14 @@ mod tests {
use crate::{FieldBytes, SecretKey};
use elliptic_curve::group::ff::{Field, PrimeField};

/// t = (modulus - 1) >> S
const T: [u64; 4] = [
0x4f3b9cac2fc63255,
0xfbce6faada7179e8,
0x0fffffffffffffff,
0x0ffffffff0000000,
];

#[test]
fn two_inv_constant() {
assert_eq!(Scalar::from(2u32) * Scalar::TWO_INV, Scalar::ONE);
Expand All @@ -698,6 +706,12 @@ mod tests {
Scalar::ROOT_OF_UNITY.pow_vartime(&[1u64 << Scalar::S, 0, 0, 0]),
Scalar::ONE
);

// MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY
assert_eq!(
Scalar::MULTIPLICATIVE_GENERATOR.pow_vartime(&T),
Scalar::ROOT_OF_UNITY
)
}

#[test]
Expand All @@ -710,13 +724,6 @@ mod tests {

#[test]
fn delta_constant() {
const T: [u64; 4] = [
0x4f3b9cac2fc63255,
0xfbce6faada7179e8,
0x0fffffffffffffff,
0x0ffffffff0000000,
];

// DELTA^{t} mod m == 1
assert_eq!(Scalar::DELTA.pow_vartime(&T), Scalar::ONE);
}
Expand Down
25 changes: 16 additions & 9 deletions p384/src/arithmetic/field.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -156,6 +156,16 @@ mod tests {
use super::FieldElement;
use elliptic_curve::ff::PrimeField;

/// t = (modulus - 1) >> S
const T: [u64; 6] = [
0x000000007fffffff,
0x7fffffff80000000,
0xffffffffffffffff,
0xffffffffffffffff,
0xffffffffffffffff,
0x7fffffffffffffff,
];

#[test]
fn two_inv_constant() {
assert_eq!(
Expand All @@ -171,6 +181,12 @@ mod tests {
FieldElement::ROOT_OF_UNITY.pow_vartime(&[1u64 << FieldElement::S, 0, 0, 0]),
FieldElement::ONE
);

// MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY
assert_eq!(
FieldElement::MULTIPLICATIVE_GENERATOR.pow_vartime(&T),
FieldElement::ROOT_OF_UNITY
)
}

#[test]
Expand All @@ -183,15 +199,6 @@ mod tests {

#[test]
fn delta_constant() {
const T: [u64; 6] = [
0x000000007fffffff,
0x7fffffff80000000,
0xffffffffffffffff,
0xffffffffffffffff,
0xffffffffffffffff,
0x7fffffffffffffff,
];

// DELTA^{t} mod m == 1
assert_eq!(FieldElement::DELTA.pow_vartime(&T), FieldElement::ONE);
}
Expand Down
25 changes: 16 additions & 9 deletions p384/src/arithmetic/scalar.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -356,6 +356,16 @@ mod tests {
use crate::FieldBytes;
use elliptic_curve::ff::PrimeField;

/// t = (modulus - 1) >> S
const T: [u64; 6] = [
0x76760cb5666294b9,
0xac0d06d9245853bd,
0xe3b1a6c0fa1b96ef,
0xffffffffffffffff,
0xffffffffffffffff,
0x7fffffffffffffff,
];

#[test]
fn two_inv_constant() {
assert_eq!(Scalar::from(2u32) * Scalar::TWO_INV, Scalar::ONE);
Expand All @@ -368,6 +378,12 @@ mod tests {
Scalar::ROOT_OF_UNITY.pow_vartime(&[1u64 << Scalar::S, 0, 0, 0]),
Scalar::ONE
);

// MULTIPLICATIVE_GENERATOR^{t} mod m == ROOT_OF_UNITY
assert_eq!(
Scalar::MULTIPLICATIVE_GENERATOR.pow_vartime(&T),
Scalar::ROOT_OF_UNITY
)
}

#[test]
Expand All @@ -380,15 +396,6 @@ mod tests {

#[test]
fn delta_constant() {
const T: [u64; 6] = [
0x76760cb5666294b9,
0xac0d06d9245853bd,
0xe3b1a6c0fa1b96ef,
0xffffffffffffffff,
0xffffffffffffffff,
0x7fffffffffffffff,
];

// DELTA^{t} mod m == 1
assert_eq!(Scalar::DELTA.pow_vartime(&T), Scalar::ONE);
}
Expand Down