p256/
scalar.rs

1use alloc::vec::Vec;
2use core::{cmp::Ordering, ops::ShrAssign};
3
4use elliptic_curve::{
5    bigint::{ArrayEncoding, Encoding, U256},
6    ops::{Invert, Reduce},
7    rand_core::RngCore,
8    scalar::{FromUintUnchecked, IsHigh},
9    subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption},
10    zeroize::DefaultIsZeroes,
11    Field, PrimeField, ScalarPrimitive,
12};
13use hex_literal::hex;
14use openvm_algebra_guest::IntMod;
15
16use crate::{internal::P256Scalar, point::FieldBytes, NistP256, ORDER_HEX};
17
18impl P256Scalar {
19    /// Returns the SEC1 encoding of this scalar.
20    pub fn to_bytes(&self) -> FieldBytes {
21        self.to_be_bytes().into()
22    }
23}
24// --- Implement elliptic_curve traits on P256Scalar ---
25
26impl Copy for P256Scalar {}
27
28impl From<u64> for P256Scalar {
29    fn from(value: u64) -> Self {
30        Self::from_u64(value)
31    }
32}
33
34impl Default for P256Scalar {
35    fn default() -> Self {
36        <Self as IntMod>::ZERO
37    }
38}
39
40// Requires canonical form
41impl ConstantTimeEq for P256Scalar {
42    fn ct_eq(&self, other: &Self) -> Choice {
43        self.as_le_bytes().ct_eq(other.as_le_bytes())
44    }
45}
46
47impl ConditionallySelectable for P256Scalar {
48    fn conditional_select(a: &P256Scalar, b: &P256Scalar, choice: Choice) -> P256Scalar {
49        P256Scalar::from_le_bytes_unchecked(
50            &a.as_le_bytes()
51                .iter()
52                .zip(b.as_le_bytes().iter())
53                .map(|(a, b)| u8::conditional_select(a, b, choice))
54                .collect::<Vec<_>>(),
55        )
56    }
57}
58
59impl Field for P256Scalar {
60    const ZERO: Self = <Self as IntMod>::ZERO;
61    const ONE: Self = <Self as IntMod>::ONE;
62
63    fn random(mut _rng: impl RngCore) -> Self {
64        unimplemented!()
65    }
66
67    fn square(&self) -> Self {
68        self * self
69    }
70
71    fn double(&self) -> Self {
72        self + self
73    }
74
75    fn invert(&self) -> CtOption<Self> {
76        // needs to be in canonical form for ct_eq
77        self.assert_reduced();
78        let is_zero = self.ct_eq(&<Self as IntMod>::ZERO);
79        CtOption::new(
80            <P256Scalar as openvm_algebra_guest::Field>::invert(self),
81            !is_zero,
82        )
83    }
84
85    #[allow(clippy::many_single_char_names)]
86    fn sqrt(&self) -> CtOption<Self> {
87        match <Self as openvm_algebra_guest::Sqrt>::sqrt(self) {
88            Some(sqrt) => CtOption::new(sqrt, 1.into()),
89            None => CtOption::new(<Self as Field>::ZERO, 0.into()),
90        }
91    }
92
93    fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
94        ff::helpers::sqrt_ratio_generic(num, div)
95    }
96}
97
98const fn seven_le() -> [u8; 32] {
99    let mut buf = [0u8; 32];
100    buf[0] = 7;
101    buf
102}
103
104impl PrimeField for P256Scalar {
105    type Repr = FieldBytes;
106
107    const MODULUS: &'static str = ORDER_HEX;
108    const NUM_BITS: u32 = 256;
109    const CAPACITY: u32 = 255;
110    const TWO_INV: Self = Self::from_const_bytes(hex!(
111        "a992317e61e5dc7942cf8bd3567d73deffffffffffffff7f00000080ffffff7f"
112    ));
113    const MULTIPLICATIVE_GENERATOR: Self = Self::from_const_bytes(seven_le());
114    const S: u32 = 4;
115    const ROOT_OF_UNITY: Self = Self::from_const_bytes(hex!(
116        "02661eb4fbd79205af8d3704d0ca4615fc3d2a84ce7a80ba9209772a067fc9ff"
117    ));
118    const ROOT_OF_UNITY_INV: Self = Self::from_const_bytes(hex!(
119        "6437c757067f9c3737414c797c11ace3ae1c135804fa45c62a6fd462556aa6a0"
120    ));
121    const DELTA: Self = Self::from_const_bytes(hex!(
122        "817d05a5391e0000000000000000000000000000000000000000000000000000"
123    ));
124
125    /// Attempts to parse the given byte array as an SEC1-encoded scalar.
126    ///
127    /// Returns None if the byte array does not contain a big-endian integer in the range
128    /// [0, p).
129    fn from_repr(bytes: FieldBytes) -> CtOption<Self> {
130        let ret = Self::from_be_bytes_unchecked(bytes.as_slice());
131        CtOption::new(ret, (ret.is_reduced() as u8).into())
132    }
133
134    // Endianness should match from_repr
135    fn to_repr(&self) -> FieldBytes {
136        *FieldBytes::from_slice(&self.to_be_bytes())
137    }
138
139    fn is_odd(&self) -> Choice {
140        (self.as_le_bytes()[0] & 1).into()
141    }
142}
143
144impl ShrAssign<usize> for P256Scalar {
145    fn shr_assign(&mut self, _rhs: usize) {
146        // I don't think this is used anywhere
147        unimplemented!()
148    }
149}
150
151impl Reduce<U256> for P256Scalar {
152    type Bytes = FieldBytes;
153
154    fn reduce(w: U256) -> Self {
155        <Self as openvm_algebra_guest::Reduce>::reduce_le_bytes(&w.to_le_bytes())
156    }
157
158    #[inline]
159    fn reduce_bytes(bytes: &FieldBytes) -> Self {
160        Self::reduce(U256::from_be_byte_array(*bytes))
161    }
162}
163
164impl PartialOrd for P256Scalar {
165    // requires self and other to be in canonical form
166    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
167        self.assert_reduced();
168        other.assert_reduced();
169        Some(
170            self.to_be_bytes()
171                .iter()
172                .zip(other.to_be_bytes().iter())
173                .map(|(a, b)| a.cmp(b))
174                .find(|ord| *ord != Ordering::Equal)
175                .unwrap_or(Ordering::Equal),
176        )
177    }
178}
179
180impl IsHigh for P256Scalar {
181    fn is_high(&self) -> Choice {
182        // self > n/2
183        // iff self + self overflows
184        // iff self + self < self
185        ((self + self < *self) as u8).into()
186    }
187}
188
189impl Invert for P256Scalar {
190    type Output = CtOption<Self>;
191
192    fn invert(&self) -> CtOption<Self> {
193        <Self as Field>::invert(self)
194    }
195}
196
197impl FromUintUnchecked for P256Scalar {
198    type Uint = U256;
199
200    fn from_uint_unchecked(uint: Self::Uint) -> Self {
201        Self::from_le_bytes_unchecked(&uint.to_le_bytes())
202    }
203}
204
205impl From<ScalarPrimitive<NistP256>> for P256Scalar {
206    fn from(scalar: ScalarPrimitive<NistP256>) -> Self {
207        Self::from_le_bytes_unchecked(&scalar.as_uint().to_le_bytes())
208    }
209}
210
211impl From<P256Scalar> for ScalarPrimitive<NistP256> {
212    fn from(scalar: P256Scalar) -> ScalarPrimitive<NistP256> {
213        ScalarPrimitive::from_slice(&scalar.to_be_bytes()).unwrap()
214    }
215}
216
217impl DefaultIsZeroes for P256Scalar {}
218
219impl AsRef<P256Scalar> for P256Scalar {
220    fn as_ref(&self) -> &P256Scalar {
221        self
222    }
223}
224
225impl From<P256Scalar> for U256 {
226    fn from(scalar: P256Scalar) -> Self {
227        U256::from_be_slice(&scalar.to_be_bytes())
228    }
229}
230
231impl From<P256Scalar> for FieldBytes {
232    fn from(scalar: P256Scalar) -> Self {
233        *FieldBytes::from_slice(&scalar.to_be_bytes())
234    }
235}
p256/scalar.rs

p256/
scalar.rs
