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    #[must_use]
68    fn square(&self) -> Self {
69        self * self
70    }
71
72    #[must_use]
73    fn double(&self) -> Self {
74        self + self
75    }
76
77    fn invert(&self) -> CtOption<Self> {
78        // needs to be in canonical form for ct_eq
79        self.assert_reduced();
80        let is_zero = self.ct_eq(&<Self as IntMod>::ZERO);
81        CtOption::new(
82            <P256Scalar as openvm_algebra_guest::Field>::invert(self),
83            !is_zero,
84        )
85    }
86
87    #[allow(clippy::many_single_char_names)]
88    fn sqrt(&self) -> CtOption<Self> {
89        match <Self as openvm_algebra_guest::Sqrt>::sqrt(self) {
90            Some(sqrt) => CtOption::new(sqrt, 1.into()),
91            None => CtOption::new(<Self as Field>::ZERO, 0.into()),
92        }
93    }
94
95    fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
96        ff::helpers::sqrt_ratio_generic(num, div)
97    }
98}
99
100const fn seven_le() -> [u8; 32] {
101    let mut buf = [0u8; 32];
102    buf[0] = 7;
103    buf
104}
105
106impl PrimeField for P256Scalar {
107    type Repr = FieldBytes;
108
109    const MODULUS: &'static str = ORDER_HEX;
110    const NUM_BITS: u32 = 256;
111    const CAPACITY: u32 = 255;
112    const TWO_INV: Self = Self::from_const_bytes(hex!(
113        "a992317e61e5dc7942cf8bd3567d73deffffffffffffff7f00000080ffffff7f"
114    ));
115    const MULTIPLICATIVE_GENERATOR: Self = Self::from_const_bytes(seven_le());
116    const S: u32 = 4;
117    const ROOT_OF_UNITY: Self = Self::from_const_bytes(hex!(
118        "02661eb4fbd79205af8d3704d0ca4615fc3d2a84ce7a80ba9209772a067fc9ff"
119    ));
120    const ROOT_OF_UNITY_INV: Self = Self::from_const_bytes(hex!(
121        "6437c757067f9c3737414c797c11ace3ae1c135804fa45c62a6fd462556aa6a0"
122    ));
123    const DELTA: Self = Self::from_const_bytes(hex!(
124        "817d05a5391e0000000000000000000000000000000000000000000000000000"
125    ));
126
127    /// Attempts to parse the given byte array as an SEC1-encoded scalar.
128    ///
129    /// Returns None if the byte array does not contain a big-endian integer in the range
130    /// [0, p).
131    fn from_repr(bytes: FieldBytes) -> CtOption<Self> {
132        let ret = Self::from_be_bytes_unchecked(bytes.as_slice());
133        CtOption::new(ret, (ret.is_reduced() as u8).into())
134    }
135
136    // Endianness should match from_repr
137    fn to_repr(&self) -> FieldBytes {
138        *FieldBytes::from_slice(&self.to_be_bytes())
139    }
140
141    fn is_odd(&self) -> Choice {
142        (self.as_le_bytes()[0] & 1).into()
143    }
144}
145
146impl ShrAssign<usize> for P256Scalar {
147    fn shr_assign(&mut self, _rhs: usize) {
148        // I don't think this is used anywhere
149        unimplemented!()
150    }
151}
152
153impl Reduce<U256> for P256Scalar {
154    type Bytes = FieldBytes;
155
156    fn reduce(w: U256) -> Self {
157        <Self as openvm_algebra_guest::Reduce>::reduce_le_bytes(&w.to_le_bytes())
158    }
159
160    #[inline]
161    fn reduce_bytes(bytes: &FieldBytes) -> Self {
162        Self::reduce(U256::from_be_byte_array(*bytes))
163    }
164}
165
166impl PartialOrd for P256Scalar {
167    // requires self and other to be in canonical form
168    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
169        self.assert_reduced();
170        other.assert_reduced();
171        Some(
172            self.to_be_bytes()
173                .iter()
174                .zip(other.to_be_bytes().iter())
175                .map(|(a, b)| a.cmp(b))
176                .find(|ord| *ord != Ordering::Equal)
177                .unwrap_or(Ordering::Equal),
178        )
179    }
180}
181
182impl IsHigh for P256Scalar {
183    fn is_high(&self) -> Choice {
184        // self > n/2
185        // iff self + self overflows
186        // iff self + self < self
187        ((self + self < *self) as u8).into()
188    }
189}
190
191impl Invert for P256Scalar {
192    type Output = CtOption<Self>;
193
194    fn invert(&self) -> CtOption<Self> {
195        <Self as Field>::invert(self)
196    }
197}
198
199impl FromUintUnchecked for P256Scalar {
200    type Uint = U256;
201
202    fn from_uint_unchecked(uint: Self::Uint) -> Self {
203        Self::from_le_bytes_unchecked(&uint.to_le_bytes())
204    }
205}
206
207impl From<ScalarPrimitive<NistP256>> for P256Scalar {
208    fn from(scalar: ScalarPrimitive<NistP256>) -> Self {
209        Self::from_le_bytes_unchecked(&scalar.as_uint().to_le_bytes())
210    }
211}
212
213impl From<P256Scalar> for ScalarPrimitive<NistP256> {
214    fn from(scalar: P256Scalar) -> ScalarPrimitive<NistP256> {
215        ScalarPrimitive::from_slice(&scalar.to_be_bytes()).unwrap()
216    }
217}
218
219impl DefaultIsZeroes for P256Scalar {}
220
221impl AsRef<P256Scalar> for P256Scalar {
222    fn as_ref(&self) -> &P256Scalar {
223        self
224    }
225}
226
227impl From<P256Scalar> for U256 {
228    fn from(scalar: P256Scalar) -> Self {
229        U256::from_be_slice(&scalar.to_be_bytes())
230    }
231}
232
233impl From<P256Scalar> for FieldBytes {
234    fn from(scalar: P256Scalar) -> Self {
235        *FieldBytes::from_slice(&scalar.to_be_bytes())
236    }
237}
p256/scalar.rs

p256/
scalar.rs
