From 87488ec1f6de0634c31b61939c7eea8959f74fa9 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@electriccoin.co>
Date: Wed, 3 Mar 2021 20:37:51 +0000
Subject: [PATCH 1/5] CI: Add no-std build check

---
 .github/workflows/ci.yml | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 2566161..dc5ba6c 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -188,3 +188,26 @@ jobs:
         with:
           command: fmt
           args: -- --check
+
+  no-std:
+    name: Check no-std target ${{ matrix.target }}
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        target:
+          - thumbv6m-none-eabi
+          - wasm32-unknown-unknown
+          - wasm32-wasi
+
+    steps:
+      - uses: actions/checkout@v2
+      - uses: actions-rs/toolchain@v1
+        with:
+          toolchain: stable
+          override: true
+      - run: rustup target add ${{ matrix.target }}
+      - name: Build
+        uses: actions-rs/cargo@v1
+        with:
+          command: build
+          args: --verbose --target ${{ matrix.target }} --no-default-features

From 6a47700b1da7a251d3629e1e36ab1dcb0d7168f7 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@electriccoin.co>
Date: Mon, 20 Sep 2021 16:34:28 +0100
Subject: [PATCH 2/5] fields: Ensure that trait impl dependencies match trait
 bounds

The `FieldExt` trait was originally the only trait implemented in this
crate. When we added `ff` support, we reworked `FieldExt` to be an
extension trait on top of `ff::PrimeField`, but left the existing impls
in `FieldExt`. This resulted in some circular dependencies that prevent
us from making `FieldExt` conditional (e.g. for no-std support).

This commit removes the cycles like so:

- `ff::PrimeField::{from_repr, to_repr}` were implemented as calls to
  `FieldExt::{from_bytes, to_bytes}`. The field encoding/decoding logic
  is moved into the `ff::PrimeField` trait impl, and `FieldExt` now
  calls into `ff::PrimeField`.

- `ff::Field::sqrt` was implemented in terms of `FieldExt::sqrt_alt`.
  Given that the latter is a trivial wrapper around the `SqrtTables`
  implementation, we duplicate the call to eliminate the cycle.

- `ff::Field::random` used `FieldExt::from_bytes_wide`, which wraps
  either `Fp::from_u512` or `Fq::from_u512`. We now use these internal
  methods directly.
---
 src/fields/fp.rs | 96 ++++++++++++++++++++++++------------------------
 src/fields/fq.rs | 96 ++++++++++++++++++++++++------------------------
 2 files changed, 98 insertions(+), 94 deletions(-)

diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index eb943b0..065a453 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -466,10 +466,16 @@ impl Group for Fp {
 
 impl ff::Field for Fp {
     fn random(mut rng: impl RngCore) -> Self {
-        let mut random_bytes = [0; 64];
-        rng.fill_bytes(&mut random_bytes[..]);
-
-        Self::from_bytes_wide(&random_bytes)
+        Self::from_u512([
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+        ])
     }
 
     fn zero() -> Self {
@@ -491,7 +497,7 @@ impl ff::Field for Fp {
 
     /// Computes the square root of this element, if it exists.
     fn sqrt(&self) -> CtOption<Self> {
-        let (is_square, res) = self.sqrt_alt();
+        let (is_square, res) = FP_TABLES.sqrt_alt(self);
         CtOption::new(res, is_square)
     }
 
@@ -535,15 +541,47 @@ impl ff::PrimeField for Fp {
     const S: u32 = S;
 
     fn from_repr(repr: Self::Repr) -> CtOption<Self> {
-        Self::from_bytes(&repr)
+        let mut tmp = Fp([0, 0, 0, 0]);
+
+        tmp.0[0] = u64::from_le_bytes(repr[0..8].try_into().unwrap());
+        tmp.0[1] = u64::from_le_bytes(repr[8..16].try_into().unwrap());
+        tmp.0[2] = u64::from_le_bytes(repr[16..24].try_into().unwrap());
+        tmp.0[3] = u64::from_le_bytes(repr[24..32].try_into().unwrap());
+
+        // Try to subtract the modulus
+        let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);
+        let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);
+        let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);
+        let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);
+
+        // If the element is smaller than MODULUS then the
+        // subtraction will underflow, producing a borrow value
+        // of 0xffff...ffff. Otherwise, it'll be zero.
+        let is_some = (borrow as u8) & 1;
+
+        // Convert to Montgomery form by computing
+        // (a.R^0 * R^2) / R = a.R
+        tmp *= &R2;
+
+        CtOption::new(tmp, Choice::from(is_some))
     }
 
     fn to_repr(&self) -> Self::Repr {
-        self.to_bytes()
+        // Turn into canonical form by computing
+        // (a.R) / R = a
+        let tmp = Fp::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);
+
+        let mut res = [0; 32];
+        res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());
+        res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());
+        res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());
+        res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());
+
+        res
     }
 
     fn is_odd(&self) -> Choice {
-        Choice::from(self.to_bytes()[0] & 1)
+        Choice::from(self.to_repr()[0] & 1)
     }
 
     fn multiplicative_generator() -> Self {
@@ -551,7 +589,7 @@ impl ff::PrimeField for Fp {
     }
 
     fn root_of_unity() -> Self {
-        Self::ROOT_OF_UNITY
+        ROOT_OF_UNITY
     }
 }
 
@@ -660,48 +698,12 @@ impl FieldExt for Fp {
         Fp::from_raw([v as u64, (v >> 64) as u64, 0, 0])
     }
 
-    /// Attempts to convert a little-endian byte representation of
-    /// a scalar into a `Fp`, failing if the input is not canonical.
     fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fp> {
-        let mut tmp = Fp([0, 0, 0, 0]);
-
-        tmp.0[0] = u64::from_le_bytes(bytes[0..8].try_into().unwrap());
-        tmp.0[1] = u64::from_le_bytes(bytes[8..16].try_into().unwrap());
-        tmp.0[2] = u64::from_le_bytes(bytes[16..24].try_into().unwrap());
-        tmp.0[3] = u64::from_le_bytes(bytes[24..32].try_into().unwrap());
-
-        // Try to subtract the modulus
-        let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);
-        let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);
-        let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);
-        let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);
-
-        // If the element is smaller than MODULUS then the
-        // subtraction will underflow, producing a borrow value
-        // of 0xffff...ffff. Otherwise, it'll be zero.
-        let is_some = (borrow as u8) & 1;
-
-        // Convert to Montgomery form by computing
-        // (a.R^0 * R^2) / R = a.R
-        tmp *= &R2;
-
-        CtOption::new(tmp, Choice::from(is_some))
+        <Self as ff::PrimeField>::from_repr(*bytes)
     }
 
-    /// Converts an element of `Fp` into a byte representation in
-    /// little-endian byte order.
     fn to_bytes(&self) -> [u8; 32] {
-        // Turn into canonical form by computing
-        // (a.R) / R = a
-        let tmp = Fp::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);
-
-        let mut res = [0; 32];
-        res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());
-        res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());
-        res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());
-        res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());
-
-        res
+        <Self as ff::PrimeField>::to_repr(self)
     }
 
     /// Converts a 512-bit little endian integer into
diff --git a/src/fields/fq.rs b/src/fields/fq.rs
index b624a67..c8be606 100644
--- a/src/fields/fq.rs
+++ b/src/fields/fq.rs
@@ -466,10 +466,16 @@ impl Group for Fq {
 
 impl ff::Field for Fq {
     fn random(mut rng: impl RngCore) -> Self {
-        let mut random_bytes = [0; 64];
-        rng.fill_bytes(&mut random_bytes[..]);
-
-        Self::from_bytes_wide(&random_bytes)
+        Self::from_u512([
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+            rng.next_u64(),
+        ])
     }
 
     fn zero() -> Self {
@@ -491,7 +497,7 @@ impl ff::Field for Fq {
 
     /// Computes the square root of this element, if it exists.
     fn sqrt(&self) -> CtOption<Self> {
-        let (is_square, res) = self.sqrt_alt();
+        let (is_square, res) = FQ_TABLES.sqrt_alt(self);
         CtOption::new(res, is_square)
     }
 
@@ -535,15 +541,47 @@ impl ff::PrimeField for Fq {
     const S: u32 = S;
 
     fn from_repr(repr: Self::Repr) -> CtOption<Self> {
-        Self::from_bytes(&repr)
+        let mut tmp = Fq([0, 0, 0, 0]);
+
+        tmp.0[0] = u64::from_le_bytes(repr[0..8].try_into().unwrap());
+        tmp.0[1] = u64::from_le_bytes(repr[8..16].try_into().unwrap());
+        tmp.0[2] = u64::from_le_bytes(repr[16..24].try_into().unwrap());
+        tmp.0[3] = u64::from_le_bytes(repr[24..32].try_into().unwrap());
+
+        // Try to subtract the modulus
+        let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);
+        let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);
+        let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);
+        let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);
+
+        // If the element is smaller than MODULUS then the
+        // subtraction will underflow, producing a borrow value
+        // of 0xffff...ffff. Otherwise, it'll be zero.
+        let is_some = (borrow as u8) & 1;
+
+        // Convert to Montgomery form by computing
+        // (a.R^0 * R^2) / R = a.R
+        tmp *= &R2;
+
+        CtOption::new(tmp, Choice::from(is_some))
     }
 
     fn to_repr(&self) -> Self::Repr {
-        self.to_bytes()
+        // Turn into canonical form by computing
+        // (a.R) / R = a
+        let tmp = Fq::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);
+
+        let mut res = [0; 32];
+        res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());
+        res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());
+        res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());
+        res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());
+
+        res
     }
 
     fn is_odd(&self) -> Choice {
-        Choice::from(self.to_bytes()[0] & 1)
+        Choice::from(self.to_repr()[0] & 1)
     }
 
     fn multiplicative_generator() -> Self {
@@ -551,7 +589,7 @@ impl ff::PrimeField for Fq {
     }
 
     fn root_of_unity() -> Self {
-        Self::ROOT_OF_UNITY
+        ROOT_OF_UNITY
     }
 }
 
@@ -660,48 +698,12 @@ impl FieldExt for Fq {
         Fq::from_raw([v as u64, (v >> 64) as u64, 0, 0])
     }
 
-    /// Attempts to convert a little-endian byte representation of
-    /// a scalar into a `Fq`, failing if the input is not canonical.
     fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fq> {
-        let mut tmp = Fq([0, 0, 0, 0]);
-
-        tmp.0[0] = u64::from_le_bytes(bytes[0..8].try_into().unwrap());
-        tmp.0[1] = u64::from_le_bytes(bytes[8..16].try_into().unwrap());
-        tmp.0[2] = u64::from_le_bytes(bytes[16..24].try_into().unwrap());
-        tmp.0[3] = u64::from_le_bytes(bytes[24..32].try_into().unwrap());
-
-        // Try to subtract the modulus
-        let (_, borrow) = sbb(tmp.0[0], MODULUS.0[0], 0);
-        let (_, borrow) = sbb(tmp.0[1], MODULUS.0[1], borrow);
-        let (_, borrow) = sbb(tmp.0[2], MODULUS.0[2], borrow);
-        let (_, borrow) = sbb(tmp.0[3], MODULUS.0[3], borrow);
-
-        // If the element is smaller than MODULUS then the
-        // subtraction will underflow, producing a borrow value
-        // of 0xffff...ffff. Otherwise, it'll be zero.
-        let is_some = (borrow as u8) & 1;
-
-        // Convert to Montgomery form by computing
-        // (a.R^0 * R^2) / R = a.R
-        tmp *= &R2;
-
-        CtOption::new(tmp, Choice::from(is_some))
+        <Self as ff::PrimeField>::from_repr(*bytes)
     }
 
-    /// Converts an element of `Fq` into a byte representation in
-    /// little-endian byte order.
     fn to_bytes(&self) -> [u8; 32] {
-        // Turn into canonical form by computing
-        // (a.R) / R = a
-        let tmp = Fq::montgomery_reduce(self.0[0], self.0[1], self.0[2], self.0[3], 0, 0, 0, 0);
-
-        let mut res = [0; 32];
-        res[0..8].copy_from_slice(&tmp.0[0].to_le_bytes());
-        res[8..16].copy_from_slice(&tmp.0[1].to_le_bytes());
-        res[16..24].copy_from_slice(&tmp.0[2].to_le_bytes());
-        res[24..32].copy_from_slice(&tmp.0[3].to_le_bytes());
-
-        res
+        <Self as ff::PrimeField>::to_repr(self)
     }
 
     /// Converts a 512-bit little endian integer into

From 8fabb44ad4d2bfb2ee309838e52c3834b06be2e0 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@electriccoin.co>
Date: Mon, 20 Sep 2021 17:26:34 +0100
Subject: [PATCH 3/5] fields: Use `ff::PrimeField` instead of `FieldExt` where
 possible

---
 src/curves.rs    | 17 +++++++++--------
 src/fields/fp.rs | 14 ++++++++------
 src/fields/fq.rs | 14 ++++++++------
 3 files changed, 25 insertions(+), 20 deletions(-)

diff --git a/src/curves.rs b/src/curves.rs
index 93778e2..dc01128 100644
--- a/src/curves.rs
+++ b/src/curves.rs
@@ -5,7 +5,8 @@ use core::cmp;
 use core::fmt::Debug;
 use core::iter::Sum;
 use core::ops::{Add, Mul, Neg, Sub};
-use ff::Field;
+
+use ff::{Field, PrimeField};
 use group::{
     cofactor::{CofactorCurve, CofactorGroup},
     prime::{PrimeCurve, PrimeCurveAffine, PrimeGroup},
@@ -68,7 +69,7 @@ macro_rules! new_curve_impl {
                     let x3 = x.square() * x;
                     let y = (x3 + $name::curve_constant_b()).sqrt();
                     if let Some(y) = Option::<$base>::from(y) {
-                        let sign = y.to_bytes()[0] & 1;
+                        let sign = y.is_odd().unwrap_u8();
                         let y = if ysign ^ sign == 0 { y } else { -y };
 
                         let p = $name_affine {
@@ -465,7 +466,7 @@ macro_rules! new_curve_impl {
                 //
                 // NOTE: We skip the leading bit because it's always unset.
                 for bit in other
-                    .to_bytes()
+                    .to_repr()
                     .iter()
                     .rev()
                     .flat_map(|byte| (0..8).rev().map(move |i| Choice::from((byte >> i) & 1u8)))
@@ -576,7 +577,7 @@ macro_rules! new_curve_impl {
                 //
                 // NOTE: We skip the leading bit because it's always unset.
                 for bit in other
-                    .to_bytes()
+                    .to_repr()
                     .iter()
                     .rev()
                     .flat_map(|byte| (0..8).rev().map(move |i| Choice::from((byte >> i) & 1u8)))
@@ -646,11 +647,11 @@ macro_rules! new_curve_impl {
                 let ysign = Choice::from(tmp[31] >> 7);
                 tmp[31] &= 0b0111_1111;
 
-                $base::from_bytes(&tmp).and_then(|x| {
+                $base::from_repr(tmp).and_then(|x| {
                     CtOption::new(Self::identity(), x.is_zero() & (!ysign)).or_else(|| {
                         let x3 = x.square() * x;
                         (x3 + $name::curve_constant_b()).sqrt().and_then(|y| {
-                            let sign = Choice::from(y.to_bytes()[0] & 1);
+                            let sign = y.is_odd();
 
                             let y = $base::conditional_select(&y, &-y, ysign ^ sign);
 
@@ -678,8 +679,8 @@ macro_rules! new_curve_impl {
                     [0; 32]
                 } else {
                     let (x, y) = (self.x, self.y);
-                    let sign = (y.to_bytes()[0] & 1) << 7;
-                    let mut xbytes = x.to_bytes();
+                    let sign = y.is_odd().unwrap_u8() << 7;
+                    let mut xbytes = x.to_repr();
                     xbytes[31] |= sign;
                     xbytes
                 }
diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index 065a453..b8573c1 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -2,6 +2,8 @@ use core::convert::TryInto;
 use core::fmt;
 use core::ops::{Add, Mul, Neg, Sub};
 use lazy_static::lazy_static;
+
+use ff::PrimeField;
 use rand::RngCore;
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
@@ -23,7 +25,7 @@ pub struct Fp(pub(crate) [u64; 4]);
 
 impl fmt::Debug for Fp {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        let tmp = self.to_bytes();
+        let tmp = self.to_repr();
         write!(f, "0x")?;
         for &b in tmp.iter().rev() {
             write!(f, "{:02x}", b)?;
@@ -66,8 +68,8 @@ impl PartialEq for Fp {
 
 impl std::cmp::Ord for Fp {
     fn cmp(&self, other: &Self) -> std::cmp::Ordering {
-        let left = self.to_bytes();
-        let right = other.to_bytes();
+        let left = self.to_repr();
+        let right = other.to_repr();
         left.iter()
             .zip(right.iter())
             .rev()
@@ -437,13 +439,13 @@ impl Fp {
 
 impl From<Fp> for [u8; 32] {
     fn from(value: Fp) -> [u8; 32] {
-        value.to_bytes()
+        value.to_repr()
     }
 }
 
 impl<'a> From<&'a Fp> for [u8; 32] {
     fn from(value: &'a Fp) -> [u8; 32] {
-        value.to_bytes()
+        value.to_repr()
     }
 }
 
@@ -767,7 +769,7 @@ impl FieldExt for Fp {
 }
 
 #[cfg(test)]
-use ff::{Field, PrimeField};
+use ff::Field;
 
 #[test]
 fn test_inv() {
diff --git a/src/fields/fq.rs b/src/fields/fq.rs
index c8be606..6c2518f 100644
--- a/src/fields/fq.rs
+++ b/src/fields/fq.rs
@@ -2,6 +2,8 @@ use core::convert::TryInto;
 use core::fmt;
 use core::ops::{Add, Mul, Neg, Sub};
 use lazy_static::lazy_static;
+
+use ff::PrimeField;
 use rand::RngCore;
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
@@ -23,7 +25,7 @@ pub struct Fq(pub(crate) [u64; 4]);
 
 impl fmt::Debug for Fq {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        let tmp = self.to_bytes();
+        let tmp = self.to_repr();
         write!(f, "0x")?;
         for &b in tmp.iter().rev() {
             write!(f, "{:02x}", b)?;
@@ -66,8 +68,8 @@ impl PartialEq for Fq {
 
 impl std::cmp::Ord for Fq {
     fn cmp(&self, other: &Self) -> std::cmp::Ordering {
-        let left = self.to_bytes();
-        let right = other.to_bytes();
+        let left = self.to_repr();
+        let right = other.to_repr();
         left.iter()
             .zip(right.iter())
             .rev()
@@ -437,13 +439,13 @@ impl Fq {
 
 impl From<Fq> for [u8; 32] {
     fn from(value: Fq) -> [u8; 32] {
-        value.to_bytes()
+        value.to_repr()
     }
 }
 
 impl<'a> From<&'a Fq> for [u8; 32] {
     fn from(value: &'a Fq) -> [u8; 32] {
-        value.to_bytes()
+        value.to_repr()
     }
 }
 
@@ -767,7 +769,7 @@ impl FieldExt for Fq {
 }
 
 #[cfg(test)]
-use ff::{Field, PrimeField};
+use ff::Field;
 
 #[test]
 fn test_inv() {

From 9999964d17a5aafbe9aa811ff47310f57a852bf9 Mon Sep 17 00:00:00 2001
From: Jack Grigg <jack@electriccoin.co>
Date: Mon, 20 Sep 2021 17:44:11 +0100
Subject: [PATCH 4/5] Add no-std support

We re-introduce the Tonelli-Shank square root algoritm that was removed
in zcash/halo2#120, to use in no-std mode (the table-based impl requires
allocations, and also uses 29kiB of memory which is a problem for
constrained environments that typically need no-std).
---
 Cargo.toml               | 19 +++++++----
 src/arithmetic.rs        |  4 +++
 src/arithmetic/curves.rs | 21 ++++++++++--
 src/arithmetic/fields.rs | 72 +++++++++++++++++++++++++++++++++++++---
 src/curves.rs            | 16 +++++++--
 src/fields/fp.rs         | 54 ++++++++++++++++++++++++------
 src/fields/fq.rs         | 54 ++++++++++++++++++++++++------
 src/lib.rs               | 10 +++++-
 src/pallas.rs            |  4 +++
 src/vesta.rs             |  2 ++
 10 files changed, 216 insertions(+), 40 deletions(-)

diff --git a/Cargo.toml b/Cargo.toml
index d9593d7..50b86c2 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -25,6 +25,7 @@ rand_xorshift = "0.3"
 [[bench]]
 name = "hashtocurve"
 harness = false
+required-features = ["std"]
 
 [[bench]]
 name = "fp"
@@ -37,16 +38,20 @@ harness = false
 [[bench]]
 name = "point"
 harness = false
+required-features = ["std"]
 
 [dependencies]
-subtle = "2.3"
-ff = "0.11"
-group = "0.11"
-rand = "0.8"
-blake2b_simd = "0.5"
-lazy_static = "1.4.0"
+blake2b_simd = { version = "0.5", default-features = false }
+ff = { version = "0.11", default-features = false }
+group = { version = "0.11", default-features = false }
+rand = { version = "0.8", default-features = false }
 static_assertions = "1.1.0"
+subtle = { version = "2.3", default-features = false }
+
+# std dependencies
+lazy_static = { version = "1.4.0", optional = true }
 
 [features]
-default = ["bits"]
+default = ["bits", "std"]
 bits = ["ff/bits"]
+std = ["group/alloc", "lazy_static", "rand/getrandom"]
diff --git a/src/arithmetic.rs b/src/arithmetic.rs
index c2b802c..bb5fb1d 100644
--- a/src/arithmetic.rs
+++ b/src/arithmetic.rs
@@ -9,12 +9,16 @@ pub use ff::Field;
 mod curves;
 mod fields;
 
+pub(crate) use fields::*;
+
 pub use curves::*;
+#[cfg(feature = "std")]
 pub use fields::*;
 
 /// This represents an element of a group with basic operations that can be
 /// performed. This allows an FFT implementation (for example) to operate
 /// generically over either a field or elliptic curve group.
+#[cfg(feature = "std")]
 pub trait Group: Copy + Clone + Send + Sync + 'static {
     /// The group is assumed to be of prime order $p$. `Scalar` is the
     /// associated scalar field of size $p$.
diff --git a/src/arithmetic/curves.rs b/src/arithmetic/curves.rs
index a0b34ed..0088945 100644
--- a/src/arithmetic/curves.rs
+++ b/src/arithmetic/curves.rs
@@ -1,18 +1,29 @@
 //! This module contains the `Curve`/`CurveAffine` abstractions that allow us to
 //! write code that generalizes over a pair of groups.
 
-use core::cmp;
-use core::ops::{Add, Mul, Sub};
+#[cfg(feature = "std")]
 use group::prime::{PrimeCurve, PrimeCurveAffine};
+#[cfg(feature = "std")]
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
+#[cfg(feature = "std")]
 use super::{FieldExt, Group};
 
-use std::io::{self, Read, Write};
+#[cfg(feature = "std")]
+use std::{
+    boxed::Box,
+    cmp,
+    io::{self, Read, Write},
+    ops::{Add, Mul, Sub},
+};
 
 /// This trait is a common interface for dealing with elements of an elliptic
 /// curve group in a "projective" form, where that arithmetic is usually more
 /// efficient.
+///
+/// Currently requires the `std` feature flag because of `hash_to_curve`, and
+/// `CurveAffine::{read, write}`.
+#[cfg(feature = "std")]
 pub trait CurveExt:
     PrimeCurve<Affine = <Self as CurveExt>::AffineExt>
     + group::Group<Scalar = <Self as CurveExt>::ScalarExt>
@@ -81,6 +92,7 @@ pub trait CurveExt:
 
 /// This trait is the affine counterpart to `Curve` and is used for
 /// serialization, storage in memory, and inspection of $x$ and $y$ coordinates.
+#[cfg(feature = "std")]
 pub trait CurveAffine:
     PrimeCurveAffine<
         Scalar = <Self as CurveAffine>::ScalarExt,
@@ -135,12 +147,14 @@ pub trait CurveAffine:
 }
 
 /// The affine coordinates of a point on an elliptic curve.
+#[cfg(feature = "std")]
 #[derive(Clone, Copy, Debug, Default)]
 pub struct Coordinates<C: CurveAffine> {
     pub(crate) x: C::Base,
     pub(crate) y: C::Base,
 }
 
+#[cfg(feature = "std")]
 impl<C: CurveAffine> Coordinates<C> {
     /// Returns the x-coordinate.
     ///
@@ -171,6 +185,7 @@ impl<C: CurveAffine> Coordinates<C> {
     }
 }
 
+#[cfg(feature = "std")]
 impl<C: CurveAffine> ConditionallySelectable for Coordinates<C> {
     fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
         Coordinates {
diff --git a/src/arithmetic/fields.rs b/src/arithmetic/fields.rs
index e9caea2..d755c9d 100644
--- a/src/arithmetic/fields.rs
+++ b/src/arithmetic/fields.rs
@@ -2,20 +2,28 @@
 //! code that generalizes over a pair of fields.
 
 use core::mem::size_of;
+
 use static_assertions::const_assert;
-use std::assert;
-use std::convert::TryInto;
-use std::marker::PhantomData;
 use subtle::{Choice, CtOption};
 
+#[cfg(feature = "std")]
 use super::Group;
 
-use std::io::{self, Read, Write};
+#[cfg(feature = "std")]
+use std::{
+    assert,
+    boxed::Box,
+    convert::TryInto,
+    io::{self, Read, Write},
+    marker::PhantomData,
+    vec::Vec,
+};
 
 const_assert!(size_of::<usize>() >= 4);
 
 /// This trait is a common interface for dealing with elements of a finite
 /// field.
+#[cfg(feature = "std")]
 pub trait FieldExt: ff::PrimeField + From<bool> + Ord + Group<Scalar = Self> {
     /// Modulus of the field written as a string for display purposes
     const MODULUS: &'static str;
@@ -130,7 +138,58 @@ pub trait FieldExt: ff::PrimeField + From<bool> + Ord + Group<Scalar = Self> {
     }
 }
 
+/// Tonelli-Shank's square-root algorithm for `p mod 16 = 1`.
+///
+/// https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
+///
+/// `tm1d2` should be set to `(t - 1) // 2`, where `t = (modulus - 1) >> F::S`.
+#[cfg(not(feature = "std"))]
+pub(crate) fn sqrt_tonelli_shank<F: ff::PrimeField, S: AsRef<[u64]>>(
+    f: &F,
+    tm1d2: S,
+) -> CtOption<F> {
+    use subtle::{ConditionallySelectable, ConstantTimeEq};
+
+    // w = self^((t - 1) // 2)
+    let w = f.pow_vartime(tm1d2);
+
+    let mut v = F::S;
+    let mut x = w * f;
+    let mut b = x * w;
+
+    // Initialize z as the 2^S root of unity.
+    let mut z = F::root_of_unity();
+
+    for max_v in (1..=F::S).rev() {
+        let mut k = 1;
+        let mut tmp = b.square();
+        let mut j_less_than_v: Choice = 1.into();
+
+        for j in 2..max_v {
+            let tmp_is_one = tmp.ct_eq(&F::one());
+            let squared = F::conditional_select(&tmp, &z, tmp_is_one).square();
+            tmp = F::conditional_select(&squared, &tmp, tmp_is_one);
+            let new_z = F::conditional_select(&z, &squared, tmp_is_one);
+            j_less_than_v &= !j.ct_eq(&v);
+            k = u32::conditional_select(&j, &k, tmp_is_one);
+            z = F::conditional_select(&z, &new_z, j_less_than_v);
+        }
+
+        let result = x * z;
+        x = F::conditional_select(&result, &x, b.ct_eq(&F::one()));
+        z = z.square();
+        b *= z;
+        v = k;
+    }
+
+    CtOption::new(
+        x,
+        (x * x).ct_eq(f), // Only return Some if it's the square root.
+    )
+}
+
 /// Parameters for a perfect hash function used in square root computation.
+#[cfg(feature = "std")]
 #[derive(Debug)]
 struct SqrtHasher<F: FieldExt> {
     hash_xor: u32,
@@ -138,6 +197,7 @@ struct SqrtHasher<F: FieldExt> {
     marker: PhantomData<F>,
 }
 
+#[cfg(feature = "std")]
 impl<F: FieldExt> SqrtHasher<F> {
     /// Returns a perfect hash of x for use with SqrtTables::inv.
     fn hash(&self, x: &F) -> usize {
@@ -150,6 +210,7 @@ impl<F: FieldExt> SqrtHasher<F> {
 }
 
 /// Tables used for square root computation.
+#[cfg(feature = "std")]
 #[derive(Debug)]
 pub struct SqrtTables<F: FieldExt> {
     hasher: SqrtHasher<F>,
@@ -160,9 +221,12 @@ pub struct SqrtTables<F: FieldExt> {
     g3: Box<[F; 129]>,
 }
 
+#[cfg(feature = "std")]
 impl<F: FieldExt> SqrtTables<F> {
     /// Build tables given parameters for the perfect hash.
     pub fn new(hash_xor: u32, hash_mod: usize) -> Self {
+        use std::vec;
+
         let hasher = SqrtHasher {
             hash_xor,
             hash_mod,
diff --git a/src/curves.rs b/src/curves.rs
index dc01128..d402de5 100644
--- a/src/curves.rs
+++ b/src/curves.rs
@@ -2,10 +2,13 @@
 //! groups.
 
 use core::cmp;
-use core::fmt::Debug;
+use core::fmt;
 use core::iter::Sum;
 use core::ops::{Add, Mul, Neg, Sub};
 
+#[cfg(feature = "std")]
+use std::boxed::Box;
+
 use ff::{Field, PrimeField};
 use group::{
     cofactor::{CofactorCurve, CofactorGroup},
@@ -16,6 +19,8 @@ use rand::RngCore;
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
 use super::{Fp, Fq};
+
+#[cfg(feature = "std")]
 use crate::arithmetic::{Coordinates, CurveAffine, CurveExt, FieldExt, Group};
 
 macro_rules! new_curve_impl {
@@ -48,8 +53,8 @@ macro_rules! new_curve_impl {
             infinity: Choice,
         }
 
-        impl std::fmt::Debug for $name_affine {
-            fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
+        impl fmt::Debug for $name_affine {
+            fn fmt(&self, f: &mut fmt::Formatter<'_>) -> Result<(), fmt::Error> {
                 if self.infinity.into() {
                     write!(f, "Infinity")
                 } else {
@@ -97,6 +102,7 @@ macro_rules! new_curve_impl {
             }
         }
 
+        #[cfg(feature = "std")]
         impl group::WnafGroup for $name {
             fn recommended_wnaf_for_num_scalars(num_scalars: usize) -> usize {
                 // Copied from bls12_381::g1, should be updated.
@@ -116,6 +122,7 @@ macro_rules! new_curve_impl {
             }
         }
 
+        #[cfg(feature = "std")]
         impl CurveExt for $name {
             type ScalarExt = $scalar;
             type Base = $base;
@@ -687,6 +694,7 @@ macro_rules! new_curve_impl {
             }
         }
 
+        #[cfg(feature = "std")]
         impl CurveAffine for $name_affine {
             type ScalarExt = $scalar;
             type Base = $base;
@@ -770,6 +778,7 @@ macro_rules! new_curve_impl {
         impl_binops_multiplicative!($name, $scalar);
         impl_binops_multiplicative_mixed!($name_affine, $scalar, $name);
 
+        #[cfg(feature = "std")]
         impl Group for $name {
             type Scalar = $scalar;
 
@@ -870,6 +879,7 @@ macro_rules! impl_projective_curve_specific {
     };
 }
 
+#[cfg(feature = "std")]
 macro_rules! impl_projective_curve_ext {
     ($name:ident, $iso:ident, $base:ident, special_a0_b5) => {
         fn hash_to_curve<'a>(domain_prefix: &'a str) -> Box<dyn Fn(&[u8]) -> Self + 'a> {
diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index b8573c1..200e20d 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -1,16 +1,21 @@
 use core::convert::TryInto;
 use core::fmt;
 use core::ops::{Add, Mul, Neg, Sub};
-use lazy_static::lazy_static;
 
 use ff::PrimeField;
 use rand::RngCore;
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
+#[cfg(feature = "std")]
+use lazy_static::lazy_static;
+
 #[cfg(feature = "bits")]
 use ff::{FieldBits, PrimeFieldBits};
 
-use crate::arithmetic::{adc, mac, sbb, FieldExt, Group, SqrtTables};
+use crate::arithmetic::{adc, mac, sbb};
+
+#[cfg(feature = "std")]
+use crate::arithmetic::{FieldExt, Group, SqrtTables};
 
 /// This represents an element of $\mathbb{F}_p$ where
 ///
@@ -66,23 +71,23 @@ impl PartialEq for Fp {
     }
 }
 
-impl std::cmp::Ord for Fp {
-    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+impl core::cmp::Ord for Fp {
+    fn cmp(&self, other: &Self) -> core::cmp::Ordering {
         let left = self.to_repr();
         let right = other.to_repr();
         left.iter()
             .zip(right.iter())
             .rev()
             .find_map(|(left_byte, right_byte)| match left_byte.cmp(right_byte) {
-                std::cmp::Ordering::Equal => None,
+                core::cmp::Ordering::Equal => None,
                 res => Some(res),
             })
-            .unwrap_or(std::cmp::Ordering::Equal)
+            .unwrap_or(core::cmp::Ordering::Equal)
     }
 }
 
-impl std::cmp::PartialOrd for Fp {
-    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+impl core::cmp::PartialOrd for Fp {
+    fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
         Some(self.cmp(other))
     }
 }
@@ -219,6 +224,7 @@ const ROOT_OF_UNITY: Fp = Fp::from_raw([
 /// GENERATOR^{2^s} where t * 2^s + 1 = p
 /// with t odd. In other words, this
 /// is a t root of unity.
+#[cfg(feature = "std")]
 const DELTA: Fp = Fp::from_raw([
     0x6a6ccd20dd7b9ba2,
     0xf5e4f3f13eee5636,
@@ -449,6 +455,7 @@ impl<'a> From<&'a Fp> for [u8; 32] {
     }
 }
 
+#[cfg(feature = "std")]
 impl Group for Fp {
     type Scalar = Fp;
 
@@ -499,8 +506,22 @@ impl ff::Field for Fp {
 
     /// Computes the square root of this element, if it exists.
     fn sqrt(&self) -> CtOption<Self> {
-        let (is_square, res) = FP_TABLES.sqrt_alt(self);
-        CtOption::new(res, is_square)
+        #[cfg(feature = "std")]
+        {
+            let (is_square, res) = FP_TABLES.sqrt_alt(self);
+            CtOption::new(res, is_square)
+        }
+
+        #[cfg(not(feature = "std"))]
+        crate::arithmetic::sqrt_tonelli_shank(
+            self,
+            &[
+                0x04a6_7c8d_cc96_9876,
+                0x0000_0000_1123_4c7e,
+                0x0000_0000_0000_0000,
+                0x0000_0000_2000_0000,
+            ],
+        )
     }
 
     /// Computes the multiplicative inverse of this element,
@@ -642,11 +663,13 @@ impl PrimeFieldBits for Fp {
     }
 }
 
+#[cfg(feature = "std")]
 lazy_static! {
     // The perfect hash parameters are found by `squareroottab.sage` in zcash/pasta.
     static ref FP_TABLES: SqrtTables<Fp> = SqrtTables::new(0x11BE, 1098);
 }
 
+#[cfg(feature = "std")]
 impl FieldExt for Fp {
     const MODULUS: &'static str =
         "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001";
@@ -768,7 +791,7 @@ impl FieldExt for Fp {
     }
 }
 
-#[cfg(test)]
+#[cfg(all(test, feature = "std"))]
 use ff::Field;
 
 #[test]
@@ -786,6 +809,7 @@ fn test_inv() {
     assert_eq!(inv, INV);
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_rescue() {
     // NB: TWO_INV is standing in as a "random" field element
@@ -797,6 +821,7 @@ fn test_rescue() {
     );
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_sqrt() {
     // NB: TWO_INV is standing in as a "random" field element
@@ -804,6 +829,7 @@ fn test_sqrt() {
     assert!(v == Fp::TWO_INV || (-v) == Fp::TWO_INV);
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_pow_by_t_minus1_over2() {
     // NB: TWO_INV is standing in as a "random" field element
@@ -811,6 +837,7 @@ fn test_pow_by_t_minus1_over2() {
     assert!(v == ff::Field::pow_vartime(&Fp::TWO_INV, &Fp::T_MINUS1_OVER2));
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_sqrt_ratio_and_alt() {
     // (true, sqrt(num/div)), if num and div are nonzero and num/div is a square in the field
@@ -857,6 +884,7 @@ fn test_sqrt_ratio_and_alt() {
     assert!(v == expected);
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_zeta() {
     assert_eq!(
@@ -872,6 +900,7 @@ fn test_zeta() {
     assert!(c == Fp::one());
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_root_of_unity() {
     assert_eq!(
@@ -880,16 +909,19 @@ fn test_root_of_unity() {
     );
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_inv_root_of_unity() {
     assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::ROOT_OF_UNITY.invert().unwrap());
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_inv_2() {
     assert_eq!(Fp::TWO_INV, Fp::from(2).invert().unwrap());
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_delta() {
     assert_eq!(Fp::DELTA, GENERATOR.pow(&[1u64 << Fp::S, 0, 0, 0]));
diff --git a/src/fields/fq.rs b/src/fields/fq.rs
index 6c2518f..95fed38 100644
--- a/src/fields/fq.rs
+++ b/src/fields/fq.rs
@@ -1,16 +1,21 @@
 use core::convert::TryInto;
 use core::fmt;
 use core::ops::{Add, Mul, Neg, Sub};
-use lazy_static::lazy_static;
 
 use ff::PrimeField;
 use rand::RngCore;
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
+#[cfg(feature = "std")]
+use lazy_static::lazy_static;
+
 #[cfg(feature = "bits")]
 use ff::{FieldBits, PrimeFieldBits};
 
-use crate::arithmetic::{adc, mac, sbb, FieldExt, Group, SqrtTables};
+use crate::arithmetic::{adc, mac, sbb};
+
+#[cfg(feature = "std")]
+use crate::arithmetic::{FieldExt, Group, SqrtTables};
 
 /// This represents an element of $\mathbb{F}_q$ where
 ///
@@ -66,23 +71,23 @@ impl PartialEq for Fq {
     }
 }
 
-impl std::cmp::Ord for Fq {
-    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+impl core::cmp::Ord for Fq {
+    fn cmp(&self, other: &Self) -> core::cmp::Ordering {
         let left = self.to_repr();
         let right = other.to_repr();
         left.iter()
             .zip(right.iter())
             .rev()
             .find_map(|(left_byte, right_byte)| match left_byte.cmp(right_byte) {
-                std::cmp::Ordering::Equal => None,
+                core::cmp::Ordering::Equal => None,
                 res => Some(res),
             })
-            .unwrap_or(std::cmp::Ordering::Equal)
+            .unwrap_or(core::cmp::Ordering::Equal)
     }
 }
 
-impl std::cmp::PartialOrd for Fq {
-    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+impl core::cmp::PartialOrd for Fq {
+    fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
         Some(self.cmp(other))
     }
 }
@@ -219,6 +224,7 @@ const ROOT_OF_UNITY: Fq = Fq::from_raw([
 /// GENERATOR^{2^s} where t * 2^s + 1 = q
 /// with t odd. In other words, this
 /// is a t root of unity.
+#[cfg(feature = "std")]
 const DELTA: Fq = Fq::from_raw([
     0x8494392472d1683c,
     0xe3ac3376541d1140,
@@ -449,6 +455,7 @@ impl<'a> From<&'a Fq> for [u8; 32] {
     }
 }
 
+#[cfg(feature = "std")]
 impl Group for Fq {
     type Scalar = Fq;
 
@@ -499,8 +506,22 @@ impl ff::Field for Fq {
 
     /// Computes the square root of this element, if it exists.
     fn sqrt(&self) -> CtOption<Self> {
-        let (is_square, res) = FQ_TABLES.sqrt_alt(self);
-        CtOption::new(res, is_square)
+        #[cfg(feature = "std")]
+        {
+            let (is_square, res) = FQ_TABLES.sqrt_alt(self);
+            CtOption::new(res, is_square)
+        }
+
+        #[cfg(not(feature = "std"))]
+        crate::arithmetic::sqrt_tonelli_shank(
+            self,
+            &[
+                0x04ca_546e_c623_7590,
+                0x0000_0000_1123_4c7e,
+                0x0000_0000_0000_0000,
+                0x0000_0000_2000_0000,
+            ],
+        )
     }
 
     /// Computes the multiplicative inverse of this element,
@@ -642,11 +663,13 @@ impl PrimeFieldBits for Fq {
     }
 }
 
+#[cfg(feature = "std")]
 lazy_static! {
     // The perfect hash parameters are found by `squareroottab.sage` in zcash/pasta.
     static ref FQ_TABLES: SqrtTables<Fq> = SqrtTables::new(0x116A9E, 1206);
 }
 
+#[cfg(feature = "std")]
 impl FieldExt for Fq {
     const MODULUS: &'static str =
         "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001";
@@ -768,7 +791,7 @@ impl FieldExt for Fq {
     }
 }
 
-#[cfg(test)]
+#[cfg(all(test, feature = "std"))]
 use ff::Field;
 
 #[test]
@@ -786,6 +809,7 @@ fn test_inv() {
     assert_eq!(inv, INV);
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_rescue() {
     // NB: TWO_INV is standing in as a "random" field element
@@ -797,6 +821,7 @@ fn test_rescue() {
     );
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_sqrt() {
     // NB: TWO_INV is standing in as a "random" field element
@@ -804,6 +829,7 @@ fn test_sqrt() {
     assert!(v == Fq::TWO_INV || (-v) == Fq::TWO_INV);
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_pow_by_t_minus1_over2() {
     // NB: TWO_INV is standing in as a "random" field element
@@ -811,6 +837,7 @@ fn test_pow_by_t_minus1_over2() {
     assert!(v == ff::Field::pow_vartime(&Fq::TWO_INV, &Fq::T_MINUS1_OVER2));
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_sqrt_ratio_and_alt() {
     // (true, sqrt(num/div)), if num and div are nonzero and num/div is a square in the field
@@ -857,6 +884,7 @@ fn test_sqrt_ratio_and_alt() {
     assert!(v == expected);
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_zeta() {
     assert_eq!(
@@ -871,6 +899,7 @@ fn test_zeta() {
     assert!(c == Fq::one());
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_root_of_unity() {
     assert_eq!(
@@ -879,16 +908,19 @@ fn test_root_of_unity() {
     );
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_inv_root_of_unity() {
     assert_eq!(Fq::ROOT_OF_UNITY_INV, Fq::ROOT_OF_UNITY.invert().unwrap());
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_inv_2() {
     assert_eq!(Fq::TWO_INV, Fq::from(2).invert().unwrap());
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_delta() {
     assert_eq!(Fq::DELTA, GENERATOR.pow(&[1u64 << Fq::S, 0, 0, 0]));
diff --git a/src/lib.rs b/src/lib.rs
index 5cb9de9..add7d5d 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,5 +1,6 @@
 //! Implementation of the Pallas / Vesta curve cycle.
 
+#![no_std]
 #![cfg_attr(docsrs, feature(doc_cfg))]
 #![allow(unknown_lints)]
 #![allow(clippy::op_ref, clippy::same_item_push, clippy::upper_case_acronyms)]
@@ -8,21 +9,28 @@
 #![deny(missing_docs)]
 #![deny(unsafe_code)]
 
+#[cfg(any(feature = "std", test))]
+#[macro_use]
+extern crate std;
+
 #[macro_use]
 mod macros;
 mod curves;
 mod fields;
 
 pub mod arithmetic;
-mod hashtocurve;
 pub mod pallas;
 pub mod vesta;
 
+#[cfg(feature = "std")]
+mod hashtocurve;
+
 pub use curves::*;
 pub use fields::*;
 
 pub extern crate group;
 
+#[cfg(feature = "std")]
 #[test]
 fn test_endo_consistency() {
     use crate::arithmetic::{CurveExt, FieldExt};
diff --git a/src/pallas.rs b/src/pallas.rs
index 4c00a99..c9754ee 100644
--- a/src/pallas.rs
+++ b/src/pallas.rs
@@ -14,6 +14,7 @@ pub type Point = Ep;
 /// A Pallas point in the affine coordinate space (or the point at infinity).
 pub type Affine = EpAffine;
 
+#[cfg(feature = "std")]
 #[test]
 #[allow(clippy::many_single_char_names)]
 fn test_iso_map() {
@@ -64,6 +65,7 @@ fn test_iso_map() {
     assert!(p2 == p.double());
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_iso_map_identity() {
     use crate::arithmetic::CurveExt;
@@ -98,6 +100,7 @@ fn test_iso_map_identity() {
     assert!(bool::from(p.is_identity()));
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_map_to_curve_simple_swu() {
     use crate::arithmetic::CurveExt;
@@ -132,6 +135,7 @@ fn test_map_to_curve_simple_swu() {
     );
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_hash_to_curve() {
     use crate::arithmetic::CurveExt;
diff --git a/src/vesta.rs b/src/vesta.rs
index e6dddb1..cafee9e 100644
--- a/src/vesta.rs
+++ b/src/vesta.rs
@@ -14,6 +14,7 @@ pub type Point = Eq;
 /// A Vesta point in the affine coordinate space (or the point at infinity).
 pub type Affine = EqAffine;
 
+#[cfg(feature = "std")]
 #[test]
 fn test_map_to_curve_simple_swu() {
     use crate::arithmetic::CurveExt;
@@ -48,6 +49,7 @@ fn test_map_to_curve_simple_swu() {
     );
 }
 
+#[cfg(feature = "std")]
 #[test]
 fn test_hash_to_curve() {
     use crate::arithmetic::CurveExt;

From 2b350118b0c51dab5aed48e218d1ffeceb44f1ff Mon Sep 17 00:00:00 2001
From: str4d <jack@electriccoin.co>
Date: Tue, 21 Sep 2021 10:44:07 +1200
Subject: [PATCH 5/5] Fix naming of Tonelli-Shanks

Co-authored-by: Daira Hopwood <daira@jacaranda.org>
---
 src/arithmetic/fields.rs | 4 ++--
 src/fields/fp.rs         | 2 +-
 src/fields/fq.rs         | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/arithmetic/fields.rs b/src/arithmetic/fields.rs
index d755c9d..53554fc 100644
--- a/src/arithmetic/fields.rs
+++ b/src/arithmetic/fields.rs
@@ -138,13 +138,13 @@ pub trait FieldExt: ff::PrimeField + From<bool> + Ord + Group<Scalar = Self> {
     }
 }
 
-/// Tonelli-Shank's square-root algorithm for `p mod 16 = 1`.
+/// Tonelli–Shanks' square-root algorithm for `p mod 16 = 1`.
 ///
 /// https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
 ///
 /// `tm1d2` should be set to `(t - 1) // 2`, where `t = (modulus - 1) >> F::S`.
 #[cfg(not(feature = "std"))]
-pub(crate) fn sqrt_tonelli_shank<F: ff::PrimeField, S: AsRef<[u64]>>(
+pub(crate) fn sqrt_tonelli_shanks<F: ff::PrimeField, S: AsRef<[u64]>>(
     f: &F,
     tm1d2: S,
 ) -> CtOption<F> {
diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index 200e20d..0650751 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -513,7 +513,7 @@ impl ff::Field for Fp {
         }
 
         #[cfg(not(feature = "std"))]
-        crate::arithmetic::sqrt_tonelli_shank(
+        crate::arithmetic::sqrt_tonelli_shanks(
             self,
             &[
                 0x04a6_7c8d_cc96_9876,
diff --git a/src/fields/fq.rs b/src/fields/fq.rs
index 95fed38..1a137fc 100644
--- a/src/fields/fq.rs
+++ b/src/fields/fq.rs
@@ -513,7 +513,7 @@ impl ff::Field for Fq {
         }
 
         #[cfg(not(feature = "std"))]
-        crate::arithmetic::sqrt_tonelli_shank(
+        crate::arithmetic::sqrt_tonelli_shanks(
             self,
             &[
                 0x04ca_546e_c623_7590,