diff --git a/bign256/src/arithmetic/scalar.rs b/bign256/src/arithmetic/scalar.rs
index 38a09277..5f689a01 100644
--- a/bign256/src/arithmetic/scalar.rs
+++ b/bign256/src/arithmetic/scalar.rs
@@ -223,6 +223,15 @@ impl From<&SecretKey> for Scalar {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<U256> for Scalar {
     type Error = Error;
 
diff --git a/bp256/src/r1/arithmetic.rs b/bp256/src/r1/arithmetic.rs
index 1bf7a3fb..0e31ab28 100644
--- a/bp256/src/r1/arithmetic.rs
+++ b/bp256/src/r1/arithmetic.rs
@@ -2,7 +2,7 @@
 
 use super::BrainpoolP256r1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, Error, PrimeCurveArithmetic};
 use primeorder::{PrimeCurveParams, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -76,3 +76,12 @@ impl From<&Scalar> for ScalarPrimitive {
         ScalarPrimitive::new(scalar.into()).unwrap()
     }
 }
+
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self, Error> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
diff --git a/bp256/src/t1/arithmetic.rs b/bp256/src/t1/arithmetic.rs
index 511bd678..916000cb 100644
--- a/bp256/src/t1/arithmetic.rs
+++ b/bp256/src/t1/arithmetic.rs
@@ -2,7 +2,7 @@
 
 use super::BrainpoolP256t1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, Error, PrimeCurveArithmetic};
 use primeorder::{PrimeCurveParams, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -76,3 +76,12 @@ impl From<&Scalar> for ScalarPrimitive {
         ScalarPrimitive::new(scalar.into()).unwrap()
     }
 }
+
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self, Error> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
diff --git a/bp384/src/r1/arithmetic.rs b/bp384/src/r1/arithmetic.rs
index aad1882d..070abf24 100644
--- a/bp384/src/r1/arithmetic.rs
+++ b/bp384/src/r1/arithmetic.rs
@@ -2,7 +2,7 @@
 
 use super::BrainpoolP384r1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, Error, PrimeCurveArithmetic};
 use primeorder::{PrimeCurveParams, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -82,3 +82,12 @@ impl From<&Scalar> for ScalarPrimitive {
         ScalarPrimitive::new(scalar.into()).unwrap()
     }
 }
+
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self, Error> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
diff --git a/bp384/src/t1/arithmetic.rs b/bp384/src/t1/arithmetic.rs
index 76f15515..adc73df8 100644
--- a/bp384/src/t1/arithmetic.rs
+++ b/bp384/src/t1/arithmetic.rs
@@ -2,7 +2,7 @@
 
 use super::BrainpoolP384t1;
 use crate::{FieldElement, Scalar};
-use elliptic_curve::{CurveArithmetic, PrimeCurveArithmetic};
+use elliptic_curve::{CurveArithmetic, Error, PrimeCurveArithmetic};
 use primeorder::{PrimeCurveParams, point_arithmetic};
 
 /// Elliptic curve point in affine coordinates.
@@ -82,3 +82,12 @@ impl From<&Scalar> for ScalarPrimitive {
         ScalarPrimitive::new(scalar.into()).unwrap()
     }
 }
+
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self, Error> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
diff --git a/k256/src/arithmetic/affine.rs b/k256/src/arithmetic/affine.rs
index 79245c34..cbfebdee 100644
--- a/k256/src/arithmetic/affine.rs
+++ b/k256/src/arithmetic/affine.rs
@@ -329,6 +329,15 @@ impl From<&PublicKey> for AffinePoint {
     }
 }
 
+/// The constant-time alternative is available at [`NonIdentity::new()`].
+impl TryFrom<AffinePoint> for NonIdentity<AffinePoint> {
+    type Error = Error;
+
+    fn try_from(affine_point: AffinePoint) -> Result<Self> {
+        NonIdentity::new(affine_point).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<AffinePoint> for PublicKey {
     type Error = Error;
 
diff --git a/k256/src/arithmetic/projective.rs b/k256/src/arithmetic/projective.rs
index a9178146..161f98c2 100644
--- a/k256/src/arithmetic/projective.rs
+++ b/k256/src/arithmetic/projective.rs
@@ -664,6 +664,15 @@ impl From<&PublicKey> for ProjectivePoint {
     }
 }
 
+/// The constant-time alternative is available at [`NonIdentity::new()`].
+impl TryFrom<ProjectivePoint> for NonIdentity<ProjectivePoint> {
+    type Error = Error;
+
+    fn try_from(point: ProjectivePoint) -> Result<Self> {
+        NonIdentity::new(point).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<ProjectivePoint> for PublicKey {
     type Error = Error;
 
diff --git a/k256/src/arithmetic/scalar.rs b/k256/src/arithmetic/scalar.rs
index fb402856..3d6d5535 100644
--- a/k256/src/arithmetic/scalar.rs
+++ b/k256/src/arithmetic/scalar.rs
@@ -12,7 +12,7 @@ use core::{
     ops::{Add, AddAssign, Mul, MulAssign, Neg, Shr, ShrAssign, Sub, SubAssign},
 };
 use elliptic_curve::{
-    Curve, ScalarPrimitive,
+    Curve, Error, ScalarPrimitive,
     bigint::{Limb, U256, U512, Word, prelude::*},
     ff::{self, Field, PrimeField},
     ops::{Invert, Reduce, ReduceNonZero},
@@ -413,6 +413,15 @@ impl From<&Scalar> for ScalarPrimitive<Secp256k1> {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self, Error> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl FromUintUnchecked for Scalar {
     type Uint = U256;
 
diff --git a/p192/src/arithmetic/scalar.rs b/p192/src/arithmetic/scalar.rs
index 5b24238b..706f5cc0 100644
--- a/p192/src/arithmetic/scalar.rs
+++ b/p192/src/arithmetic/scalar.rs
@@ -253,6 +253,15 @@ impl From<&Scalar> for ScalarPrimitive<NistP192> {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<U192> for Scalar {
     type Error = Error;
 
diff --git a/p224/src/arithmetic/scalar.rs b/p224/src/arithmetic/scalar.rs
index c8b393ba..6ddf5af3 100644
--- a/p224/src/arithmetic/scalar.rs
+++ b/p224/src/arithmetic/scalar.rs
@@ -254,6 +254,15 @@ impl From<&SecretKey> for Scalar {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<Uint> for Scalar {
     type Error = Error;
 
diff --git a/p256/src/arithmetic/scalar.rs b/p256/src/arithmetic/scalar.rs
index 122ebd0d..e95a5bde 100644
--- a/p256/src/arithmetic/scalar.rs
+++ b/p256/src/arithmetic/scalar.rs
@@ -12,7 +12,7 @@ use core::{
     ops::{Add, AddAssign, Mul, MulAssign, Neg, Shr, ShrAssign, Sub, SubAssign},
 };
 use elliptic_curve::{
-    Curve, ScalarPrimitive,
+    Curve, Error, ScalarPrimitive,
     bigint::{Limb, U256, prelude::*},
     group::ff::{self, Field, PrimeField},
     ops::{Invert, Reduce, ReduceNonZero},
@@ -533,6 +533,15 @@ impl From<&Scalar> for ScalarBits {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self, Error> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl Add<Scalar> for Scalar {
     type Output = Scalar;
 
diff --git a/p384/src/arithmetic/scalar.rs b/p384/src/arithmetic/scalar.rs
index efc925fe..6dc05b1e 100644
--- a/p384/src/arithmetic/scalar.rs
+++ b/p384/src/arithmetic/scalar.rs
@@ -292,6 +292,15 @@ impl From<&SecretKey> for Scalar {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<U384> for Scalar {
     type Error = Error;
 
diff --git a/p521/src/arithmetic/scalar.rs b/p521/src/arithmetic/scalar.rs
index 1b342771..9766d825 100644
--- a/p521/src/arithmetic/scalar.rs
+++ b/p521/src/arithmetic/scalar.rs
@@ -698,6 +698,15 @@ impl From<&SecretKey> for Scalar {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<U576> for Scalar {
     type Error = Error;
 
diff --git a/primeorder/src/affine.rs b/primeorder/src/affine.rs
index dcfaf339..259eacfb 100644
--- a/primeorder/src/affine.rs
+++ b/primeorder/src/affine.rs
@@ -367,6 +367,18 @@ where
     }
 }
 
+/// The constant-time alternative is available at [`NonIdentity::new()`].
+impl<C> TryFrom<AffinePoint<C>> for NonIdentity<AffinePoint<C>>
+where
+    C: PrimeCurveParams,
+{
+    type Error = Error;
+
+    fn try_from(affine_point: AffinePoint<C>) -> Result<Self> {
+        NonIdentity::new(affine_point).into_option().ok_or(Error)
+    }
+}
+
 impl<C> TryFrom<EncodedPoint<C>> for AffinePoint<C>
 where
     C: PrimeCurveParams,
diff --git a/primeorder/src/projective.rs b/primeorder/src/projective.rs
index bec5dd1f..b032f639 100644
--- a/primeorder/src/projective.rs
+++ b/primeorder/src/projective.rs
@@ -477,6 +477,18 @@ where
     }
 }
 
+/// The constant-time alternative is available at [`NonIdentity::new()`].
+impl<C> TryFrom<ProjectivePoint<C>> for NonIdentity<ProjectivePoint<C>>
+where
+    C: PrimeCurveParams,
+{
+    type Error = Error;
+
+    fn try_from(point: ProjectivePoint<C>) -> Result<Self> {
+        NonIdentity::new(point).into_option().ok_or(Error)
+    }
+}
+
 impl<C> TryFrom<ProjectivePoint<C>> for PublicKey<C>
 where
     C: PrimeCurveParams,
diff --git a/sm2/src/arithmetic/scalar.rs b/sm2/src/arithmetic/scalar.rs
index e732c99f..e4d25702 100644
--- a/sm2/src/arithmetic/scalar.rs
+++ b/sm2/src/arithmetic/scalar.rs
@@ -238,6 +238,15 @@ impl From<&SecretKey> for Scalar {
     }
 }
 
+/// The constant-time alternative is available at [`NonZeroScalar::new()`].
+impl TryFrom<Scalar> for NonZeroScalar {
+    type Error = Error;
+
+    fn try_from(scalar: Scalar) -> Result<Self> {
+        NonZeroScalar::new(scalar).into_option().ok_or(Error)
+    }
+}
+
 impl TryFrom<U256> for Scalar {
     type Error = Error;