arithmetic: Rewrite limbs_reduce_once.

Move the function to `arithmetic` from `limb`. This is step towards
moving all arithmetic out of `limb`.

Change the signature so that the reduction is non separately instead
of in-place. It was already being done separately in `bigint` and it
costs very little, if anything, to do the same in the other caller in
`ec`.

Optimize the implementation to take advantage of the fact that `r`
and `a` do not alias each other. To do so, replace
`LIMBS_reduce_once` with two separate helper functions, `LIMBS_sub`
and `LIMBS_cmov`.

As part of doing this, ensure we're not passing any empty slices to
the relevant C code.

build.rs

@@ -870,9 +870,10 @@ fn prefix_all_symbols(pp: char, prefix_prefix: &str, prefix: &str) -> String {
         "LIMBS_are_zero",
         "LIMBS_equal",
         "LIMBS_less_than",
-        "LIMBS_reduce_once",
+        "LIMBS_select",
         "LIMBS_select_512_32",
         "LIMBS_shl_mod",
+        "LIMBS_sub",
         "LIMBS_sub_mod",
         "LIMBS_window5_split_window",
         "LIMBS_window5_unsplit_window",

crypto/limbs/limbs.c

@@ -18,7 +18,6 @@
 #include "../fipsmodule/bn/internal.h"
 #include "limbs.inl"
 
-
 /* XXX: We assume that the conversion from |Carry| to |Limb| is constant-time,
  * but we haven't verified that assumption. TODO: Fix it so we don't need to
  * make that assumption. */
@@ -61,25 +60,12 @@ Limb LIMBS_less_than(const Limb a[], const Limb b[], size_t num_limbs) {
   return constant_time_is_nonzero_w(borrow);
 }
 
-/* if (r >= m) { r -= m; } */
-void LIMBS_reduce_once(Limb r[], const Limb m[], size_t num_limbs) {
+// r, `a` and/or `b` may alias.
+Limb LIMBS_sub(Limb r[], const Limb a[], const Limb b[], size_t num_limbs) {
   debug_assert_nonsecret(num_limbs >= 1);
-  /* This could be done more efficiently if we had |num_limbs| of extra space
-   * available, by storing |r - m| and then doing a conditional copy of either
-   * |r| or |r - m|. But, in order to operate in constant space, with an eye
-   * towards this function being used in RSA in the future, we do things a
-   * slightly less efficient way. */
-  Limb lt = LIMBS_less_than(r, m, num_limbs);
-  Carry borrow =
-      limb_sub(&r[0], r[0], constant_time_select_w(lt, 0, m[0]));
-  for (size_t i = 1; i < num_limbs; ++i) {
-    /* XXX: This is probably particularly inefficient because the operations in
-     * constant_time_select affect the carry flag, so there will likely be
-     * loads and stores of |borrow|. */
-    borrow =
-        limb_sbb(&r[i], r[i], constant_time_select_w(lt, 0, m[i]), borrow);
-  }
-  dev_assert_secret(borrow == 0);
+  Limb underflow =
+      constant_time_is_nonzero_w(limbs_sub(r, a, b, num_limbs));
+  return underflow;
 }
 
 void LIMBS_add_mod(Limb r[], const Limb a[], const Limb b[], const Limb m[],
@@ -122,6 +108,13 @@ void LIMBS_shl_mod(Limb r[], const Limb a[], const Limb m[], size_t num_limbs) {
   }
 }
 
+// r, a, and/or b may alias.
+void LIMBS_select(Limb r[], const Limb a[], const Limb b[], size_t num_limbs, Limb cond) {
+    for (size_t i = 0; i < num_limbs; ++i) {
+        r[i] = constant_time_select_w(cond, a[i], b[i]);
+    }
+}
+
 int LIMBS_select_512_32(Limb r[], const Limb table[], size_t num_limbs,
                         crypto_word_t index) {
   if (num_limbs % (512 / LIMB_BITS) != 0) {

crypto/limbs/limbs.h

@@ -27,7 +27,6 @@ typedef crypto_word_t Limb;
 
 Limb LIMBS_are_zero(const Limb a[], size_t num_limbs);
 Limb LIMBS_equal(const Limb a[], const Limb b[], size_t num_limbs);
-void LIMBS_reduce_once(Limb r[], const Limb m[], size_t num_limbs);
 void LIMBS_add_mod(Limb r[], const Limb a[], const Limb b[], const Limb m[],
                    size_t num_limbs);
 void LIMBS_sub_mod(Limb r[], const Limb a[], const Limb b[], const Limb m[],

src/arithmetic.rs

@@ -23,6 +23,7 @@ mod constant;
 #[cfg(feature = "alloc")]
 pub mod bigint;
 
+pub mod add;
 pub mod montgomery;
 
 mod n0;

src/arithmetic/add.rs

@@ -0,0 +1,36 @@
+// Copyright 2015-2025 Brian Smith.
+//
+// Permission to use, copy, modify, and/or distribute this software for any
+// purpose with or without fee is hereby granted, provided that the above
+// copyright notice and this permission notice appear in all copies.
+//
+// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES
+// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY
+// SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
+// OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
+// CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+
+use crate::{c, error::LenMismatchError, limb::*, polyfill::AliasingSlices as _};
+use core::num::NonZeroUsize;
+
+/// Equivalent to `r = if a < m { a } else { a - m };`
+#[inline]
+pub fn limbs_reduce_once(r: &mut [Limb], a: &[Limb], m: &[Limb]) -> Result<(), LenMismatchError> {
+    let underflow = limbs_sub(r, a, m)?;
+    limbs_cmov(r, a, underflow)
+}
+
+// `r = a - b`, returning true on underflow, false otherwise.
+fn limbs_sub(r: &mut [Limb], a: &[Limb], b: &[Limb]) -> Result<LimbMask, LenMismatchError> {
+    prefixed_extern! {
+        // `r`, 'a', and/or `b` may alias.
+        fn LIMBS_sub(r: *mut Limb, a: *const Limb, b: *const Limb, num_limbs: c::NonZero_size_t)
+            -> LimbMask;
+    }
+    let num_limbs = NonZeroUsize::new(r.len()).ok_or_else(|| LenMismatchError::new(r.len()))?;
+    (r, a, b).with_pointers(num_limbs.into(), |r, a, b| unsafe {
+        LIMBS_sub(r, a, b, num_limbs)
+    })
+}

src/arithmetic/bigint.rs

@@ -42,7 +42,7 @@ pub(crate) use self::{
     modulusvalue::OwnedModulusValue,
     private_exponent::PrivateExponent,
 };
-use super::{montgomery::*, LimbSliceError, MAX_LIMBS};
+use super::{add::*, montgomery::*, LimbSliceError, MAX_LIMBS};
 use crate::{
     bits::BitLength,
     c,
@@ -172,7 +172,8 @@ pub fn elem_reduced_once<A, M>(
     assert_eq!(m.len_bits(), other_modulus_len_bits);
 
     let mut r = a.limbs.clone();
-    limb::limbs_reduce_once_constant_time(&mut r, m.limbs());
+    limbs_reduce_once(&mut r, &a.limbs, m.limbs())
+        .unwrap_or_else(unwrap_impossible_len_mismatch_error);
     Elem {
         limbs: BoxedLimbs::new_unchecked(r.into_limbs()),
         encoding: PhantomData,

src/ec/suite_b/ops.rs

@@ -14,7 +14,7 @@
 
 use crate::{
     arithmetic::limbs_from_hex,
-    arithmetic::montgomery::*,
+    arithmetic::{add::*, montgomery::*},
     constant_time::LeakyWord,
     cpu,
     error::{self, LenMismatchError},
@@ -490,10 +490,15 @@ fn twin_mul_inefficient(
 
 // This assumes n < q < 2*n.
 impl Modulus<N> {
-    pub fn elem_reduced_to_scalar(&self, elem: &Elem<Unencoded>) -> Scalar<Unencoded> {
+    pub fn elem_reduced_to_scalar(&self, a: &Elem<Unencoded>) -> Scalar<Unencoded> {
         let num_limbs = self.num_limbs.into();
-        let mut r_limbs = elem.limbs;
-        limbs_reduce_once_constant_time(&mut r_limbs[..num_limbs], &self.limbs[..num_limbs]);
+        let mut r_limbs = a.limbs;
+        limbs_reduce_once(
+            &mut r_limbs[..num_limbs],
+            &a.limbs[..num_limbs],
+            &self.limbs[..num_limbs],
+        )
+        .unwrap_or_else(unwrap_impossible_len_mismatch_error);
         Scalar {
             limbs: r_limbs,
             m: PhantomData,
@@ -571,13 +576,12 @@ pub(super) fn scalar_parse_big_endian_partially_reduced_variable_consttime(
     bytes: untrusted::Input,
 ) -> Result<Scalar, error::Unspecified> {
     let num_limbs = n.num_limbs.into();
+    let mut unreduced = [0; elem::NumLimbs::MAX];
+    let unreduced = &mut unreduced[..num_limbs];
+    parse_big_endian_and_pad_consttime(bytes, unreduced)?;
     let mut r = Scalar::zero();
-    {
-        let r = &mut r.limbs[..num_limbs];
-        parse_big_endian_and_pad_consttime(bytes, r)?;
-        limbs_reduce_once_constant_time(r, &n.limbs[..num_limbs]);
-    }
-
+    limbs_reduce_once(&mut r.limbs[..num_limbs], unreduced, &n.limbs[..num_limbs])
+        .map_err(error::erase::<LenMismatchError>)?;
     Ok(r)
 }
 

src/limb.rs

@@ -21,7 +21,7 @@
 use crate::{
     c, constant_time,
     error::{self, LenMismatchError},
-    polyfill::{slice, usize_from_u32, ArrayFlatMap},
+    polyfill::{slice, usize_from_u32, AliasingSlices, ArrayFlatMap},
 };
 use core::num::NonZeroUsize;
 
@@ -154,16 +154,6 @@ pub fn limbs_minimal_bits(a: &[Limb]) -> bits::BitLength {
     bits::BitLength::from_bits(0)
 }
 
-/// Equivalent to `if (r >= m) { r -= m; }`
-#[inline]
-pub fn limbs_reduce_once_constant_time(r: &mut [Limb], m: &[Limb]) {
-    prefixed_extern! {
-        fn LIMBS_reduce_once(r: *mut Limb, m: *const Limb, num_limbs: c::size_t);
-    }
-    assert_eq!(r.len(), m.len());
-    unsafe { LIMBS_reduce_once(r.as_mut_ptr(), m.as_ptr(), m.len()) };
-}
-
 #[derive(Clone, Copy, PartialEq)]
 pub enum AllowZero {
     No,
@@ -376,6 +366,25 @@ pub(crate) fn limbs_negative_odd(r: &mut [Limb], a: &[Limb]) {
     r[0] |= 1;
 }
 
+// `if cond { r = a; }`
+pub fn limbs_cmov(r: &mut [Limb], a: &[Limb], cond: LimbMask) -> Result<(), LenMismatchError> {
+    prefixed_extern! {
+        // r, a, and/or b may alias.
+        fn LIMBS_select(
+            r: *mut Limb,
+            a: *const Limb,
+            b: *const Limb,
+            num_limbs: c::NonZero_size_t,
+            cond: LimbMask);
+    }
+    let len = r.len();
+    (r, a).with_pointers(len, |r, a, b| {
+        if let Some(num_limbs) = NonZeroUsize::new(len) {
+            unsafe { LIMBS_select(r, b, a, num_limbs, cond) }
+        }
+    })
+}
+
 #[cfg(any(test, feature = "alloc"))]
 prefixed_extern! {
     fn LIMB_shr(a: Limb, shift: c::size_t) -> Limb;