diff --git a/CHANGELOG.md b/CHANGELOG.md
index 817e41fb7..c3e9c2196 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,7 +8,12 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Added
 - Implement `Zeroize` for `EncodedUint` ([#1342])
 
+### Fixed
+- `u32` overflow of the safegcd iteration count at precisions of 93558 bits and above, which made
+  `invert_mod`/`invert_odd_mod` spuriously report no inverse and `gcd` return wrong results ([#1346])
+
 [#1342]: https://github.com/RustCrypto/crypto-bigint/pull/1342
+[#1346]: https://github.com/RustCrypto/crypto-bigint/pull/1346
 
 ## 0.7.5 (2026-06-22)
 ### Added
diff --git a/src/modular/safegcd.rs b/src/modular/safegcd.rs
index f7b23e175..b279a40f1 100644
--- a/src/modular/safegcd.rs
+++ b/src/modular/safegcd.rs
@@ -343,12 +343,23 @@ const fn shr_in_place_wide<const L: usize, const H: usize>(
 
 /// Calculate the maximum number of iterations required according to
 /// safegcd-bounds: <https://github.com/sipa/safegcd-bounds>
+///
+/// Computed in `u64` because `45907 * bits + 30179` exceeds `u32::MAX` once `bits >= 93558`.
+/// The count itself (about `2.3 * bits`) only exceeds `u32::MAX` for `bits` above `1864517463`,
+/// which panics rather than wrapping.
 // NOTE: the division is non-constant-time, but this is used to compute the number of iterations we
 // perform which is leaked in timing information
 #[inline]
 #[allow(clippy::integer_division_remainder_used, reason = "public parameter")]
+#[allow(clippy::cast_lossless, reason = "`const fn`")]
+#[allow(clippy::cast_possible_truncation, reason = "checked by the assertion")]
 const fn iterations(bits: u32) -> u32 {
-    (45907 * bits + 30179) / 19929
+    let iterations = (45907 * bits as u64 + 30179) / 19929;
+    assert!(
+        iterations <= u32::MAX as u64,
+        "precision too large for safegcd"
+    );
+    iterations as u32
 }
 
 /// A `Uint` which carries a separate sign in order to maintain the same range.
@@ -530,7 +541,7 @@ impl<const LIMBS: usize> PartialEq for SignedInt<LIMBS> {
 
 #[cfg(test)]
 mod tests {
-    use super::SafeGcdInverter;
+    use super::{SafeGcdInverter, iterations};
     use crate::{U128, U256, modular::safegcd::shr_in_place_wide};
 
     #[test]
@@ -568,4 +579,23 @@ mod tests {
         );
         assert_eq!(b_hi, U128::from_u128(0x111111112222222));
     }
+
+    #[test]
+    fn iterations_do_not_overflow() {
+        // Values from the `safegcd-bounds` formula evaluated in arbitrary precision.
+        assert_eq!(iterations(256), 591);
+        assert_eq!(iterations(93_504), 215_390);
+        // `45907 * bits + 30179` first exceeds `u32::MAX` here.
+        assert_eq!(iterations(93_558), 215_514);
+        assert_eq!(iterations(93_568), 215_537);
+        assert_eq!(iterations(98_304), 226_447);
+        // The largest precision whose count still fits in `u32`.
+        assert_eq!(iterations(1_864_517_463), 4_294_967_294);
+    }
+
+    #[test]
+    #[should_panic(expected = "precision too large for safegcd")]
+    fn iterations_panics_beyond_u32() {
+        iterations(1_864_517_464);
+    }
 }
diff --git a/src/modular/safegcd/boxed.rs b/src/modular/safegcd/boxed.rs
index 09f4695a5..35d730abe 100644
--- a/src/modular/safegcd/boxed.rs
+++ b/src/modular/safegcd/boxed.rs
@@ -441,8 +441,62 @@ impl fmt::Debug for SignedBoxedInt {
 
 #[cfg(test)]
 mod tests {
-    use super::BoxedSafeGcdInverter;
-    use crate::BoxedUint;
+    use super::{BoxedSafeGcdInverter, gcd_odd, invert_odd_mod};
+    use crate::{BoxedUint, Odd, Resize};
+    use num_bigint::BigUint;
+    use num_integer::Integer;
+
+    /// The smallest precision at which `45907 * bits + 30179` no longer fits in `u32`.
+    const LARGE_BITS: u32 = 93_568;
+
+    /// A deterministic, odd, full-width `BoxedUint` of `bits` bits; different seeds give
+    /// unrelated values.
+    fn large_odd(bits: u32, seed: u32) -> BoxedUint {
+        let mut bytes: alloc::vec::Vec<u8> = (0..bits >> 3)
+            .map(|i| {
+                let h = (i ^ seed.wrapping_mul(0x9E37_79B9)).wrapping_mul(0x85EB_CA6B);
+                let h = (h ^ (h >> 13)).wrapping_mul(0xC2B2_AE35);
+                (h ^ (h >> 16)).to_le_bytes()[0]
+            })
+            .collect();
+        bytes[0] |= 0x80;
+        *bytes.last_mut().unwrap() |= 1;
+        BoxedUint::from_be_slice(&bytes, bits).unwrap()
+    }
+
+    fn to_big(x: &BoxedUint) -> BigUint {
+        BigUint::from_bytes_be(&x.to_be_bytes())
+    }
+
+    #[test]
+    fn invert_odd_mod_large_precision() {
+        let m = large_odd(LARGE_BITS, 1);
+        let a = BoxedUint::from(65537u32).resize(LARGE_BITS);
+        assert_eq!(to_big(&a).gcd(&to_big(&m)), BigUint::from(1u32));
+        let m = Odd::new(m).unwrap();
+
+        for inv in [
+            invert_odd_mod::<false>(&a, &m).unwrap(),
+            invert_odd_mod::<true>(&a, &m).unwrap(),
+        ] {
+            assert_eq!(
+                (to_big(&a) * to_big(&inv)) % to_big(m.as_ref()),
+                BigUint::from(1u32)
+            );
+        }
+    }
+
+    #[test]
+    fn gcd_odd_large_precision() {
+        // Two unrelated full-width values: the reduction needs the whole iteration budget,
+        // unlike a pair with a large common factor and small cofactors.
+        let f = Odd::new(large_odd(LARGE_BITS, 2)).unwrap();
+        let g = large_odd(LARGE_BITS, 4);
+        let expected = to_big(f.as_ref()).gcd(&to_big(&g));
+
+        assert_eq!(to_big(gcd_odd::<false>(&f, &g).as_ref()), expected);
+        assert_eq!(to_big(gcd_odd::<true>(&f, &g).as_ref()), expected);
+    }
 
     #[test]
     fn invert() {
diff --git a/src/uint/boxed/invert_mod.rs b/src/uint/boxed/invert_mod.rs
index db56af268..537c5eafd 100644
--- a/src/uint/boxed/invert_mod.rs
+++ b/src/uint/boxed/invert_mod.rs
@@ -184,10 +184,40 @@ impl InvertMod for BoxedUint {
 
 #[cfg(test)]
 mod tests {
-    use crate::{Limb, Odd, Resize, U256};
+    use crate::{Limb, NonZero, Odd, Resize, U256};
 
     use super::BoxedUint;
     use hex_literal::hex;
+    use num_bigint::BigUint;
+    use num_integer::Integer;
+
+    /// `invert_mod` at a precision where the safegcd iteration count overflowed `u32`
+    /// (`45907 * bits + 30179 > u32::MAX` from 93558 bits), with an even modulus so that
+    /// both the odd-modulus and the `2^k` paths are exercised.
+    #[test]
+    fn invert_mod_large_precision_even_modulus() {
+        const BITS: u32 = 93_568;
+        let mut bytes: alloc::vec::Vec<u8> = (0..BITS >> 3)
+            .map(|i| {
+                let h = (i ^ 0xDA94_2042).wrapping_mul(0x85EB_CA6B);
+                let h = (h ^ (h >> 13)).wrapping_mul(0xC2B2_AE35);
+                (h ^ (h >> 16)).to_le_bytes()[0]
+            })
+            .collect();
+        bytes[0] |= 0x80;
+        *bytes.last_mut().unwrap() &= !1;
+        let m = BoxedUint::from_be_slice(&bytes, BITS).unwrap();
+        let a = BoxedUint::from(65537u32).resize(BITS);
+
+        let to_big = |x: &BoxedUint| BigUint::from_bytes_be(&x.to_be_bytes());
+        assert_eq!(to_big(&a).gcd(&to_big(&m)), BigUint::from(1u32));
+
+        let inv = a.invert_mod(&NonZero::new(m.clone()).unwrap()).unwrap();
+        assert_eq!(
+            (to_big(&a) * to_big(&inv)) % to_big(&m),
+            BigUint::from(1u32)
+        );
+    }
 
     #[test]
     fn invert_mod2k() {