diff --git a/src/algorithms/rsa.rs b/src/algorithms/rsa.rs
index 6473f378..50925e70 100644
--- a/src/algorithms/rsa.rs
+++ b/src/algorithms/rsa.rs
@@ -245,6 +245,38 @@ pub fn recover_primes(n: &BigUint, e: &BigUint, d: &BigUint) -> Result<(BigUint,
     Ok((p, q))
 }
 
+/// Compute the modulus of a key from its primes.
+pub(crate) fn compute_modulus(primes: &[BigUint]) -> BigUint {
+    let mut n = BigUint::one();
+
+    for prime in primes {
+        n *= prime;
+    }
+
+    n
+}
+
+/// Compute the private exponent from its primes and public exponent
+pub(crate) fn compute_private_exponent(primes: &[BigUint], exp: &BigUint) -> Result<BigUint> {
+    let mut totient = BigUint::one();
+
+    for prime in primes {
+        totient *= prime - BigUint::one();
+    }
+
+    std::println!("exp {:?}", exp.to_bytes_be());
+    std::println!("totient {:?}", totient.to_bytes_be());
+    if let Some(d) = exp.mod_inverse(totient) {
+        std::println!("d {:?}", d);
+        std::println!("d {:?}", d.to_bytes_be());
+        std::println!("d {:?}", d.to_biguint().unwrap().to_bytes_be());
+        Ok(d.to_biguint().unwrap())
+    } else {
+        // `exp` evenly divides `totient`
+        Err(Error::InvalidPrime)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use num_traits::FromPrimitive;
diff --git a/src/key.rs b/src/key.rs
index 9589e1d3..12de6343 100644
--- a/src/key.rs
+++ b/src/key.rs
@@ -11,7 +11,7 @@ use serde::{Deserialize, Serialize};
 use zeroize::{Zeroize, ZeroizeOnDrop};
 
 use crate::algorithms::generate::generate_multi_prime_key_with_exp;
-use crate::algorithms::rsa::recover_primes;
+use crate::algorithms::rsa::{compute_modulus, compute_private_exponent, recover_primes};
 
 use crate::dummy_rng::DummyRng;
 use crate::errors::{Error, Result};
@@ -279,6 +279,29 @@ impl RsaPrivateKey {
         Ok(k)
     }
 
+    /// Constructs an RSA key pair from its primes.
+    ///
+    /// This will rebuild the private exponent and the modulus.
+    pub fn from_primes(primes: Vec<BigUint>, public_exponent: BigUint) -> Result<RsaPrivateKey> {
+        if primes.len() < 2 {
+            return Err(Error::NprimesTooSmall);
+        }
+
+        // Makes sure that primes is pairwise unequal.
+        for (i, prime1) in primes.iter().enumerate() {
+            for prime2 in primes.iter().take(i) {
+                if prime1 == prime2 {
+                    return Err(Error::InvalidPrime);
+                }
+            }
+        }
+
+        let n = compute_modulus(&primes);
+        let d = compute_private_exponent(&primes, &public_exponent)?;
+
+        Self::from_components(n, public_exponent, d, primes)
+    }
+
     /// Get the public key from the private key, cloning `n` and `e`.
     ///
     /// Generally this is not needed since `RsaPrivateKey` implements the `PublicKey` trait,
@@ -753,4 +776,46 @@ mod tests {
             Error::ModulusTooLarge
         );
     }
+
+    #[test]
+    fn build_key_from_primes() {
+        let primes = vec![
+            BigUint::from_bytes_be(&hex!("00d3f729b732696acc814a007b27bc786c11c3ebee55b7935d4bde4dc50032b496a082f0ccc37472c2f8c6344cbd570808f381c80d0b01107069368ad32a2e0b0ca4174b17b15f21093f917158cb46a96c113fa421ca73f3c6a5e5e93c68ad7255f59c792bbc40c135fb2dfe488bdf266aba6c0c38733f07a50d14e0557cee0c51")),
+            BigUint::from_bytes_be(&hex!("00c8936e1179ef258bb3cea300deae7da9660cff7f6f0a1cceea74327921a1bf35f7548e3274f1536d0acc29b54b2f6048c412ce5dbf668735ab0eed1808f6678a108d7f0b6445b3a69cb897a08e3190388c6c559a72f12d74e62a283532d2ea20d0eb98e13c5add9067879638868bd6badea24f93d02bc13b8edcf29b720e6381")),
+        ];
+
+        let exp = BigUint::from_u64(RsaPrivateKey::EXP).expect("invalid static exponent");
+        let key =
+            RsaPrivateKey::from_primes(primes, exp).expect("failed to import key from primes");
+
+        assert_eq!(key.n().to_bytes_be(), &hex!("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"));
+
+        println!("dp: {:?}", key.dp().unwrap().to_bytes_be());
+        println!("dq: {:?}", key.dq().unwrap().to_bytes_be());
+        println!("qinv: {:?}", key.qinv().unwrap().to_bytes_be());
+        assert_eq!(
+            key.d().to_bytes_be(),
+            &hex!(
+                "
+            1a07a707bbcb5956b4a292ef030432
+            0b6a2d1569e45b3cd1f3ca5198189a
+            dfaa03151d77feb5c026d594533911
+            10c2aef10f633d4c1d6d91953445a2
+            286a76c5e20277b8ab106526f06390
+            eaaad4e3dff2ccf8a561808b4df97a
+            91448cb3a34ed7178b865346a22654
+            f7bc13fea2a81670e3aabf46f7db52
+            b7242986a1fc929ad6879fbce52135
+            32f0b5021bcdcdabd25fe941fbe7fa
+            69587ad40a5febecc896aa1d5265b6
+            2eba328789a3a37a5d96108049e063
+            ea68165cdacf8b0da578006fc4acfc
+            de38b878d901a288ec7ccff7353cd5
+            008b391dacd4215d64011de2ca9fca
+            23c88979cb86ee52518cb865436105
+            ffd1d5f6826bc3d48d9ec0cdafe301
+"
+            )
+        );
+    }
 }