Adds RsaPrivateKey::from_primes and RsaPrivateKey::from_p_q methods (#386)

This is used on Yubico HSM for import/export under wrap as well as when
importing a key unsealed.

src/algorithms/generate.rs

@@ -1,14 +1,16 @@
 //! Generate prime components for the RSA Private Key
 
 use alloc::vec::Vec;
-use num_bigint::traits::ModInverse;
 use num_bigint::{BigUint, RandPrime};
 #[allow(unused_imports)]
 use num_traits::Float;
-use num_traits::{One, Zero};
+use num_traits::Zero;
 use rand_core::CryptoRngCore;
 
-use crate::errors::{Error, Result};
+use crate::{
+    algorithms::rsa::{compute_modulus, compute_private_exponent_euler_totient},
+    errors::{Error, Result},
+};
 
 pub struct RsaPrivateKeyComponents {
     pub n: BigUint,
@@ -89,13 +91,7 @@ pub(crate) fn generate_multi_prime_key_with_exp<R: CryptoRngCore + ?Sized>(
             }
         }
 
-        let mut n = BigUint::one();
+        let n = compute_modulus(&primes);
-        let mut totient = BigUint::one();
-
-        for prime in &primes {
-            n *= prime;
-            totient *= prime - BigUint::one();
-        }
 
         if n.bits() != bit_size {
             // This should never happen for nprimes == 2 because
@@ -104,11 +100,9 @@ pub(crate) fn generate_multi_prime_key_with_exp<R: CryptoRngCore + ?Sized>(
             continue 'next;
         }
 
-        // NOTE: `mod_inverse` checks if `exp` evenly divides `totient` and returns `None` if so.
+        if let Ok(d) = compute_private_exponent_euler_totient(&primes, exp) {
-        // This ensures that `exp` is not a factor of any `(prime - 1)`.
-        if let Some(d) = exp.mod_inverse(totient) {
             n_final = n;
-            d_final = d.to_biguint().unwrap();
+            d_final = d;
             break;
         }
     }

src/algorithms/rsa.rs

@@ -245,6 +245,64 @@ 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 {
+    primes.iter().product()
+}
+
+/// Compute the private exponent from its primes (p and q) and public exponent
+/// This uses Euler's totient function
+#[inline]
+pub(crate) fn compute_private_exponent_euler_totient(
+    primes: &[BigUint],
+    exp: &BigUint,
+) -> Result<BigUint> {
+    if primes.len() < 2 {
+        return Err(Error::InvalidPrime);
+    }
+
+    let mut totient = BigUint::one();
+
+    for prime in primes {
+        totient *= prime - BigUint::one();
+    }
+
+    // NOTE: `mod_inverse` checks if `exp` evenly divides `totient` and returns `None` if so.
+    // This ensures that `exp` is not a factor of any `(prime - 1)`.
+    if let Some(d) = exp.mod_inverse(totient) {
+        Ok(d.to_biguint().unwrap())
+    } else {
+        // `exp` evenly divides `totient`
+        Err(Error::InvalidPrime)
+    }
+}
+
+/// Compute the private exponent from its primes (p and q) and public exponent
+///
+/// This is using the method defined by
+/// [NIST 800-56B Section 6.2.1](https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Br2.pdf#page=47).
+/// (Carmichael function)
+///
+/// FIPS 186-4 **requires** the private exponent to be less than λ(n), which would
+/// make Euler's totiem unreliable.
+#[inline]
+pub(crate) fn compute_private_exponent_carmicheal(
+    p: &BigUint,
+    q: &BigUint,
+    exp: &BigUint,
+) -> Result<BigUint> {
+    let p1 = p - BigUint::one();
+    let q1 = q - BigUint::one();
+
+    let lcm = p1.lcm(&q1);
+    if let Some(d) = exp.mod_inverse(lcm) {
+        Ok(d.to_biguint().unwrap())
+    } else {
+        // `exp` evenly divides `lcm`
+        Err(Error::InvalidPrime)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use num_traits::FromPrimitive;

src/key.rs

@@ -11,7 +11,10 @@ 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_carmicheal, compute_private_exponent_euler_totient,
+    recover_primes,
+};
 
 use crate::dummy_rng::DummyRng;
 use crate::errors::{Error, Result};
@@ -279,6 +282,46 @@ impl RsaPrivateKey {
         Ok(k)
     }
 
+    /// Constructs an RSA key pair from its two primes p and q.
+    ///
+    /// This will rebuild the private exponent and the modulus.
+    ///
+    /// Private exponent will be rebuilt using the method defined in
+    /// [NIST 800-56B Section 6.2.1](https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-56Br2.pdf#page=47).
+    pub fn from_p_q(p: BigUint, q: BigUint, public_exponent: BigUint) -> Result<RsaPrivateKey> {
+        if p == q {
+            return Err(Error::InvalidPrime);
+        }
+
+        let n = compute_modulus(&[p.clone(), q.clone()]);
+        let d = compute_private_exponent_carmicheal(&p, &q, &public_exponent)?;
+
+        Self::from_components(n, public_exponent, d, vec![p, q])
+    }
+
+    /// 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_euler_totient(&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,
@@ -495,6 +538,7 @@ mod tests {
 
     use hex_literal::hex;
     use num_traits::{FromPrimitive, ToPrimitive};
+    use pkcs8::DecodePrivateKey;
     use rand_chacha::{rand_core::SeedableRng, ChaCha8Rng};
 
     #[test]
@@ -753,4 +797,47 @@ mod tests {
             Error::ModulusTooLarge
         );
     }
+
+    #[test]
+    fn build_key_from_primes() {
+        const RSA_2048_PRIV_DER: &[u8] = include_bytes!("../tests/examples/pkcs8/rsa2048-priv.der");
+        let ref_key = RsaPrivateKey::from_pkcs8_der(RSA_2048_PRIV_DER).unwrap();
+        assert_eq!(ref_key.validate(), Ok(()));
+
+        let primes = ref_key.primes().to_vec();
+
+        let exp = ref_key.e().clone();
+        let key =
+            RsaPrivateKey::from_primes(primes, exp).expect("failed to import key from primes");
+        assert_eq!(key.validate(), Ok(()));
+
+        assert_eq!(key.n(), ref_key.n());
+
+        assert_eq!(key.dp(), ref_key.dp());
+        assert_eq!(key.dq(), ref_key.dq());
+
+        assert_eq!(key.d(), ref_key.d());
+    }
+
+    #[test]
+    fn build_key_from_p_q() {
+        const RSA_2048_SP800_PRIV_DER: &[u8] =
+            include_bytes!("../tests/examples/pkcs8/rsa2048-sp800-56b-priv.der");
+        let ref_key = RsaPrivateKey::from_pkcs8_der(RSA_2048_SP800_PRIV_DER).unwrap();
+        assert_eq!(ref_key.validate(), Ok(()));
+
+        let primes = ref_key.primes().to_vec();
+        let exp = ref_key.e().clone();
+
+        let key = RsaPrivateKey::from_p_q(primes[0].clone(), primes[1].clone(), exp)
+            .expect("failed to import key from primes");
+        assert_eq!(key.validate(), Ok(()));
+
+        assert_eq!(key.n(), ref_key.n());
+
+        assert_eq!(key.dp(), ref_key.dp());
+        assert_eq!(key.dq(), ref_key.dq());
+
+        assert_eq!(key.d(), ref_key.d());
+    }
 }