crypto/rsa: fix keys with p < q

Updates #70643

Change-Id: I4aee8373dbddf774564902b3957c6eba11d15fc9
Reviewed-on: https://go-review.googlesource.com/c/go/+/632955
Reviewed-by: Roland Shoemaker <roland@golang.org>
Auto-Submit: Filippo Valsorda <filippo@golang.org>
Reviewed-by: Russ Cox <rsc@golang.org>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>

src/crypto/internal/fips140/rsa/rsa.go

@@ -265,8 +265,12 @@ func checkPrivateKey(priv *PrivateKey) error {
 	}
 
 	// Check that qInv * q ≡ 1 mod p.
-	one := q.Nat().Mul(priv.qInv, p)
-	if one.IsOne() != 1 {
+	qP, err := bigmod.NewNat().SetOverflowingBytes(q.Nat().Bytes(q), p)
+	if err != nil {
+		// q >= 2^⌈log2(p)⌉
+		qP = bigmod.NewNat().Mod(q.Nat(), p)
+	}
+	if qP.Mul(priv.qInv, p).IsOne() != 1 {
 		return errors.New("crypto/rsa: invalid CRT coefficient")
 	}
 

src/crypto/rsa/rsa_test.go

@@ -8,6 +8,7 @@ import (
 	"bufio"
 	"bytes"
 	"crypto"
+	"crypto/internal/boring"
 	"crypto/internal/cryptotest"
 	"crypto/internal/fips140"
 	"crypto/rand"
@@ -352,6 +353,30 @@ func testEverything(t *testing.T, priv *PrivateKey) {
 	if err == nil {
 		t.Errorf("DecryptPKCS1v15 accepted a long ciphertext")
 	}
+
+	der, err := x509.MarshalPKCS8PrivateKey(priv)
+	if err != nil {
+		t.Errorf("MarshalPKCS8PrivateKey: %v", err)
+	}
+	key, err := x509.ParsePKCS8PrivateKey(der)
+	if err != nil {
+		t.Errorf("ParsePKCS8PrivateKey: %v", err)
+	}
+	if !key.(*PrivateKey).Equal(priv) {
+		t.Errorf("private key mismatch")
+	}
+
+	der, err = x509.MarshalPKIXPublicKey(&priv.PublicKey)
+	if err != nil {
+		t.Errorf("MarshalPKIXPublicKey: %v", err)
+	}
+	pub, err := x509.ParsePKIXPublicKey(der)
+	if err != nil {
+		t.Errorf("ParsePKIXPublicKey: %v", err)
+	}
+	if !pub.(*PublicKey).Equal(&priv.PublicKey) {
+		t.Errorf("public key mismatch")
+	}
 }
 
 func TestKeyTooSmall(t *testing.T) {
@@ -1015,3 +1040,21 @@ var testEncryptOAEPData = []testEncryptOAEPStruct{
 		},
 	},
 }
+
+func TestPSmallerThanQ(t *testing.T) {
+	// This key has a 256-bit P and a 257-bit Q.
+	k := parseKey(testingKey(`-----BEGIN RSA TESTING KEY-----
+MIIBOgIBAAJBAKj34GkxFhD90vcNLYLInFEX6Ppy1tPf9Cnzj4p4WGeKLs1Pt8Qu
+KUpRKfFLfRYC9AIKjbJTWit+CqvjWYzvQwECAwEAAQJAIJLixBy2qpFoS4DSmoEm
+o3qGy0t6z09AIJtH+5OeRV1be+N4cDYJKffGzDa88vQENZiRm0GRq6a+HPGQMd2k
+TQIhAKMSvzIBnni7ot/OSie2TmJLY4SwTQAevXysE2RbFDYdAiEBCUEaRQnMnbp7
+9mxDXDf6AU0cN/RPBjb9qSHDcWZHGzUCIG2Es59z8ugGrDY+pxLQnwfotadxd+Uy
+v/Ow5T0q5gIJAiEAyS4RaI9YG8EWx/2w0T67ZUVAw8eOMB6BIUg0Xcu+3okCIBOs
+/5OiPgoTdSy7bcF9IGpSE8ZgGKzgYQVZeN97YE00
+-----END RSA TESTING KEY-----`))
+	t.Setenv("GODEBUG", "rsa1024min=0")
+	if boring.Enabled {
+		t.Skip("BoringCrypto mode returns the wrong error from SignPSS")
+	}
+	testEverything(t, k)
+}