diff --git a/core/crypto/rsa_common.go b/core/crypto/rsa_common.go
index c7e305439a..2b05eb6a35 100644
--- a/core/crypto/rsa_common.go
+++ b/core/crypto/rsa_common.go
@@ -12,9 +12,12 @@ const WeakRsaKeyEnv = "LIBP2P_ALLOW_WEAK_RSA_KEYS"
 
 var MinRsaKeyBits = 2048
 
+var maxRsaKeyBits = 8192
+
 // ErrRsaKeyTooSmall is returned when trying to generate or parse an RSA key
 // that's smaller than MinRsaKeyBits bits. In test
 var ErrRsaKeyTooSmall error
+var ErrRsaKeyTooBig error = fmt.Errorf("rsa keys must be <= %d bits", maxRsaKeyBits)
 
 func init() {
 	if _, ok := os.LookupEnv(WeakRsaKeyEnv); ok {
diff --git a/core/crypto/rsa_go.go b/core/crypto/rsa_go.go
index bfbd987bee..8981ba6aa6 100644
--- a/core/crypto/rsa_go.go
+++ b/core/crypto/rsa_go.go
@@ -31,6 +31,9 @@ func GenerateRSAKeyPair(bits int, src io.Reader) (PrivKey, PubKey, error) {
 	if bits < MinRsaKeyBits {
 		return nil, nil, ErrRsaKeyTooSmall
 	}
+	if bits > maxRsaKeyBits {
+		return nil, nil, ErrRsaKeyTooBig
+	}
 	priv, err := rsa.GenerateKey(src, bits)
 	if err != nil {
 		return nil, nil, err
@@ -124,6 +127,9 @@ func UnmarshalRsaPrivateKey(b []byte) (key PrivKey, err error) {
 	if sk.N.BitLen() < MinRsaKeyBits {
 		return nil, ErrRsaKeyTooSmall
 	}
+	if sk.N.BitLen() > maxRsaKeyBits {
+		return nil, ErrRsaKeyTooBig
+	}
 	return &RsaPrivateKey{sk: *sk}, nil
 }
 
@@ -141,6 +147,9 @@ func UnmarshalRsaPublicKey(b []byte) (key PubKey, err error) {
 	if pk.N.BitLen() < MinRsaKeyBits {
 		return nil, ErrRsaKeyTooSmall
 	}
+	if pk.N.BitLen() > maxRsaKeyBits {
+		return nil, ErrRsaKeyTooBig
+	}
 
 	return &RsaPublicKey{k: *pk}, nil
 }
diff --git a/core/crypto/rsa_test.go b/core/crypto/rsa_test.go
index 69151b86c9..f4a7971a59 100644
--- a/core/crypto/rsa_test.go
+++ b/core/crypto/rsa_test.go
@@ -68,6 +68,44 @@ func TestRSASmallKey(t *testing.T) {
 	}
 }
 
+func TestRSABigKeyFailsToGenerate(t *testing.T) {
+	_, _, err := GenerateRSAKeyPair(maxRsaKeyBits*2, rand.Reader)
+	if err != ErrRsaKeyTooBig {
+		t.Fatal("should have refused to create too big RSA key")
+	}
+}
+
+func TestRSABigKey(t *testing.T) {
+	// Make the global limit smaller for this test to run faster.
+	// Note we also change the limit below, but this is different
+	origSize := maxRsaKeyBits
+	maxRsaKeyBits = 2048
+	defer func() { maxRsaKeyBits = origSize }() //
+
+	maxRsaKeyBits *= 2
+	badPriv, badPub, err := GenerateRSAKeyPair(maxRsaKeyBits, rand.Reader)
+	if err != nil {
+		t.Fatalf("should have succeeded, got: %s", err)
+	}
+	pubBytes, err := MarshalPublicKey(badPub)
+	if err != nil {
+		t.Fatal(err)
+	}
+	privBytes, err := MarshalPrivateKey(badPriv)
+	if err != nil {
+		t.Fatal(err)
+	}
+	maxRsaKeyBits /= 2
+	_, err = UnmarshalPublicKey(pubBytes)
+	if err != ErrRsaKeyTooBig {
+		t.Fatal("should have refused to unmarshal a too big key")
+	}
+	_, err = UnmarshalPrivateKey(privBytes)
+	if err != ErrRsaKeyTooBig {
+		t.Fatal("should have refused to unmarshal a too big key")
+	}
+}
+
 func TestRSASignZero(t *testing.T) {
 	priv, pub, err := GenerateRSAKeyPair(2048, rand.Reader)
 	if err != nil {