diff --git a/src/Crypto/RsaKeypair.php b/src/Crypto/RsaKeypair.php
index cab7f6b..9ec1f47 100644
--- a/src/Crypto/RsaKeypair.php
+++ b/src/Crypto/RsaKeypair.php
@@ -1,6 +1,7 @@
 <?php
 namespace ActivityPub\Crypto;
 
+use BadMethodCallException;
 use phpseclib\Crypt\RSA;
 
 class RsaKeypair
@@ -46,7 +47,7 @@ class RsaKeypair
      */
     public function sign( $data )
     {
-        if ( ! $this->privateKey ) {
+        if ( empty( $this->privateKey ) ) {
             throw new BadMethodCallException(
                 'Unable to sign data without a private key'
             );
@@ -95,7 +96,7 @@ class RsaKeypair
      */
     public function fromPublicKey( string $publicKey )
     {
-        return new RsaKeypair( $publicKey, null );
+        return new RsaKeypair( $publicKey, '' );
     }
 }
 ?>
diff --git a/test/RsaKeypairTest.php b/test/RsaKeypairTest.php
index fe6ed9c..568db9b 100644
--- a/test/RsaKeypairTest.php
+++ b/test/RsaKeypairTest.php
@@ -1,8 +1,10 @@
 <?php
 namespace ActivityPub\Test;
 
+use BadMethodCallException;
 use ActivityPub\Crypto\RsaKeypair;
 use PHPUnit\Framework\TestCase;
+use PHPUnit\Framework\Error\Error;
 
 class RsaKeypairTest extends TestCase
 {
@@ -12,5 +14,74 @@ class RsaKeypairTest extends TestCase
         $this->assertStringStartsWith( '-----BEGIN PUBLIC KEY-----', $keypair->getPublicKey() );
         $this->assertStringEndsWith( '-----END PUBLIC KEY-----', $keypair->getPublicKey() );
     }
+
+    public function testItSignsAndValidatesSignatures()
+    {
+        $keypair = RsaKeypair::generate();
+        $data = 'This is some data';
+        $signature = $keypair->sign( $data );
+        $this->assertInternalType( 'string', $signature );
+        $this->assertNotEmpty( $signature );
+        $verified = $keypair->verify( $data, $signature );
+        $this->assertTrue( $verified );
+    }
+
+    public function testItGivesErrorValidatingInvalidSignature()
+    {
+        $keypair = RsaKeypair::generate();
+        $data = 'This is some data';
+        $signature = 'not a real signature';
+        $this->expectException( Error::class );
+        $verified = $keypair->verify( $data, $signature );
+    }
+
+    public function testItReturnsNotVerifiedForValidButWrongSignature()
+    {
+        $keypairOne = RsaKeypair::generate();
+        $data = 'This is some data';
+        $signature = $keypairOne->sign( $data );
+        $keypairTwo = RsaKeypair::generate();
+        $verified = $keypairTwo->verify( $data, $signature );
+        $this->assertFalse( $verified );
+    }
+
+    public function testItCreatesValidPublicKeyOnly()
+    {
+        $fullKeypair = RsaKeypair::generate();
+        $publicKeyOnly = RsaKeypair::fromPublicKey( $fullKeypair->getPublicKey() );
+        $data = 'This is some data';
+        $signature = $fullKeypair->sign( $data );
+        $verified = $publicKeyOnly->verify( $data, $signature );
+        $this->assertTrue( $verified );
+    }
+
+    public function testItCannotSignWithPublicKeyOnly()
+    {
+        $fullKeypair = RsaKeypair::generate();
+        $publicKeyOnly = RsaKeypair::fromPublicKey( $fullKeypair->getPublicKey() );
+        $data = 'This is some data';
+        $this->expectException( BadMethodCallException::class );
+        $this->expectExceptionMessage( 'Unable to sign data without a private key' );
+        $signature = $publicKeyOnly->sign( $data );
+    }
+
+    public function testItSignsAndVerifiesEmptyData()
+    {
+        $keypair = RsaKeypair::generate();
+        $data = '';
+        $signature = $keypair->sign( $data );
+        $verified = $keypair->verify( $data, $signature );
+        $this->assertTrue( $verified );
+    }
+
+    public function testItHandlesInvalidPublicKeyOnly()
+    {
+        $fullKeypair = RsaKeypair::generate();
+        $publicKeyOnly = RsaKeypair::fromPublicKey( 'not a real public key' );
+        $data = 'This is some data';
+        $signature = $fullKeypair->sign( $data );
+        $verified = $publicKeyOnly->verify( $data, $signature );
+        $this->assertFalse( $verified );
+    }
 }
 ?>