diff --git a/src/Algorithm.php b/src/Algorithm.php
index a3f6dc4..c01571b 100644
--- a/src/Algorithm.php
+++ b/src/Algorithm.php
@@ -18,6 +18,9 @@ abstract class Algorithm
             case 'hmac-sha256':
                 return new HmacAlgorithm('sha256');
                 break;
+            case 'rsa-sha512':
+                return new RsaAlgorithm('sha512');
+                break;
             default:
                 throw new Exception("No algorithm named '$name'");
                 break;
diff --git a/src/RsaAlgorithm.php b/src/RsaAlgorithm.php
new file mode 100644
index 0000000..d9a5b8f
--- /dev/null
+++ b/src/RsaAlgorithm.php
@@ -0,0 +1,64 @@
+<?php
+
+namespace HttpSignatures;
+
+use phpseclib3\Crypt\PublicKeyLoader;
+use phpseclib3\Crypt\RSA;
+
+class RsaAlgorithm implements AlgorithmInterface
+{
+    /** @var string */
+    private $digestName;
+
+    /**
+     * @param string $digestName
+     */
+    public function __construct($digestName)
+    {
+        $this->digestName = $digestName;
+    }
+
+    /**
+     * @return string
+     */
+    public function name()
+    {
+        return sprintf('rsa-%s', $this->digestName);
+    }
+
+    /**
+     * @param string $key
+     * @param string $data
+     *
+     * @return string
+     */
+    public function sign($signingKey, $data)
+    {
+        $rsa = PublicKeyLoader::load($signingKey)
+            ->withHash($this->digestName)
+            ->withPadding(RSA::SIGNATURE_PKCS1);
+        $signature = $rsa->sign($data);
+
+        return $signature;
+    }
+
+    public function verify($message, $signature, $verifyingKey)
+    {
+        $rsa = PublicKeyLoader::load($verifyingKey)
+            ->withHash($this->digestName)
+            ->withPadding(RSA::SIGNATURE_PKCS1);
+        try {
+            $valid = $rsa->verify($message, base64_decode($signature));
+
+            return $valid;
+        } catch (\Exception $e) {
+            if ('Invalid signature' != $e->getMessage()) {
+                // Unhandled error state
+                throw $e;
+            } else {
+                // Tolerate malformed signature
+                return false;
+            }
+        }
+    }
+}