Write public RSA key to disk

I think it's useful even though we don't read it.

common/src/main/java/dev/openrs2/common/crypto/RsaKeyProvider.kt

@@ -7,16 +7,18 @@ import javax.inject.Provider
 
 class RsaKeyProvider : Provider<RSAPrivateCrtKeyParameters> {
     override fun get(): RSAPrivateCrtKeyParameters {
-        return if (Files.exists(PATH)) {
-            Rsa.readPrivateKey(PATH)
+        return if (Files.exists(PRIVATE_PATH)) {
+            Rsa.readPrivateKey(PRIVATE_PATH)
         } else {
-            val (_, private) = Rsa.generateKeyPair()
-            Rsa.writePrivateKey(PATH, private)
+            val (public, private) = Rsa.generateKeyPair()
+            Rsa.writePublicKey(PUBLIC_PATH, public)
+            Rsa.writePrivateKey(PRIVATE_PATH, private)
             private
         }
     }
 
     companion object {
-        private val PATH = Paths.get("conf/private.key")
+        private val PUBLIC_PATH = Paths.get("conf/public.key")
+        private val PRIVATE_PATH = Paths.get("conf/private.key")
     }
 }

conf/.gitignore

@@ -1 +1,2 @@
 /private.key
+/public.key