签名时“此签名算法的密钥太短”

我正在InvalidKeyException尝试初始化一个Signature对象：

java.security.InvalidKeyException: Key is too short for this signature algorithm

代码：

String pkcs8 = 'MIIBVAIBADANBgkqhkiG9w0BAQEFAASCAT4wggE6AgEAAkEA34N+ujANvgJ0vc696v2T/L3QUxwNf5VEf9sO/NESOBx9ZNhTHKtmY3vdmW1LVmT07vxVlaMgRhxG90h/HKCD7wIDAQABAkB2kN2PzN/tVIYzDdGnLz7qipJRFAeBD2CX5k9sA0gD5PLtpV0IVxYvSw7rUAOR/GywklF+QWKYwfCqkhMkEJMRAiEA+8fQcNEajDWB/R2VgPPWA8indGQdZT8m9lvo0xYD97kCIQDjQmkd82+UPlRB+g7GwTJw9GIiRvdps3yIKZlCKfHc5wIhAJCDb7BRVNuFGscdY+JQEla5pOO5UuX6CXL97fS6fiyBAiBRFKKYUwAeLda161dWRhuO/UH95L/k8Gqf0eeiGYD3RQIgEiAhiX1quSuBL7LrLGISGyJVy0dw+IXosqFHYeutmEI='
KeySpec keySpec = new PKCS8EncodedKeySpec(pkcs8.decodeBase64())
KeyFactory keyFactory = KeyFactory.getInstance("RSA", "SunRsaSign")
PrivateKey pk = keyFactory.generatePrivate(keySpec)
Signature signature = Signature.getInstance("SHA512withRSA", "SunRsaSign")
signature.initSign(pk) // <--- InvalidKeyException

这就是我获得私钥的方式pkcs8：

# generate a private key just for this example
openssl genrsa 512 > mykey.pem
# convert it into pkcs8 format to be able to read it from Java later
openssl pkcs8 -topk8 -inform pem -in mykey.pem -outform pem -nocrypt -out file.pkcs8

这是标准的私钥外观：

Sun RSA private CRT key, 512 bits
  modulus:          11706359850928035656926954612512379852454997399434114135854653766733637189933721115314465909375387122765789791657314272666480346477870633114913813167113199
  public exponent:  65537
  private exponent: 6209799048133316441293705496192881663344339603450371209133573984169170039947484349841188666943972061768383840284881642579217732240489331444594222111429393
  prime p:          113883566165066111166981826386356612269934395331161452768365784963361173403577
  prime q:          102792354025518497728065227780488381725246951885773034739853555051227644026087
  prime exponent p: 65365278008836639419826790688453702902877034572485301544697611535190715149441
  prime exponent q: 36673799866101187327427577642604625501620828371654868216232903920042186438469
  crt coefficient:  8198401844921780663468999895368137692410993828212557924743840907863587133506

如何使签名生效？

JDK 1.6