Current strand spaces model can not analyze some complex security protocols on account of their poor cryptographic primitives’ abstract. So it is very necessary to extend original theory of strand spaces so that it can be applied to analyze real world protocols. The penetrator’s strands are extended through adding signature, signature verification and HMAC (keyed-hashing for message authentication code) traces to them. A new notion of ideal is defined and the relevant propositions or theorems are therefore modified and proved. The extended honest ideals model not only inherits its original characters, but also is adaptive to the analysis of protocols with more cryptographic primitives such as JFK or IKE2.