In this paper, we propose an extended chaotic maps-based keyword search scheme over encrypted data resist outside and inside keyword guessing attacks in cloud storage services, which achieves the essential requirements of a secure cloud storage service. A secure cloud storage service has to satisfy five security requirements: consistency, ciphertext indistinguishability, trapdoor indistinguishability and resist off-line keyword guessing attacks (including offline outside keyword guessing attack and off-line inside keyword guessing attack). Moreover, due to the characteristics of extended chaotic maps and session key establishment, which allow two communication parties to agree a common session key and the agreed session key is only known by the data sender and the authorized data receiver. Therefore, in this paper, we integrated the concept of session key establishment and extended chaotic maps into our proposed scheme which aims to resist the off-line keyword guessing attacks not only from the outside cloud attackers but also from an inside malicious cloud server. To the best of our knowledge, none of the recently proposed secure keyword search schemes can resist inside keyword guessing attacks and this work is the first attempt to provide a secure keyword search scheme without inside keyword guessing attacks in cloud storage services.