With the increasing development of pervasive computing and wireless bandwidth communication, more mobile devices are used to access sensitive data stored in remote servers. In such applications, a practical issue emerges such as how to exploit the sufficient resource of a server so that the file owners can enforce fine-grained access control over the remotely stored files, while enable resource-limited mobile devices to easily access the protected data, especially if the storage server maintained by a third party is untrusted. This challenge mainly arises from the asymmetric capacity among the participants, i.e., the capacity limited mobile devices and the resource abundant server (and file owners equipped with fixed computers). To meet the security requirements in mobile access to sensitive data, we propose a new encryption paradigm, referred to as asymmetric cross-cryptosystem reencryption (ACCRE) by leveraging the asymmetric capacity of the participants. In ACCRE, relatively light-weight identity-based encryption (IBE) is deployed in mobile devices, while resource-consuming but versatile identity-based broadcast encryption (IBBE) is deployed in servers and fixed computers of the file owners. The core of ACCRE is a novel ciphertext conversion mechanism that allows an authorized proxy to convert a complicated IBBE ciphertext into a simple IBE ciphertext affordable to mobile devices, without leaking any sensitive information to the proxy. Following this paradigm, we propose an efficient ACCRE scheme with its security formally reduced to the security of the underlying IBE and IBBE schemes. Thorough theoretical analyses and extensive experiments confirm that the scheme takes Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. ASIA CCS'very small cost for mobile devices to access encrypted data and is practical to secure mobile computing applications.