Read-mapping, i.e., finding certain patterns in a long DNA sequence, is an important operation for molecular biology. It is widely used in a variety of biological analyses including SNP discovery, genotyping and personal genomics. As next-generation DNA sequencing machines are generating an enormous amount of sequence data, it is a good choice to implement the read-mapping algorithm in the MapReduce framework and outsource the computation to the cloud. Data privacy becomes a big concern in this situation as DNA sequences are very sensitive. In response, encryption may be used to protect the data. However, it is very difficult for the cloud to process cipher texts. In the MapReduce framework, even if values (data to be processed) may be protected by encryption, keys cannot be encrypted using sematic secure encryption schemes as it will affect the MapReduce scheduling mechanism. But if no protection is utilized, attackers may extract useful information from unprotected keys. We propose a solution that can securely outsource read-mapping computations in the MapReduce framework by leveraging inherent tamper resistant properties of FPGAs. We also provide a method to protect the keys generated in this process. We implement our solution using FPGAs and apply it to some data sets. The security evaluation and experimental results show that with this method, DNA sequence privacy is well protected, and the extra cost is acceptable.