The recent introduction of new DNA sequencing techniques caused the amount of processed and stored biological data to skyrocket. In order to process these vast amounts of data, bio-centers have been tempted to use low-cost public clouds. However, genomes are privacy sensitive, since they store personal information about their donors, such as their identity, disease risks, heredity and ethnic origin. The first critical DNA processing step that can be executed in a cloud, i.e., read alignment, consists in finding the location of the DNA sequences produced by a sequencing machine in the human genome. While recent developments aim at increasing performance, only few approaches address the need for fast and privacy preserving read alignment methods. This paper introduces MaskAl, a novel approach for read alignment. MaskAl combines a fast preprocessing step on raw genomic data-filtering and masking-with established algorithms to align sanitized reads, from which sensitive parts have been masked out, and refines the alignment score using the masked out information with Intel's software guard extensions (SGX). MaskAl is a highly competitive privacy-preserving read alignment software that can be massively parallelized with public clouds and emerging enclave clouds. Finally, MaskAl is nearly as accurate as plain-text approaches (more than 96% of aligned reads with MaskAl compared to 98% with BWA) and can process alignment workloads 87% faster than current privacy-preserving approaches while using less memory and network bandwidth.