The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity and variety. Along with these standard three V's of big data, an emerging fourth "V" is veracity, which addresses the confidentiality, integrity, and availability of the data. Traditional cryptographic techniques that ensure the veracity of data can have overheads that are too large to apply to big data. This work introduces a new technique called Computing on Masked Data (CMD), which improves data veracity by allowing computations to be performed directly on masked data and ensuring that only authorized recipients can unmask the data. Using the sparse linear algebra of associative arrays, CMD can be performed with significantly less overhead than other approaches while still supporting a wide range of linear algebraic operations on the masked data. Databases with strong support of sparse operations, such as SciDB or Apache Accumulo, are ideally suited to this technique. Examples are shown for the application of CMD to a complex DNA matching algorithm and to database operations over social media data.