As part of increased efforts to provide precision medicine to patients, large clinical research networks (CRNs) are building regional and national collections of electronic health records (EHRs) and patient-reported outcomes (PROs). To protect patient privacy, each data contributor to the CRN (for example, a health-care provider) uses anonymizing and encryption technology before publishing the data. An important problem in such CRNs involves linking records of the same patient across multiple source databases. Unfortunately, in practice, the records to be matched often contain typographic errors and inconsistencies arising out of formatting and pronunciation incompatibilities, as well as incomplete information. When encryption is applied on these records, similarity search for record linkage is rendered impossible. The central idea behind our work is to create characterizing signatures for the linkage of attributes of each record using minhashes and locality sensitive hash functions before encrypting those attributes. Then, using a privacy preserving record linkage protocol we perform probabilistic matching based on Jaccard similarity measure. We have developed a proof-of-concept for this protocol and we show some experimental results based on synthetic, but realistic, data.