Publishing and sharing data is crucial for the data mining community, allowing collaboration and driving open innovation. However, many researchers cannot release their data due to privacy regulations or fear of leaking confidential business information. To alleviate such issues, we propose the Time Series Synthesis Using the Matrix Profile (TSSUMP) method, where synthesized time series can be released in lieu of the original data. The TSSUMP method synthesizes time series by preserving similarity join information (i.e., Matrix Profile) while reducing the correlation between the synthesized and the original time series. As a result, neither the values for the individual time steps nor the local patterns (or shapes) from the original data can be recovered, yet the resulting data can be used for downstream tasks that data analysts are interested in. We concentrate on similarity joins because they are one of the most widely applied time series data mining routines across different data mining tasks. We test our method on a case study of ECG and gender masking prediction. In this case study, the gender information is not only removed from the synthesized time series, but the synthesized time series also preserves enough information from the original time series. As a result, unmodified data mining tools can obtain near-identical performance on the synthesized time series as on the original time series.