We show that individual, confidential microdata records from the 2010 U.S. Census of Population and Housing can be accurately reconstructed from the published tabular summaries. Ninety-seven million person records (every resident in 70% of all census blocks) are exactly reconstructed with provable certainty using only public information. We further show that a hypothetical attacker using our methods can reidentify with 95% accuracy population unique individuals who are perfectly reconstructed and not in the modal race and ethnicity category in their census block (3.4 million persons)--a result that is only possible because their confidential records were used in the published tabulations. Finally, we show that the methods used for the 2020 Census, based on a differential privacy framework, provide better protection against this type of attack, with better published data accuracy, than feasible alternatives.