The two-volume set LNCS 10769 and 10770 includes the peer-reviewed proceedings of the 21st IACR International Conference on the Practice and Theory of Public-Key Cryptography, PKC 2018, which took place in March 2018 in Rio de Janeiro, Brazil. These volumes contain 49 revised papers that were carefully selected from 186 submitted contributions. The papers are organized into thematic sections covering various aspects of public-key cryptography, including security concepts, encryption methods, and cryptographic protocols. This collection provides a comprehensive overview of current research findings and developments in public-key cryptography and is a valuable resource for professionals and students in the field.