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A core goal of the NIST PQC competition is to produce PKE schemes which, even if attacked with a large-scale quantum computer, maintain the security guarantees needed by applications. The main security focus in the NIST PQC context has been IND-CCA security, but other applications demand that PKE schemes provide anonymity (Bellare et al., ASIACRYPT 2001), and robustness (Abdalla et al., TCC 2010). Examples of such applications include anonymous cryptocurrencies, searchable encryption, and auction protocols. However, almost nothing is known about how to build post-quantum PKE schemes offering these security properties. In particular, the status of the NIST PQC candidates with respect to anonymity and robustness is unknown.

This paper initiates a systematic study of anonymity and robustness for post-quantum PKE schemes. Firstly, we identify implicit rejection as a crucial design choice shared …