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The International Centre for Mathematical Sciences (ICMS)

While lattice-based cryptography has been successful, a consensus is forming that we have reached a limit of what we can do from such well-established problems. Thus, researchers are introducing novel variants of these presumed-hard problems to develop quantum-safe privacy-enhancing technologies (PETs). Many PETs lack efficient lattice-based or other efficient post-quantum constructions. Examples include advanced encryption schemes with fine-grained access control, blind signatures, anonymous credentials, oblivious PRFs, and threshold constructions. Adopting novel hardness assumptions reflects a long-standing tension in cryptography: more structure enables advanced functionalities but may offer flexibility to solve presumed-hard problems, invalidating their hardness. As these assumptions proliferate, the risk grows that they remain understudied and may lack the robustness to serve as foundations for a privacy-respecting post-quantum digital society.