First trapdoor functions with secure key leasing and copy-protected inversion, addressing fundamental gaps in unclonable cryptography. Novel contribution: robust PKE-SKL/SDE schemes where quantum keys remain usable after decrypting any ciphertext.

First trapdoor functions with secure key leasing and copy-protected inversion, addressing fundamental gaps in unclonable cryptography. Novel contribution: robust PKE-SKL/SDE schemes where quantum keys remain usable after decrypting any ciphertext.