Lossy trapdoor functions from homomorphic reproducible encryption

Reproducible public-key encryption (reproducible PKE) provides an alternative way of encryption, which is called a reproduction algorithm, in addition to normally applying the encryption algorithm with the message and the randomness — applying the reproduction algorithm with the message, the secret key, and a ciphertext (possibly encrypted under a different public key).In this work, we show how to construct lossy trapdoor functions from homomorphic reproducible PKE, generalizing the DDH-based construction given by Peikert and Waters (STOC 2008). We also show that reproducible PKE can be constructed from standard number-theoretic assumptions, including DDH, QR, and DCR, and from smooth projective hash proof systems.

► We show how to construct lossy trapdoor functions from any homomorphic reproducible PKE.
► We show a construction of homomorphic reproducible PKE from standard number-theoretic assumptions including DDH, QR, and DCR.
► We show homomorphic reproducible PKE can also be constructed from smooth homomorphic projective hash proof systems.