370 Z. Huang, S. Liu, and B. Qin
of a PKE scheme to generate some “equivocable” ciphertexts which can be
efficiently opened arbitrarily. More specifically, a PKE scheme is called
sender-equivocable, if there is a simulator which can generate non-committing ci-
phertexts and later open them to any requested plaintexts by releasing some ran-
domness, such that the simulation and real encryption are indistinguishable. This
notion is similar to non-committing encryption [5]. In fact, Fehr et al. [7] have
pointed out that sender-equivocable encryption secure under chosen-plaintext at-
tacks (CPA) is a variant of non-committing encryption defined in [5]. Following
the notations in [7], security of a sender-equivocable encryption scheme against
chosen-plaintext/ciphertext attacks is denoted by NC-CPA/CCA security.
As proved in [7], NC-CPA/CCA security implies simulation-based selective
opening security against chosen-plaintext/ciphertext attacks (SIM-SO-CPA/CCA
security). This fact suggests an alternative way of constructing PKE secure
against selective opening attacks, besides the construction from lossy encryption
proposed in [3].
Discussion and Related Work. In Eurocrypt 2009, Bellare et al. [3] for-
malized the notion of security against selective opening attacks (SOA security)
for sender corruptions. This security notion captures a situation that n senders
encrypt their own messages and send the ciphertexts to a single receiver. Some
subset of the senders can be corrupted by an adversary, exposing their messages
and randomness to the adversary. SOA security requires that the unopened ci-
phertexts remain secure.
In [3], Bellare et al. proposed two kinds of SOA security: simulation-based se-
lective opening (SIM-SO) security and indistinguishability-based selective open-
ing (IND-SO) security. The relations between the two notions are figured out
by B¨ohl et al. [2]. Bellare et al. [1] showed that the standard security of PKE
does not imply SIM-SO security. Bellare et al. [3] proposed that IND-SO-CPA
security and SIM-SO-CPA security can be achieved through a special class of en-
cryption named lossy encryption, and lossy encryption can be constructed from
lossy trapdoor functions [13]. Hemenway et al. [10] showed more constructions of
lossy encryption, which achieved IND-SO-CCA security with a-priori bounded
number of challenge ciphertexts. In Eurocrypt 2012, Hofheinz [9] proposed a new
primitive called all-but-many lossy trapdoor functions, which were employed to
construct IND-SO-CCA secure and SIM-SO-CCA secure PKE with unbounded
number of challenge ciphertexts. In [4], Bellare et al. extended SOA security
from PKE to IBE.
In [7], Fehr et al. presented a totally different way of achieving SIM-SO-CCA
security, also with unbounded number of challenge ciphertexts. They formalized
the security notion of sender equivocability under chosen-plaintext/ciphertext
attacks (NC-CPA/CCA security), and proved that NC-CPA (resp. NC-CCA)
security implies SIM-SO-CPA (resp. SIM-SO-CCA) security. In [7], two PKE
schemes were proposed. The first one, constructed from trapdoor one-way per-
mutations, is NC-CPA secure, so it is SIM-SO-CPA secure. The second one
(denoted by the FHKW scheme) is constructedfromanextendedhashproof