We present the first IBE schemes that are proven secure against selective opening attack (SOA). This means that if an adversary, given a vector of ciphertexts, adaptively corrupts some fraction of the senders, exposing not only their messages
but also their coins
, the privacy of the unopened messages is guaranteed. Achieving security against such attacks is well-known to be challenging and was only recently done in the PKE case. We show that IBE schemes having a property we call 1-sided public openability (1SPO) yield SOA secure IBE schemes and then provide two 1SPO IBE schemes, the first based on the Boyen-Waters anonymous IBE and the second on Waters’ dual-system approach.