  We study certified everlasting secure functional encryption (FE) and many
other cryptographic primitives in this work. Certified everlasting security
roughly means the following. A receiver possessing a quantum cryptographic
object can issue a certificate showing that the receiver has deleted the
cryptographic object and information included in the object was lost. If the
certificate is valid, the security is guaranteed even if the receiver becomes
computationally unbounded after the deletion. Many cryptographic primitives are
known to be impossible (or unlikely) to have information-theoretical security
even in the quantum world. Hence, certified everlasting security is a nice
compromise (intrinsic to quantum).
  In this work, we define certified everlasting secure versions of FE,
compute-and-compare obfuscation, predicate encryption (PE), secret-key
encryption (SKE), public-key encryption (PKE), receiver non-committing
encryption (RNCE), and garbled circuits. We also present the following
constructions:
  - Adaptively certified everlasting secure collusion-resistant public-key FE
for all polynomial-size circuits from indistinguishability obfuscation and
one-way functions.
  - Adaptively certified everlasting secure bounded collusion-resistant
public-key FE for NC1 circuits from standard PKE.
  - Certified everlasting secure compute-and-compare obfuscation from standard
fully homomorphic encryption and standard compute-and-compare obfuscation
  - Adaptively (resp., selectively) certified everlasting secure PE from
standard adaptively (resp., selectively) secure attribute-based encryption and
certified everlasting secure compute-and-compare obfuscation.
  - Certified everlasting secure SKE and PKE from standard SKE and PKE,
respectively.
  - Certified everlasting secure RNCE from standard PKE.
  - Certified everlasting secure garbled circuits from standard SKE.
