  The no-cloning principle of quantum mechanics enables us to achieve amazing
unclonable cryptographic primitives, which is impossible in classical
cryptography. However, the security definitions for unclonable cryptography are
tricky. Achieving desirable security notions for unclonability is a challenging
task. In particular, there is no indistinguishable-secure unclonable encryption
and quantum copy-protection for single-bit output point functions in the
standard model. To tackle this problem, we introduce and study relaxed but
meaningful security notions for unclonable cryptography in this work. We call
the new security notion one-out-of-many unclonable security.
  We obtain the following results.
  - We show that one-time strong anti-piracy secure secret key single-decryptor
encryption (SDE) implies one-out-of-many indistinguishable-secure unclonable
encryption.
  - We construct a one-time strong anti-piracy secure secret key SDE scheme in
the standard model from the LWE assumption.
  - We construct one-out-of-many copy-protection for single-bit output point
functions from one-out-of-many indistinguishable-secure unclonable encryption
and the LWE assumption.
  - We construct one-out-of-many unclonable predicate encryption (PE) from
one-out-of-many indistinguishable-secure unclonable encryption and the LWE
assumption.
  Thus, we obtain one-out-of-many indistinguishable-secure unclonable
encryption, one-out-of-many copy-protection for single-bit output point
functions, and one-out-of-many unclonable PE in the standard model from the LWE
assumption. In addition, our one-time SDE scheme is the first SDE scheme that
does not rely on any oracle heuristics and strong assumptions such as
indistinguishability obfuscation and witness encryption.
