  In modern cryptography, block encryption is a fundamental cryptographic
primitive. However, it is impossible for block encryption to achieve the same
security as one-time pad. Quantum mechanics has changed the modern
cryptography, and lots of researches have shown that quantum cryptography can
outperform the limitation of traditional cryptography.
  This article proposes a new constructive mode for private quantum encryption,
named $\mathcal{EHE}$, which is a very simple method to construct quantum
encryption from classical primitive. Based on $\mathcal{EHE}$ mode, we
construct a quantum block encryption (QBE) scheme from pseudorandom functions.
If the pseudorandom functions are standard secure, our scheme is
indistinguishable encryption under chosen plaintext attack. If the pseudorandom
functions are permutation on the key space, our scheme can achieve perfect
security. In our scheme, the key can be reused and the randomness cannot, so a
$2n$-bit key can be used in an exponential number of encryptions, where the
randomness will be refreshed in each time of encryption. Thus $2n$-bit key can
perfectly encrypt $O(n2^n)$ qubits, and the perfect secrecy would not be broken
if the $2n$-bit key is reused for only exponential times.
  Comparing with quantum one-time pad (QOTP), our scheme can be the same secure
as QOTP, and the secret key can be reused (no matter whether the eavesdropping
exists or not). Thus, the limitation of perfectly secure encryption (Shannon's
theory) is broken in the quantum setting. Moreover, our scheme can be viewed as
a positive answer to the open problem in quantum cryptography "how to
unconditionally reuse or recycle the whole key of private-key quantum
encryption". In order to physically implement the QBE scheme, we only need to
implement two kinds of single-qubit gates (Pauli $X$ gate and Hadamard gate),
so it is within reach of current quantum technology.
