  Randomized encoding is a powerful cryptographic primitive with various
applications such as secure multiparty computation, verifiable computation,
parallel cryptography, and complexity lower-bounds. Intuitively, randomized
encoding $\hat{f}$ of a function $f$ is another function such that $f(x)$ can
be recovered from $\hat{f}(x)$, and nothing except for $f(x)$ is leaked from
$\hat{f}(x)$. Its quantum version, quantum randomized encoding, has been
introduced recently [Brakerski and Yuen, arXiv:2006.01085]. Intuitively,
quantum randomized encoding $\hat{F}$ of a quantum operation $F$ is another
quantum operation such that, for any quantum state $\rho$, $F(\rho)$ can be
recovered from $\hat{F}(\rho)$, and nothing except for $F(\rho)$ is leaked from
$\hat{F}(\rho)$. In this paper, we show that if quantum randomized encoding of
BB84 state generations is possible with an encoding operation $E$, then a
two-round verification of quantum computing is possible with a classical
verifier who can additionally do the operation $E$. One of the most important
goals in the field of the verification of quantum computing is to construct a
verification protocol with a verifier as classical as possible. This result
therefore demonstrates a potential application of quantum randomized encoding
to the verification of quantum computing: if we can find a good quantum
randomized encoding (in terms of the encoding complexity), then we can
construct a good verification protocol of quantum computing. We, however, also
show that too good quantum randomized encoding is impossible: if quantum
randomized encoding with a classical encoding operation is possible, then the
no-cloning is violated. We finally consider a natural modification of blind
quantum computing protocols in such a way that the server gets the output like
quantum randomized encoding. We show that the modified protocol is not secure.
