  Quantum cloud computing is emerging as a popular model for users to
experience the power of quantum computing through the internet, enabling
quantum computing as a service. The question is, when the scale of the
computational problems becomes out of reach of classical computers, how can
users be sure that the output strings sent by the server are really from a
quantum hardware? In 2008, Shepherd and Bremner proposed a cryptographic
verification protocol based on a simplified circuit model called IQP
(instantaneous quantum polynomial-time), which can potentially be applied to
most existing quantum cloud platforms. However, the Shepherd-Bremner protocol
has recently been shown to be insecure by Kahanamoku-Meyer. Here we present an
extended model of IQP-based cryptographic verification protocol, where the
Shepherd-Bremner construction can be regarded as a special case. This protocol
not only can avoid the attack by Kahanamoku-Meyer but also provide several
additional security measures for anti-forging quantum data. In particular, our
protocol admits a simultaneous encoding of multiple secret strings,
strengthening significantly the hardness for classical hacking. Furthermore, we
provide methods for estimating the correlation functions associated with the
secret strings, which are the key elements in our verification protocol.
