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Voice-activated systems are integrated into a variety of desktop, mobile, and Internet-of-Things (IoT) devices. However, voice spoofing attacks, such as impersonation and replay attacks, in which malicious attackers synthesize the voice of a victim or simply replay it, have brought growing security concerns. Existing speaker verification techniques distinguish individual speakers via the spectrographic features extracted from an audible frequency range of voice commands. However, they often have high error rates and/or long delays. In this paper, we explore a new direction of human voice research by scrutinizing the unique characteristics of human speech at the ultrasound frequency band. Our research indicates that the high-frequency ultrasound components (e.g. speech fricatives) from 20 to 48 kHz can significantly enhance the security and accuracy of speaker verification. We propose a speaker verification system, SUPERVOICE that uses a two-stream DNN architecture with a feature fusion mechanism to generate distinctive speaker models. To test the system, we create a speech dataset with 12 hours of audio (8,950 voice samples) from 127 participants. In addition, we create a second spoofed voice dataset to evaluate its security. In order to balance between controlled recordings and real-world applications, the audio recordings are collected from two quiet rooms by 8 different recording devices, including 7 smartphones and an ultrasound microphone. Our evaluation shows that SUPERVOICE achieves 0.58% equal error rate in the speaker verification task, it only takes 120 ms for testing an incoming utterance, outperforming all existing speaker verification systems. Moreover, within 91 ms processing time, SUPERVOICE achieves 0% equal error rate in detecting replay attacks launched by 5 different loudspeakers.