Software-based root-of-trust has been proposed to overcome the disadvantage of hardware-based root-of-trust, which is the high cost in deployment and upgrade (when vulnerabilities are discovered). However, prior research on software-based root-of-trust only focuses on uniprocessor platforms. The essential security properties of such software-based root-of-trust, as analyzed and demonstrated in our paper, can be violated on multicore platforms. Since multicore processors are becoming increasingly popular, it is imperative to explore the feasibility of software-based root-of-trust on them.In this paper, we analyze the challenges of designing softwarebased root-of-trust on multicore platforms and present two practical attacks that utilize the parallel computing capability to break the existing schemes. We then propose a timing-based primitive, called MT-SRoT, as the first step towards software-based root-oftrust on multicore platforms. MT-SRoT is able to ensure untampered execution of a critical security task, such as remote software attestation, on homogeneous shared-memory multicore platforms without the support of tamper-resistant hardware. We implement MT-SRoT and show its effectiveness on both Intel dual-core and quad-core processors.