Although the importance of using static analysis to detect taint-style vulnerabilities in Linux-based embedded firmware is widely recognized, existing approaches are plagued by three major limitations. (a) Approaches based on symbolic execution may miss alias information and therefore suffer from a high false-negative rate. (b) Approaches based on VSA (value set analysis) often provide an over-approximate pointer range. As a result, many false positives could be produced. (c) Existing work for detecting taint-style vulnerability does not consider indirect call resolution, whereas indirect calls are frequently used in Internet-facing embedded devices. As a result, many false negatives could be produced. In this work, we propose a precise demand-driven flow-, context- and field-sensitive alias analysis approach. Based on this new approach, we also design a novel indirect call resolution scheme. Combined with sanitization rule checking, our solution discovers taint-style vulnerabilities by static taint analysis. We implemented our idea with a prototype called EmTaint and evaluated it against 35 real-world embedded firmware samples from six popular vendors. EmTaint discovered at least 192 bugs, including 41 n-day bugs and 151 0-day bugs. At least 115 CVE/PSV numbers have been allocated from a subset of the reported vulnerabilities at the time of writing. Compared to state-of-the-art tools such as KARONTE and SaTC, EmTaint found significantly more bugs on the same dataset in less time.