Alpine Linux
Alpine Linux is a community developed operating system designed for routers, firewalls, VPNs, VoIP boxes, containers, and servers. It was designed with security in mind; it has proactive security features like PaX and SSP that prevent security holes in the software to be exploited.
VS
Tiny Core Linux
Tiny Core Linux is a 16 MB graphical Linux desktop. It is based on a recent Linux kernel, BusyBox, Tiny X, Fltk, and Flwm.