Intel’s long-awaited entrance into the smartphone chip market doesn’t seem to scare its chief competition. ARM, the British microprocessor whose chipsets run the majority of the world’s intelligent mobile devices, believes that its dominant reign is just beginning.

Warren East, ARM’s CEO, told CNN Money last week that he expects the company’s 30 percent semiconductor market share to double in the coming years as it explores new markets.

“We want to see that doubled to 60 percent,” he told CNN at last week’s Mobile World Congress. “We think we’ve got the right sort of technology for everything from very, very tiny intelligent sensors, through the consumer electronic swathe, right through to servers.”

Currently, nearly every smartphone and tablet is powered by an ARM microprocessor. Intel is looking to steal some of this market share with its own chipsets, and has recently signed a few big partners, but that doesn’t seem to bother East and the rest of the ARM team.

“Intel’s offerings today are better than they were years ago, and undoubtedly there are going to be some Intel design wins,” he told CNN. “But I look at the capabilities of those products and see the same kind of capabilities that were in ARM products several years ago.”

East’s bold 60 percent market share goal can’t be attained by simply holding off Intel in the mobile device space. ARM’s next opportunity exists in the PC processor market, a new industry that the company hopes will become its next pillar of success. IHS iSuppli speculates that ARM market share in the PC processor space can grow from virtually nothing to as high as 22 percent by 2015.

As for the mobile market, ARM may soon find itself in a bigger battle with Intel than East believes. The semiconductor giant showed off its Medfield chipset at the Mobile World Congress last week and wowed attendees and members of the media.

The recently-launched Orange Santa Clara smartphone, powered by Intel’s Medfield chipset, was found to be faster than the iPhone 4S, which runs on the ARM-based dual-core A5 processor, according to Gotta Be Mobile.

If the speed can translate to real-world usability with competitive battery efficiency, ARM may soon have more competition than it bargained for.