Will Rand Paul be able to attract a substantial number of new young voters to the Republican Party? It’s become increasingly clear that may be one of his main political goals as the libertarian-leaning Kentucky senator looks towards a potential 2016 presidential run.

In his latest attempt at youth outreach, Senator Paul traveled to the famously liberal University of California at Berkeley on Wednesday to deliver a scathing speech warning of the dangers of unchecked National Security Agency surveillance.

“I’m not here to tell you what to be,” Paul told a crowded Berkeley auditorium. “But I am here to tell you ... that your rights, especially your right to privacy, [are] under assault.”

Invoking one of the talismans of the digital age, Paul told the audience that if they own a cell phone, they are under surveillance, as the NSA collects metadata such as time and number called on all US cellular communications.

“I believe that what you do on your cell phone is none of their damn business,” said Paul, repeating an applause line he’s used in previous speeches.

Paul added that he is surprised this has occurred under Barack Obama, the first African-American president, given the history of US surveillance of civil rights leaders such as Martin Luther King Jr.

He called for a new, bipartisan committee to monitor surveillance agencies, similar to the special Church Committee which looked into CIA abuses in the mid-1970s.

That’s necessary because the intelligence community has run wild and existing oversight structures have not reined it in, according to Paul. The NSA has interpreted the Constitution so that “equal protection means Americans should be spied upon equally,” he said.

“I oppose this abuse of power with every ounce of energy I have,” Paul said.

While the speech contained a defense of GOP fiscal priorities, it also said Republicans need to change if they are to attract new constituencies to the party. Paul drew an analogy with Domino’s Pizza, asking the crowd – a target pizza audience – if they remembered when the chain admitted it had bad crust.

Republicans, too, need a different kind of crust, a different kind of party, he said. They have to “either evolve, adapt, or die”.

At the end Paul got a standing ovation. That might not be the expected response at a university Ronald Reagan targeted as a mass of hippie peaceniks when he was California governor. But that was a long time ago, in a country far away, and Paul’s brand of libertarianism has a demonstrated appeal to Millennials appalled by the NSA practices revealed by leaker Edward Snowden.

Will it overcome the aversion of many young people to GOP positions on social issues? That’s a difficult question to answer. But Paul was clearly hinting at this when he said he would not “tell you what to be.” And the right-leaning Washington Examiner reports Thursday that the Paul camp hopes that as an issue, his NSA-bashing will top the Republican Party opposition to gay marriage, in particular.

The Examiner notes that Paul recently said in an interview that “The Republican Party is not going to give up on having quite a few people who do believe in traditional marriage. But the Republican Party also has to find a place for young people and others who don’t want to be festooned by those issues.”

Of course, growing the party is one thing. Winning a nomination is another. Paul still faces the hurdle that his non-interventions positions on foreign policy are at odds with large sections of his own party. That’s been highlighted by the Russian seizure of Crimea. Paul’s potential party rivals, such as Sen. Ted Cruz of Texas, have been far more full-throated in their condemnation of Russian President Vladimir Putin, and of a perceived weak response by President Obama.

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It’s this issue that has caused some pundits to say Paul faces a very uphill climb to his own party’s nomination, and can’t be judged a front-runner by any means.

“What we see, I think, is a miscalculation by Paul about how to expand the party and his own appeal,” writes conservative Jennifer Rubin on her “Right Turn” blog at the Washington Post. “He cannot ... find sufficient libertarian replacements for evangelical primary voters who are staunchly Reaganite, pro-Israel [and otherwise hawkish] on foreign policy and pro-life,” writes Rubin.