Last night's Republican debate is over, and we're now a safe enough distance to look back. The debate was nominally focused on national security, which means we heard discussion on shutting down the internet, monitoring the internet, warrants — or lack of them — for internet-connected phones, and shouting about who wants to expand the Patriot Act the most. Here's a brief look at the highlights.

"Closing that internet up"

Donald Trump, after earlier comments on "closing that internet up," clarified that he was only looking to close "areas" of the internet.

I would certainly be open to closing areas where we are at war with somebody. I sure as hell don't want to let people that want to kill us and kill our nation use our Internet. Yes, sir, I am.

Later on:

So, they can kill us, but we can't kill them? That's what you're saying. And as far as the Internet is concerned, we're not talking about closing the Internet. I'm talking about parts of Syria, parts of Iraq, where ISIS is, spotting it.

Now, you could close it. What I like even better than that is getting our smartest and getting our best to infiltrate their Internet, so that we know exactly where they're going, exactly where they're going to be. I like that better.

ISIS phones

While speaking about immigration, Trump also made this claim about "cell phones with ISIS flags on them":

We are not talking about isolation. We're talking about security. We're not talking about religion. We're talking about security. Our country is out of control. People are pouring across the southern border. I will build a wall. It will be a great wall.

People will not come in unless they come in legally. Drugs will not come through that wall. As far as other people into migration where they're going, tens of thousands of people having cell phones with ISIS flags on them. I don't think so, Wolf. They're not coming to this country. And if I'm president and if Obama has brought some to this country, they are leaving. They're going. They're gone.

Encryption

Encryption also made a cameo, with Ohio Governor John Kasich leading the charge:

In addition to that, Wolf, there is a big problem. It's called encryption. And the people in San Bernardino were communicating with people who the FBI had been watching. But because their phone was encrypted, because the intelligence officials could not see who they were talking to, it was lost.

We have to solve the encryption problem. It is not easy.

A report this week suggested that the shooters' phones had "built-in encryption," but it's unclear what, exactly, that means, as all phones have some level of "built-in encryption."

Carly Fiorina similarly suggested that Silicon Valley companies need to only be asked to cooperate with agencies like the FBI on investigations:

They do not need to be forced. They need to be asked to bring the best and brightest, the most recent technology to the table. I was asked as a CEO. I complied happily. And they will as well. But they have not been asked.

She did essentially comply when asked — pitching in help to the NSA as CEO of HP — but, not to put too fine a point on it, the rest is completely wrong. The FBI has "asked" companies like Apple plenty of times, and those companies haven't been keen on helping out.

Social media

Fiorina also brought up the fact that the Department of Homeland Security hasn't been checking social media of visa applicants:

And yet, we also know that ISIS is recruiting who are not in those databases. So of course, we're going to miss them. And then we now learn that DHS says, "No, we can't check their social media."

For heaven's sakes, every parent in America is checking social media and every employer is as well, but our government can't do it.

Cruz similarly said:

We didn't monitor the Facebook posting of the female San Bernardino terrorist because the Obama DHS thought it would be inappropriate. She made a public call to jihad, and they didn't target it.

This is true, but what happened in the San Bernardino review is more complicated than either of them suggest, and DHS at least has the option of looking at social media. It's unclear generally what effects the process would have on the speed of the application process. (Update: minutes after posting this story, it was reported, counter to previous reports, that the shooters did not post support for jihad on social media.)

Surveillance

Chris Christie explained five times that he was a former federal prosecutor, and was against degrading any state surveillance powers:

Now, I spent seven years of my life in the immediate aftermath of September 11th doing this work, working with the Patriot Act, working with our law enforcement, working with the surveillance community to make sure that we keep America safe.

What we need to do, Wolf, is restore those tools that have been taken away by the president and others, restore those tools to the NSA and to our entire surveillance and law enforcement community.

In one particularly heated exchange, Cruz and Rubio argued over the benefits of the USA Freedom Act, which amended the Patriot Act. Cruz made this claim:

What he knows is that the old program covered 20 percent to 30 percent of phone numbers to search for terrorists. The new program covers nearly 100 percent. That gives us greater ability to stop acts of terrorism, and [Rubio] knows that that's the case.

When responding, Rubio said:

This bill did, however, take away a valuable tool that allowed the National Security Agency and other law -- and other intelligence agencies to quickly and rapidly access phone records and match them up with other phone records to see who terrorists have been calling.

It's complicated. The law makes a broader potential "universe" of records available, but access to it is, at least relatively, limited.

Fiorina also explained why she believes the Patriot Act should be expanded.

Number one, we need to recognize that technology has moved on. The Patriot Act was signed in 2001, roughly. The iPhone was invented in 2007. The iPad was invented in 2011. Snapchat and Twitter, all the rest of it, have been around just for several years. Technology has moved on, and the terrorists have moved on with it.

It should be noted that Rand Paul is one GOP candidate who has gone on record, including at the debate, as being against enhanced state surveillance. He said this last night:

Rubio says we should collect all Americans' records all of the time. The Constitution says otherwise. I think they're both wrong. I think we defeat terrorism by showing them that we do not fear them.

"Penetrate the internet"

Trump also made the suggestion that the United States "should be able to penetrate the internet."

These are terrible people in ISIS, not masterminds. And we have to change it from every standpoint. But we should be using our brilliant people, our most brilliant minds to figure a way that ISIS cannot use the Internet. And then on second, we should be able to penetrate the Internet and find out exactly where ISIS is and everything about ISIS. And we can do that if we use our good people.

It's unclear what, exactly, he meant by that. But nearly as bizarre was Kasich picking up the same language.

We need to be able to penetrate these people when they are involved in these plots and these plans. And we have to give the local authorities the ability to penetrate, to disrupt. That's what we need to do.

The next Republican debate is scheduled to penetrate your internet on January 14th, 2016.

Update, 11:20 AM ET: Includes new information on San Bernardino shooters. Also includes more information on Rand Paul's stance on surveillance.