"United States of Jihad" author on the threat at home

Following the terrorist attacks in Paris and San Bernardino, the threat of homegrown terrorism and plans to defeat ISIS have taken center stage at the presidential race.

Some candidates have promised aggressive measures, such as Sen. Ted Cruz who vowed to "carpet-bomb ISIS," and Donald Trump, who proposed temporarily banning all Muslims from entering the country.

But while the rhetoric may resonate with voters because "they seem to provide answers," neither are viable solutions, according to CNN's national security analyst Peter Bergen.

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"Ted Cruz wants to drop the bomb on ISIS but ISIS is embedded in the civilian population. Banning all Muslims - most of the people carrying out these attacks are American residents, American citizens, so that doesn't really solve the problem either," Bergen told "CBS This Morning" Tuesday.

So far, there have been more than 300 arrests of people involved in some kind of jihadist crime, of which an alarming number - four out of five - were American citizens and residents.

In his new book, "United States of Jihad: Investigating America's Homegrown Terrorists," Bergen offers a comprehensive look at "homegrown" Islamist terrorism, including a portrait of American jihadists based on 330 militants studied since 9/11.

At an average age of 29, one-third are married and have kids, 12 percent have served time in prison and 10 percent have mental health issues.

"They're as educated as the average American, similar incomes - these are ordinary Americans. American Muslims are well integrated into American society in a way that's not true in places like Paris or London," Bergen said.

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Bergen said he also tried to answer the "puzzle" to determine the root of radicalization and point in which an individual decides to carry out a terrorist attack - but said he found "no common denominators."

"Some people have personal disappointments, or object to American foreign policy. Some people are Islamic, very radicalized - each person is a little different..." Bergen said, then added that it could also be a "cocktail" of several factors.

According to Bergen, resolving this "puzzle" is also a challenge for the FBI in their efforts to counter terror plots and detect homegrown terrorists, but he assured their defenses are "very good." Before the 9/11 attacks, just 16 people suspected of ties to terrorism were deemed on the no-fly list. That number has now jumped to 47,000.

In 2015, there were also 900 active investigations across all 50 states and 56 were arrested.

Still, according to a recent CBS News/New York Times Poll, 63 percent of Americans are very concerned about terror attacks committed by people currently in the United States, and 59 percent are concerned about terrorists entering the country.

"You're 5,000 times more likely to be killed by a fellow American with a gun than you are to be killed by a jihadi terrorist in this country. Yet we're more afraid about terrorism than we should be," Bergen said. "The government of both the Bush and Obama administration has done a very good job of containing this threat. It will be persistent, it's not going to go away, but it is managed and contained."

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But some plots slip through the cracks, like the recent mass shooting in San Bernardino by American citizen Syed Rizwan Farook and his wife, a Pakistani immigrant.

Bergen explained that while authorities "should've known more" about warning signs, the fact that the attackers were a married couple - which eliminated the need for separate meetings to plot the attack - and appeared to be "regular, outstanding members of society" with kids and a good job - made it difficult to foil.

Bergen also commented on the controversy surrounding President Obama's refusal to link ISIS with Islam. President Obama has taken heat from critics for taking pains to separate Islam from terrorism. Former President George W. Bush walked the same line following the 9/11 attacks.

Drawing comparisons to the Christian crusades, Bergen said, "It's an uncomfortable fact that this has something to do with Islam. I mean you can't just wish that away... Of course it's a cherry-picked version of Islam but it is something to do with Islam."