Elizabeth Smart says she was sexually assaulted on an airplane last year

"I'm Elizabeth Smart. I should know what to do, and at that moment I didn't know what to do," Smart told "NBC Nightly News" on Thursday.

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By Doha Madani, Joe Fryer and Elisha Fieldstadt

Kidnapping survivor Elizabeth Smart said Thursday that her new self-defense program was created after a man assaulted her on a plane last summer.

Smart, who was abducted and held captive for nine months when she was 14 years old, said in an interview with "CBS This Morning" that an unidentified man molested her while she slept on a Delta flight last year to Utah.

"I had been asleep and, all of a sudden, I woke up because I felt someone's hand rubbing in between my legs, on my inner thigh," Smart told CBS' Gayle King on Thursday.

She said that she expected the man to stop and apologize but that he said nothing to her.

Smart, 32, told "NBC Nightly News" on Thursday that she was in complete shock and felt as if she should have been better able to respond given her history.

"I'm Elizabeth Smart," she said. "I should know what to do, and at that moment I didn't know what to do."

Smart said she was initially hesitant to speak out but felt it was important to share what happened.

"It went through my mind, I have received a lot, a lot, a lot of attention over the years, and there are a lot of stories out there who are much more deserving than mine," Smart said during an interview Friday.

"What ultimately drove me to share this story in the public spotlight and put it out there is because I have met so many other women, and this experience for me just really reminded me how vulnerable we all are as women, as girls," Smart told NBC News.

Smart thought, if the man who assaulted her "was that brazen with me ... who else is he doing this to?"

The FBI in 2018 issued a warning to airlines and air travelers that the number of reports of sexual assaults on flights was increasing "at an alarming rate."

The FBI said last year that reports of sexual assaults on planes had increased by 66 percent between 2014 and 2017. The spike could be due to an increase in people reporting the assaults, but the actual number of victims is still likely underrepresented since sexual abuse victims are often reluctant to come forward.

Delta confirmed in a statement to NBC News on Thursday that Smart reached out to the airline to inform it that another passenger had acted inappropriately to her. The airline said it does not tolerate passenger misconduct.

"We took the matter seriously and have continued to cooperate with Ms. Smart and the appropriate authorities as the matter is investigated," Delta said.

Smart said that, though she was reluctant at first, she also contacted the FBI and that there is an open investigation.

The FBI said it could not confirm or deny the existence of an investigation.

Smart was taken at knifepoint in her pajamas from her Salt Lake City bedroom in 2002 by Brian David Mitchell, who kept her captive with his wife, Wanda Barzee. Mitchell is serving a life sentence for kidnapping and raping Smart, while Barzee was released from prison in 2018 after being convicted for her role in the abduction.

Smart has become an outspoken advocate against child abductions. In 2011, she founded the Elizabeth Smart Foundation, dedicated to women and girls who face abuse and sexual violence.

Smart said she began to train in self-defense with a close friend after the attack, which helped to inspire her new self-defense program for women and girls, Smart Defense.

"It doesn't matter who you are, what you're wearing. None of those things matter if you are abused or taken advantage of," she said. "It's not your fault, and you have every right to defend yourself, to take care of yourself, to do what you need to do to stay safe."