President Vladimir V. Putin of Russia, who has staked his international reputation on the success of the Games and for whom a terrorist attack would be as much a personal as a political blow, said recently that Russia would "do our best" to keep Sochi secure. In addition to forming a so-called Ring of Steel — a special security cordon for people and vehicles — in the area around Sochi, Russia plans to deploy a security force of 40,000 people and set up six missile-defense systems, among other measures.
"We have a perfect understanding of the scope of the threat and how to deal with it and how to prevent it," Putin said in a television interview this month. "We will protect our air and sea space as well as the mountain cluster."
But the last few months have revealed the difficulties in defending against terrorism. Suicide bombers have struck Volgograd, an industrial city about 400 miles north of Sochi, three times since the fall — once in October and twice within the space of 24 hours at the end of December, killing at least 34 people and injuring dozens.
Last year, Doku Umarov, an insurgent leader in the violent Islamist movement in the North Caucasus, released a video over the Internet urging his followers to use "maximum force" to keep the Sochi Games from taking place "on the bones of our ancestors." A group loyal to him has since claimed responsibility for the Volgograd bombings, but the authorities have not corroborated the claim.
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While acknowledging the concerns, international and national Olympic officials have assured athletes in phone calls, emails and meetings that security is a top priority.
"It's a subject that is brought up regularly without any particular anxiety," Jean-Claude Killy, the leader of the International Olympic Committee's commission overseeing Sochi, told the French sports newspaper L'Equipe this month. He said that the Volgograd attacks had served to "tighten the bolts" on the security around Sochi.
A Pentagon official said recently that the United States would station two Navy warships in the Black Sea, next to Sochi, in case any Americans needed to be evacuated after a terrorist attack or other emergency.
Senior American officials have said in interviews in recent weeks that they are more concerned about these Games than they have been for any since the 2004 Summer Olympics in Athens. For those Games, American officials were fearful that terrorists groups like Al Qaeda in Pakistan — which was still a fairly organized and potent force — and an indigenous Greek terrorist group would exploit the country's weak internal security. Unlike the Russians, the Greeks were far more receptive to help from American law enforcement and intelligence officials, who ultimately played a significant role in the security for the Games.
"This is unique among Olympics from a preparatory standpoint for us," said Dan Richards, the chief executive of Global Rescue, a company that provides crisis medical services. The United States Ski and Snowboard Association is one of its clients.
"The terrain works against you," Richards said, referring to Sochi's setting on the Black Sea and at the foot of the Caucasus Mountains. "But it also makes some areas hard to attack. Having individuals who are bad actors try to do something in any sizable way or organize an attack would be difficult. We haven't seen this level of sophistication yet and hopefully we never will."
There is no question that people are nervous. Greg Bretz, an American snowboarder, said he considered hiring a bodyguard to protect his father, Greg, and his father's girlfriend, who are both traveling to Sochi.
The elder Bretz declined, saying: "My thought is, they're not just sniper shooting. If they're going to do anything, they're going to blow everything up."
The American hockey player Dustin Brown played in the 2010 Vancouver Games for the United States, so his family, which went to those Olympics, had already planned to stay home this time because of the distance and the expense.
"Anybody who's not concerned is probably lying," he said about Sochi, adding, "I think it's fair to say there's some concern there."
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Several family members of American athletes said they planned to stay on the cruise ships in the Black Sea that have been turned into floating Olympics accommodations. Following official advice that has been given to some athletes' families, they also plan to forgo Team USA outfits outside the sports venues themselves; some also said they were not yet certain they would do any sightseeing.
"I don't know if we're going to be tourists, like in France or Germany," said Mike Marvin, the father of Gigi Marvin, a member of the United States women's hockey team.
Melissa James, the mother of the American figure skater Ashley Wagner, said she felt comfortable going to Sochi but was concerned about her flight connection in Kiev, which has exploded in violent anti-government demonstrations in recent weeks. It was something of a relief, she said, that the airport was not in the center of the unrest.
"It's one of the times I'm excited the airport is out in the boonies," she said.
Christian Niccum, a member of the United States luge team, said that among the emails the athletes had received about Olympic security, one stressed that they should not take part in political protests or do anything to draw attention to themselves as "loud Americans," as he put it.
That is fine with him.
"I'm not going to worry about it," he said. "To be honest, I'm just going sledding."