I find the idea you present of the "links between security and identity" to be a very interesting historical concept! The United States and Cuba have quite an interesting history considering that link! Let's begin discussing what the concept means and then continue with more specifics about the Cuban Missile Crisis and the current immigration issues.
In order to properly express the concept of the "links between security and identity," I believe it is necessary to reverse the wording to "identity and security." That is because I believe it is the identities of these two nations that constitute their issues with security.
Let's deal with the idea of identity first. Quite simply, the United States is proud to call itself a Democracy and Cuba is proud to call itself Communist. From the United States' position, we would consider ourselves "free" while the people under the Communist regime of Fidel Castro are "not free." From the opposite perspective, the people of Cuba who are loyal to Castro consider Communism to be the best form of government offering equality to all people while the United States is simply a military bully waiting to exert its power. These precise identity issues lead to issues with security.
The idea behind security, of course, is our ability (as the peoples of these nations), to feel safe. Sometimes this can involve a more military idea of armed forces keeping the peace. Sometimes this can involve worries of being invaded by illegal immigrants. Because our ideology differs so greatly in regard to Democracy vs. Communism, we often do NOT feel safe residing so very near each other.
Now let's talk about specifics, beginning with the Cuban Missile Crisis. Under the Kennedy administration, this crisis cemented the identity of both nations and threatened the security of both nations as well. Cuba was in league with the Soviet Union during the Cold War. The 1960s marked the height of this tension. In 1962 President John F. Kennedy became aware of Cuban/Soviet nuclear missiles ready to attack the United States. As a result, Kennedy ordered the island of Cuba to be surrounded (in order to prevent more nuclear warheads from arriving from the Soviet Union). Due to an adamant letter from Khrushchev (promising the removal of the missiles if the United States promised not to invade Cuba), the crisis was averted. Both countries agreed to the demands.
While Cuba still remains Communist, it is interesting to see the issues today take a totally different form in regard to security (while the issues of identity remain the same). In other words, Cuba is still a proud Communist country, and the United States is still a proud democracy, but the specific security issues have changed from missiles to illegal immigration. Obviously, we have to admit that there are some Cuban citizens who were/are unhappy with the rules of their Communist government. Many were so unhappy that they risked their lives to travel across the divide from the island of Cuba to the Florida Keys (or other areas) on makeshift boats and rafts in order to escape oppression. This happened mainly during the administration of Fidel Castro and continues to happen today. A good, very specific example of this kind of immigration was the Mariel boatlift of the 1980s which was a mass influx of these immigrants. From the expatriate Cuban standpoint, these immigrants are refugees escaping oppression. They are trying to GAIN security. From the United States' perspective, these immigrants are illegal aliens who enter our country and THREATEN our security.
I have personal experience with this, growing up in Fort Lauderdale and Miami, Florida. There is no doubt of the influx of Cuban immigrants (both legal and illegal) in that area of the country. I sat in class with many of them and learned their plights. Until these two systems of government learn to coexist, I'm afraid there will always be tensions between us. Further, we will all continue to link identity and security. Ironically, it is Kennedy who gives us the best idea to remain optimistic. Even though Kennedy's quote is about China, the entire idea is pertinent to your question:
The Chinese use two brush strokes to write the word 'crisis.' One brush stroke stands for danger; the other for opportunity. In a crisis, be aware of the danger--but recognize the opportunity.