Actually, the movie (and book) got the name from the NATO terminology for the Soviets' new super-fighter. The project that resulted in this aircraft began in the late eighties. Of course, back in the Cold War intelligence reports from the USSR were patchy, and nobody was quite certain whether the documentation they were seeing referred to conceptual designs for a future fighter, or to an actual flying prototype. It was just on the edge of plausibility that there was a real Firefox out there, not just a prototype.

It was the same in America: design and planning work on what became the F-22 began in 1981.