This article does a few things that make it seem poorly written. First, there's the sentence "But, analysing a particular colossal number and trying to determine whether it possesses prime factors is colossally difficult."
No, it's not difficult to determine whether a large number has prime factors. The answer to that question is yes. Determining which prime numbers are factors is extremely hard, and what they should have said.
Second, they use an example from GCHQ's public key cryptography work rather than the more relevant NSA work on differential cryptanalysis, which became public knowledge in the late 1980s, was discovered by IBM in 1974, and which the NSA was already "well aware of" in 1974 [0].
Second, they use an example from GCHQ's public key cryptography work rather than the more relevant NSA work on differential cryptanalysis, which became public knowledge in the late 1980s, was discovered by IBM in 1974, and which the NSA was already "well aware of" in 1974 [0].
[0]: https://en.wikipedia.org/wiki/Differential_cryptanalysis#His...