The very complex modern approaches to cryptanalysis still borrow from the oldest attacks.
A simple substitution cipher is easily broken by frequency analysis - find the most common letter in the ciphertext and it'll probably be E in the plaintext. Nothing so simple would work today, but we often see vulnerabilities in cryptosystems due to pseudorandom number generators with inadequate entropy. It's the same basic principle (exploiting a lack of randomness to identify patterns in the ciphertext), albeit with vastly more mathematical sophistication. The NSA allegedly took advantage of this principle to deliberately weaken cryptosystems by promoting an intentionally weak PRNG.
frequency analysis works easily if you know the source language, i.e. English in this case, while entropy of the message is critical to cracking, complex approaches are not the only ones which are immune to attacks, for example simple ciphers like using a one time pad is mathematically impossible to crack.
A simple substitution cipher is easily broken by frequency analysis - find the most common letter in the ciphertext and it'll probably be E in the plaintext. Nothing so simple would work today, but we often see vulnerabilities in cryptosystems due to pseudorandom number generators with inadequate entropy. It's the same basic principle (exploiting a lack of randomness to identify patterns in the ciphertext), albeit with vastly more mathematical sophistication. The NSA allegedly took advantage of this principle to deliberately weaken cryptosystems by promoting an intentionally weak PRNG.
https://en.wikipedia.org/wiki/Dual_EC_DRBG