What's the name of this cipher? And how can it be broken? Assuming that:


SHA-256 and SHA-512 are random and irreversible
the output appended to some random and long enough secret is just as random as any other data and will produce values that are just as hard to guess


Then one can conclude that a cipher can be constructed using those hash functions in the following manner:


let state and key both be 32 or 64 byte values
initialize state with a random IV and key with a random key
make v equal the hash of state + key, xor block of plaintext withv
update state with the cipher produced
repeat until all plaintext is processed
to decrypt do the same, but update the state with the cipher text


Now the question is, does such a cipher exist? Is it possible to discover the plaintext given a ciphertext without brute-forcing the key? If so, what techniques could be used for that?
This would appear to be CFB mode, only using a hash function (with a secret key as part of the input), rather than a block cipher.

As such, assuming that the hash function with the partially secret input acts as a random Oracle, this provides privacy.  However, it doesn't provide integrity (that is, the attacker can modify the ciphertext, and the resulting ciphertext will decrypt, and in fact produce semipredictable changes to the plaintext), and will probably end up being slower than a more conventional encryption method.