1. G known - how to decrypt Referring to this question: Basic attacks on McEliece; finding S and P (nobody answered)
Take a McEliece cryptosystem with public generator matrix $G′=SGP$ where $G$ is a generator matrix of a secret code with known fast decoding (not necessarily a Goppa code over $\mathbb F_2$), $S$ is random & non-singular and $P$ is a permutation.
Let's say an attacker Eve has a way to find $G$ from $G′$ but not $S$ or $P$.
How would Eve now continue the attack on a encrypted codeword $c=mSGP+e$?
2. How can an attacker get $m$ if an oracle tells him the error $e$?
So the attacker has the received garbled codeword $c = mG' + e = mSGP + e$ and knows $e$. how can he calculate $m$
a) for one special garbled codeword $c$?
b) for every new garbled codeword $c$ without solving a system of equations every time?
Thanks for your help!