Polynomial Time Attack on Wild McEliece Over Quadratic Extensions
This work addresses a critical vulnerability in post-quantum cryptography for users relying on this specific variant, representing an incremental advance in cryptanalysis.
The authors tackled the security of the McEliece cryptosystem based on Wild Goppa codes over quadratic extensions by developing a polynomial-time structural attack that exploits the distinguishability of these codes from random ones to reveal their secret algebraic structure through a filtration of nested subcodes.
We present a polynomial time structural attack against the McEliece system based on Wild Goppa codes from a quadratic finite field extension. This attack uses the fact that such codes can be distinguished from random codes to compute some filtration, that is to say a family of nested subcodes which will reveal their secret algebraic description.