Soft McEliece: MDPC code-based McEliece cryptosystems with very compact keys through real-valued intentional errors
This work addresses the key size issue in post-quantum cryptography for secure communication, representing an incremental improvement over prior MDPC-based systems.
The authors tackled the problem of large public key sizes in McEliece cryptosystems based on MDPC codes by introducing real-valued intentional errors and soft-decision decoding, achieving up to a 25% reduction in key size while maintaining security.
We propose to use real-valued errors instead of classical bit flipping intentional errors in the McEliece cryptosystem based on moderate-density parity-check (MDPC) codes. This allows to exploit the error correcting capability of these codes to the utmost, by using soft-decision iterative decoding algorithms instead of hard-decision bit flipping decoders. However, soft reliability values resulting from the use of real-valued noise can also be exploited by attackers. We devise new attack procedures aimed at this, and compute the relevant work factors and security levels. We show that, for a fixed security level, these new systems achieve the shortest public key sizes ever reached, with a reduction up to 25% with respect to previous proposals.