A digital signature scheme $\mathrm{mCFS}^{\mathrm{QC{-}LDPC}}$ based on $\mathrm{QC}$-$\mathrm{LDPC}$ codes

We propose to replace the Goppa codes with $\mathrm{QC}$-$\mathrm{LDPC}$ codes in the digital signature scheme $\mathrm{mCFS}_c$. With this modification, we obtain a considerable reduction ($50$ times on average) of the public key sizes without losing security. Our theoretical security model is the same as for the $\mathrm{mCFS}$ scheme. We discuss the possibility of applying some known methods to attacks on the hash function and on the public/private key setting. We also propose a set of parameters for several security levels; for example, we can get $80$ bits of security with the public key size $\approx 1.82$ KB, $128$ bits of security with $\approx 3.87$ KB, and $256$ bits of security with $\approx 13.88$ KB.