Polynomial-time plaintext recovery attacks on the IKKR code-based cryptosystems

Recently, Ivanov et al. proposed a new approach to construct code-based cryptosystems, namely the \begin{document}$ {\sf IKKR} $\end{document} public-key encryptions (PKE) in the International Workshop on Code-Based Cryptography (CBCrypto 2020) [ 9 ]. Unlike the usual construction in code-based encryption schemes which has restrictions on the Hamming weight of the error introduced into the ciphertext, the \begin{document}$ {\sf IKKR} $\end{document} approach allows error vectors of arbitrary weight being introduced into the ciphertext. Using this new approach, Ivanov et al. constructed two cryptosystems, namely the modified and the upgraded \begin{document}$ {\sf IKKR} $\end{document} -PKE. This paper aims to discuss the practical security of the \begin{document}$ {\sf IKKR} $\end{document} -PKE. In particular, we describe the weaknesses in the design of the public key used in the \begin{document}$ {\sf IKKR} $\end{document} -PKE. We exploit such weaknesses and propose two attacks to recover the plaintext in the \begin{document}$ {\sf IKKR} $\end{document} -PKE. The approach of our first attack is similar to the LCKN attack [ 12 ], whilst our second attack is more efficient than the LCKN attack. Our experimental results show that we can recover the plaintext from a given ciphertext in less than 176 milliseconds for schemes based on random Goppa codes and BCH codes.