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

Abstract

Recently, Ivanov et al. proposed a new approach to construct code-based cryptosystems, namely the $ {\sf IKKR} $ 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 $ {\sf IKKR} $ 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 $ {\sf IKKR} $-PKE. This paper aims to discuss the practical security of the $ {\sf IKKR} $-PKE. In particular, we describe the weaknesses in the design of the public key used in the $ {\sf IKKR} $-PKE. We exploit such weaknesses and propose two attacks to recover the plaintext in the $ {\sf IKKR} $-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.