Ciphertext-Only Attack on Linear Feedback Shift Register-Based Esmaeili-Gulliver Cryptosystem

Esmaeili and Gulliver recently proposed a secret key cryptosystem based on error-correcting codes in which a codeword modified by random insertions, deletions, and errors is used as a ciphertext. The secret keys used in this cryptosystem consist of random numbers generated by synchronized random number generators that are implemented using two distinct linear feedback shift registers (LFSRs) in each encryptor and decryptor, respectively. In this letter, we propose a ciphertext-only attack to break the Esmaeili-Gulliver cryptosystem based on LFSRs. The proposed attack requires
$O(n)$
consecutive ciphertexts, where
$n$
is the number of shift registers in the LFSR, which is the secret key size. The proposed attack consists of two steps, and the time complexity of the first step is linear in the secret key size while the second step is a polynomial-time algorithm.