New weakness in the key-scheduling algorithm of RC4

In a key scheduling algorithm (KSA) of stream ciphers, a secret key is expanded into a large initial state. An internal state reconstruction method is known as a general attack against stream ciphers; it recovers the initial state from a given pair of plaintext and ciphertext more efficiently than exhaustive key search. If the method succeeds, then it is desirable that the inverse of KSA is infeasible in order to avoid the leakage of the secret key information. This paper shows that it is easy to compute a secret key from an initial state of RC4. We propose a method to recover an l-bit secret key from only the first l bits of the initial state of RC4 using linear equations with the time complexity less than that of one execution of KSA. It can recover the secret keys of which number is 2(103.6) when the size of the secret key is 128 bits. That is, the 128-bit secret key can be recovered with a high probability when the first 128 bits of the initial state are determined using the internal state reconstruction method.