Dependence in IV-Related Bytes of RC4 Key Enhances Vulnerabilities in WPA

Abstract

The first three bytes of the RC4 key in WPA are public as they are derived from the public parameter IV, and this derivation leads to a strong mutual dependence between the first two bytes of the RC4 key. In this paper, we provide a disciplined study of RC4 biases resulting specifically in such a scenario. Motivated by the work of AlFardan et al. (2013), we first prove the interesting sawtooth distribution of the first byte in WPA and the similar nature for the biases in the initial keystream bytes towards zero. As we note, this sawtooth characteristics of these biases surface due to the dependence of the first two bytes of the RC4 key in WPA, both derived from the same byte of the IV. Our result on the nature of the first keystream byte provides a significantly improved distinguisher for RC4 used in WPA than what had been presented by Sepehrdad et al. (2011–2012). Further, we revisit the correlation of initial keystream bytes in WPA to the first three bytes of the RC4 key. As these bytes are known from the IV, one can obtain new as well as significantly improved biases in WPA than the absolute biases exploited earlier by AlFardan et al. or Isobe et al. We notice that the correlations of the keystream bytes with publicly known IV values of WPA potentially strengthen the practical plaintext recovery attack on the protocol.