How TKIP Induces Biases of Internal States of Generic RC4

RC4, designed by Rivest, is widely used including WPA, which is one of the security protocols for IEEE 802.11 wireless standard. The first 3-byte RC4 keys in WPA generated by IV are known since IV can be obtained by observing a packet. In 2014, Sen Gupta et al. found linear correlations between the keystream byte and known RC4 key bytes. In 2015, Our previous work extended linear correlations to include unknown internal states as well as the keystream byte and known RC4 key bytes. They found more than 150 linear correlations experimentally, and proved only 6 cases theoretically. In this paper, we will provide theoretical proof of 15 cases out of their unproven linear correlations. These theoretical results demonstrated how TKIP key generation procedure in WPA induces biases on internal states different from generic RC4.