The software-efficient stream cipher HC-256 was proposed by Wu at FSE 2004. Due to its impressive performance, the cipher was also a well-received entrant to the ECRYPT eSTREAM competition. The closely related stream cipher HC-128, also designed by Wu, went on to find a place in the final portfolio of the eSTREAM contest. The cipher HC-256 is word-oriented, with 32 bits in each word, and uses a 256-bit key and a 256-bit IV. Since HC-256 was published in 2004, barring a cachetiming analysis of unprotected implementations, there has not been any attack on the cipher. This paper makes two contributions. First, we build a class of distinguishers on HC-256, each of which requires testing the validity of about 2276.8 linear equations involving binary keystream variables. Thereby, our attacks improve the data complexity of the hitherto best-known distinguisher (presented by the designer along with the specifications of the cipher) by a factor of about 12. We also present another observatio...