At SAC 2009, Gennaro and Halevi showed that a key wrapping scheme using a universal hash function and ECB mode (a HtECB scheme) is broken, and the security of a scheme based on a universal hash function and CBC mode (a HtCBC scheme) has been left as an open problem. In this paper, we first generalize classical notions of universal and uniform hash functions, and propose two new notions, where w...