Klimov and Shamir proposed a new class of simple cryptographic primitives named T-functions. For two concrete proposals based on the squaring operation, a single word T-function and a previously unbroken multi-word T-function with a 256-bit state, we describe an efficient distinguishing attack having a 2³² data complexity. Furthermore, Hong et al. recently proposed two fully specified stream ciphers, consisting of multi-word T-functions with 128-bit states and filtering functions. We describe distinguishing attacks having a 2²² and a 2³⁴ data complexity, respectively. The attacks have been implemented.