Abstract. We introduce a truncated addition operation on pairs of N -bit binary numbers that interpolates between ordinary addition mod and bitwise addition in . We use truncated addition to analyze hash functions that are built from the bit operations add, rotate, and xor, such as Blake , Skein , and Cubehash . Any ARX algorithm can be approximated by replacing ordinary addition with truncated addition, and we define a metric on such algorithms which we call the sensitivity . This metric measures the smallest approximation agreeing with the full algorithm a statistically useful portion of the time (we use ). Because truncated addition greatly reduces the complexity of the non-linear operation in ARX algorithms, the approximated algorithms are more susceptible to both collision and pre-image attacks, and we outline a potential collision attack explicitly. We particularize some of these observations to the Skein hash function.