AbstractIn lightweight cryptographic primitives, round functions with simple operations XOR, modular addition, and shift (or rotation) are widely used nowadays. Among these ciphers, TEA and XTEA are two famous lightweight block ciphers. At AFRICACRYPT 2012, Jiazhe Chen, Meiqin Wang, and Bart Preneel proposed a method to establish impossible differential distinguishers for TEA and XTEA. At FSE 2012, with similar approach, Andrey Bogdanov and Meiqin Wang identified zero correlation linear distinguishers for TEA and XTEA. We find similarities in these two kinds of distinguishers and then probe into the deeper relationship between them. In this paper, we extend the TEA and XTEA to a more general TEA family‐type ciphers and study the impossible differential distinguishers and zero correlation linear distinguishers for this kind of ciphers. More specifically, with the methods proposed in these two references earlier, firstly, we prove the longest lengths for impossible differential distinguishers and zero correlation linear distinguishers on TEA family‐type ciphers. Secondly, the number of longest impossible differential distinguishers and zero correlation linear distinguishers are calculated respectively. Then, the specific forms of their input and output differences (or linear masks) are given. Thirdly, a dual property is proposed to demonstrate the deeper relationship between these two kinds of distinguishers. Finally, we give some suggestions for algorithm designers on how to shorten these two kinds of distinguishers for TEA family‐type ciphers. Copyright © 2017 John Wiley & Sons, Ltd.