The “H-coefficient technique” was introduced in 1990 and 1991 in Patarin (1991, 2025). Since then, it has been used many times to prove various results on pseudo-random functions and pseudo-random permutations (Chen et al. 2014; Gilbert and Minier 2001; Pieprzyk 1991; Yun et al. 2011). Recently, it has also been used on key-alternating ciphers (Even-Mansour), cf. Chen and Steinberger (2014) for example. We will use this technique in Chap.  4 for the specific cases of \(\varPsi ^3\) , \(\varPsi ^4\) , and then in many proofs of security of this book. In this chapter, in Sect. 3.1, we will present the “H-coefficient technique”, in a general way (not only for \(\varPsi ^k\) ), with different formulations when we study different cryptographic attacks (known-plaintext attacks, chosen-plaintext attacks, etc.). In Sect. 3.4, we will present an example with the exact values of the H coefficient on \(\varPsi ^k\) with \(q=2\) plaintext/ciphertext pairs. Finally, in Sect. 3.5, we will present two simple and powerful composition theorems based on H-coefficient method in CCA.