There cannot be any data security without cryptography. Among cryptographic algorithms, "primitives" are those at the core of all protocols, and aim to provide crucial mathematical properties. For instance, a block "block cipher" (such as the AES) with a secret key should emulate a permutation picked uniformly at random. Should it not be the case, data security would be threatened. In practice, how do we ensure that the symmetric primitives we use every day deserve our trust? From standardization process to Kolmogorov complexity, we will look at various problems that were raised in recent years, in particular pertaining to the S-box of the latest symmetric standards from Russia.