Since their discovery in the late 90's, side-channel attacks have been shown to be a great threat to the security of cryptographic implementations. In addition to the standard inputs and outputs of an algorithm, these attacks exploit the leakages coming from its implementation. As this additional information was not taken into account during the design of the standard schemes, they have been broken. A wide range of countermeasures has then been developed to increase the resilience of cryptographic schemes against these attacks. However, these countermeasures do not prevent attacks, but rather make them more complex to perform. As a result, the actual security of a given implementation needs to be tested in practice. A way to assess the security of an algorithm is to actually attack it in two steps. The first one, that we denote by information extraction, focuses on the way to use the information arising from the leakages as optimally as possible. The second one, that we denote by information exploitation, focuses on the way to use computational power to mitigate the lack of side-channel information after its extraction. This thesis follows this strategy and tackles both of these problems in two parts. In the first one, we focus on the leakage exploitation in the case of block ciphers. In this respect, we present new key enumeration and rank estimation algorithms and study their applicability. In the second part, we focus on the leakage extraction against elliptic curve cryptography. In that purpose, we present a method to use most of the available information against scalar multiplication algorithms through horizontal differential power attacks. (FSA - Sciences de l'ingénieur) -- UCL, 2018