Mutual information as an information-theoretic tool has been frequently used in many security analyses. Ch ́erisey et al. used Shannon information- theoretic tools to establish some universal inequalities between the probabil- ity of success of a side-channel attack and the minimum number of queries to reach a given success rate. α-information theory is a generalization of clas- sic information-theoretic tools which seems more persuasive in a side-channel context. Such metrics include R ́enyi’s α-entropy, α-divergence, Arimoto’s con- ditional α-entropy, Sibson’s α-information, etc. In this work, we aim at extending the work of Ch ́erisey et al. to α-information quantities depending on a parameter α. A conditional version of Sibson’s α- information is defined using a simple closed-form expression. Our definition of conditional α-information satisfies important properties such as consistency, uni- form expansion, and data processing inequalities, while other previous proposals do not satisfy all of these properties. Based on our proposal and a generalized Fano inequality, we extend the case α = 1 of previous works to any α > 0, and obtain sharp universal upper bounds for the probability of success of any type of side-channel attack. It turns out the bound is improved as α increases, and it is already very tight when α = 2.