We leverage the Gibbs inequality and its natural generalization to R\'enyi entropies to derive closed-form parametric expressions of the optimal lower bounds of $\rho$th-order guessing entropy (guessing moment) of a secret taking values on a finite set, in terms of the R\'enyi-Arimoto $\alpha$-entropy. This is carried out in an non-asymptotic regime when side information may be available. The resulting bounds yield a theoretical solution to a fundamental problem in side-channel analysis: Ensure that an adversary will not gain much guessing advantage when the leakage information is sufficiently weakened by proper countermeasures in a given cryptographic implementation. Practical evaluation for classical leakage models show that the proposed bounds greatly improve previous ones for analyzing the capability of an adversary to perform side-channel attacks.

翻译：我们利用Gibbs不等式及其向Rényi熵的自然推广，推导了在有限取值集合上秘密变量的$\rho$阶猜测熵（猜测矩）最优下界的闭式参数化表达式，该表达式以Rényi-Arimoto $\alpha$-熵给出。这一推导在可能存在辅助信息的非渐近场景中完成。所得边界为侧信道分析中的基本问题提供了理论解：确保当给定密码实现通过适当对策充分削弱泄漏信息时，攻击者将无法获得显著的猜测优势。针对经典泄漏模型的实践评估表明，所提出的边界相比此前方法，在分析攻击者执行侧信道攻击能力方面实现了大幅改进。