On the Impacts of Mathematical Realization over Practical Security of Leakage Resilient Cryptographic Schemes

In real world, in order to transform an abstract and generic cryptographic scheme into actual physical implementation, one usually undergoes two processes: mathematical realization at algorithmic level and physical realization at implementation level. In black-box model (i.e. leakage-free setting), a cryptographic scheme can be mathematically realized without affecting its theoretical security as long as the mathematical components meet the required cryptographic properties. However, up to now, no previous work formally show that whether one can mathematically realize a leakage resilient cryptographic scheme in existent ways without affecting its practical security. Our results give a negative answer to this important question by introducing attacks against several kinds of mathematical realization of a practical leakage resilient cryptographic scheme. To be specific, there may exist a big gap between the theoretical tolerance leakage bits number and the practical tolerance leakage bits number of the same leakage resilient cryptographic scheme if the mathematical components in the mathematical realization are not provably secure in leakage setting.