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

*Guangjun Fan and Yongbin Zhou and F.-X. Standaert and Dengguo Feng *

**Abstract: **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 the former process, the abstract and generic cryptographic scheme is transformed into an exact and specific mathematical scheme, while in the latter process the output of mathematical realization is being transformed into a physical cryptographic module runs as a piece of software, or hardware, or combination of both. In black-box model (i.e. leakage-free setting), a cryptographic scheme can be mathematically realized without affecting its both theoretical security and practical security of mathematical realization as long as the mathematical components meet the required cryptographic properties. However, it is unknown that whether one can mathematically realize a leakage resilient cryptographic scheme in existent ways without affecting its practical security of mathematical realization.

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. Our results show the big gap between theoretical security of leakage resilient cryptographic scheme and practical security of mathematical realization of the same scheme. Therefore, on one hand, we suggest that all (practical) leakage resilient cryptographic schemes should at least come with a kind of mathematical realization whose practical security can be guaranteed. On the other hand, our results inspire cryptographers to design advanced leakage resilient cryptographic schemes whose practical security of mathematical realization is independent of details of the mathematical realization.

**Category / Keywords: **Physical Attacks, Leakage Resilient Cryptography, Mathematical Realization, Physical Realization.

**Date: **received 12 Apr 2013, last revised 4 Jun 2014

**Contact author: **guangjunfan at 163 com

**Available format(s): **PDF | BibTeX Citation

**Version: **20140604:070618 (All versions of this report)

**Short URL: **ia.cr/2013/213

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