Cryptology ePrint Archive: Report 2013/213

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 being 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. It is well known that the process of generating random numbers can be mathematically realized with Pseudorandom Number Generator (PRNG) for cryptographic schemes in traditional leakage-free context without affecting their practical security of mathematical realization. However, it is unknown that whether one can use PRNG to mathematically realize this process for leakage resilient cryptographic schemes without affecting practical security of mathematical realization.

Our results show that if one directly uses PRNG to mathematically realize this process, some leakage resilient cryptographic schemes may not be practical secure any more. Furthermore, we give out a suggested way to mathematically realize this process with exponentially hard PRNG and extractor without affecting practical security of mathematical realization of a leakage resilient 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 when the process of generating random numbers is mathematically realized by PRNG.

Category / Keywords: Leakage Resilient Cryptography, Mathematical Realization.

Date: received 12 Apr 2013, last revised 10 Feb 2014

Contact author: guangjunfan at 163 com

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Version: 20140211:021713 (All versions of this report)

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