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Analysis & Design of Efficient Cryptographic Systems

Michael Lehmann
Fachhochschule Nordwestschweiz, Hochschule fur Technik
Fachhochschule Nordwestschweiz, Hochschule fur Technik, Project report, 2012

@article{lehmann2012analysis,

   title={Analysis & Design of Efficient Cryptographic Systems},

   author={Lehmann, Michael},

   year={2012}

}

Grain-128 is a stream cipher, which was proposed in the course of the eSTREAM project. This stream cipher is already in use today, for example in RFID applications. Therefore, the security of Grain-128 is of great interest. The Conditional Differential Analysis, the Static Cube Attack and the Dynamic Cube Attack are methods for the cryptanalysis of stream ciphers. The Static Cube Attack does not give any viable results on Grain-128, the Dynamic Cube Attack, however, delivers a feasible full recovery attack on the cipher for 207 initialisation rounds and breaks the full Grain-128 on a large subset of weak keys. Grain-128a is a new, allegedly improved version of this stream cipher, which should prevent or impede the cryptanalysis, respectively. This claim is to be examined. Furthermore, it is to be found to what extent that the computation on a GPU improves the time complexity of the Conditional Differential Analysis compared to the CPU implementation. Those attacks highly depend on the algebraic expressions of the key stream. The expressions grow by calculating a relatively simple function many times. In this way, it is tried to prevent such attacks. The comparison of Grain-128 and Grain-128a shows that not only the order of the symbolic expressions, but also the number of terms of high order grows significantly faster with the new version of the cipher. Therefore, it is found the Dynamic Cube Attack is very unlikely to deliver viable results. On the other hand, the Conditional Differential Analysis gives a distinguisher up to round 177. Moreover, the implementation on the GPU reduces the time complexity by a factor of approximately 19.
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