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Efficient implementation of generalized Maiorana–McFarland class of cryptographic functions

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Abstract

Recently, a class of cryptographic Boolean functions called generalized Maiorana–McFarland (GMM) functions was proposed in Zhang and Pasalic (IEEE Trans Inf Theory 60(10):6681–6695, 2014). In particular, it was demonstrated that certain subclasses within the GMM class satisfy all the relevant cryptographic criteria including a good resistance to (fast) algebraic cryptanalysis. However, the issue of efficient hardware implementation, which is essentially of crucial importance when such a function is used as a filtering function in certain stream cipher encryption schemes, has not been addressed in Zhang and Pasalic (2014). In this article, we analyze the complexity of hardware implementation of these subclasses and provide some exact estimates in terms of the number of elementary circuits needed. It turns out that these classes of cryptographically strong functions are also characterized with a very low hardware implementation cost, making these functions attractive candidates for the use in certain stream cipher schemes.

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Notes

  1. Note that it is not clear how a low degree for \(f_i\) affects the vulnerability of the cipher, though the implementation cost is clearly reduced by that.

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Authors and Affiliations

  1. FAMNIT and IAM, University of Primorska, Koper, Slovenia

    Enes Pasalic

  2. School of Computer Science and Engineering, NTU, Singapore, Singapore

    Anupam Chattopadhyay

  3. ISN Laboratory, Xidian University, Xi’an, 710071, China

    WeiGuo Zhang

  4. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    WeiGuo Zhang

Authors
  1. Enes Pasalic
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  2. Anupam Chattopadhyay
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  3. WeiGuo Zhang
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Corresponding author

Correspondence to Anupam Chattopadhyay.

Additional information

This work was supported by a fellowship of the German Academic Exchange Service. This work was supported in part by the National Natural Science Foundation of China under Grants 61373008 and 61672414.

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Pasalic, E., Chattopadhyay, A. & Zhang, W. Efficient implementation of generalized Maiorana–McFarland class of cryptographic functions. J Cryptogr Eng 7, 287–295 (2017). https://doi.org/10.1007/s13389-016-0139-0

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  • DOI: https://doi.org/10.1007/s13389-016-0139-0

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