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Making random permutations from physically unclonable constants

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Abstract

The recent availability of reliable schemes for physically unclonable constants (PUC) opens interesting possibilities in the field of security. In this paper, we explore the possibility of using PUCs to embed in a chip random permutations to be used, for example, as building blocks in cryptographic constructions such as sponge functions, substitution–permutation networks, and so on. We show that the most difficult part is the generation of random integers using as the only randomness source the bit-string produced by the PUC. In order to solve the integer generation problem, we propose a partial rejection method that allows the designer to trade-off between entropy and efficiency. The results show that the proposed schemes can be implemented with reasonable complexity.

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Notes

  1. There is a nomenclature clash here. What we call “permutation” in this paper is called “substitution” in the context of a substitution–permutation network (SPN). In the same context, “permutation” denotes a permutation of the bits of the bit word.

  2. We distinguish probability (32) from the corresponding for the generation of integers in (4) by adding in \(p_{N}^{(\pi )}{}\) a “\(\pi \)” for “permutation.”

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  1. University of Udine – DPIA, Via delle Scienze 206, 33100, Udine, Italy

    Riccardo Bernardini & Roberto Rinaldo

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  1. Riccardo Bernardini
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  2. Roberto Rinaldo
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Correspondence to Riccardo Bernardini.

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Bernardini, R., Rinaldo, R. Making random permutations from physically unclonable constants. Int. J. Inf. Secur. 16, 249–261 (2017). https://doi.org/10.1007/s10207-016-0324-2

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