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A Tag Based Encoding: An Efficient Encoding for Predicate Encryption in Prime Order Groups Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Pen and Paper Arguments for SIMON and SIMON-like Designs

verfasst von : Christof Beierle

Erschienen in: Security and Cryptography for Networks

Verlag: Springer International Publishing

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Abstract

In this work, we analyze the resistance of Simon-like ciphers against differential attacks without using computer-aided methods. In this context, we first define the notion of a Simon-like cipher as a generalization of the Simon design. For certain instances, we present a method for proving the resistance against differential attacks by upper bounding the probability of a differential characteristic by \(2^{-2T+2}\) where T denotes the number of rounds. Interestingly, if 2n denotes the block length, our result is sufficient in order to bound the probability by \(2^{-2n}\) for all full-round variants of Simon and Simeck. Thus, it guarantees security in a sense that, even having encryptions of the full codebook, one cannot expect a differential characteristic to hold. The important difference between previous works is that our proof can be verified by hand and thus contributes towards a better understanding of the design. However, it is to mention that we do not analyze the probability of multi-round differentials.
Although there are much better bounds known, especially for a high number of rounds, they are based on experimental search like using SAT/SMT solvers. While those results have already shown that Simon can be considered resistant against differential cryptanalysis, our argument gives more insights into the design itself. As far as we know, this work presents the first non-experimental security argument for full-round versions of several Simon-like instances.

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Vorheriges Kapitel How (Not) to Instantiate Ring-LWE
Nächstes Kapitel Bounded Size-Hiding Private Set Intersection
Fußnoten
1
As we only focus on the probabilities of differential characteristics and do not provide a full security analysis, this work should not be seen as a recommendation for using Simon. Some design choices are still unclear. To mention is the key schedule as one example.
 
2
\(\dagger \): This bit is only unknown if the bitlength is 16 bit (\(n = 16\)). Therefore, w.l.o.g. we assume this bit to be unknown. In the following, we may also consider certain bits to be unknown if the actual value does not matter for the proof.
 
3
\(\ddagger \): Of course, this bit is already equal to 1 if the bitlength n is greater than 16.
 
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Metadaten
Titel
Pen and Paper Arguments for SIMON and SIMON-like Designs
verfasst von
Christof Beierle
Copyright-Jahr
2016
Buch
Security and Cryptography for Networks

Print ISBN: 978-3-319-44617-2

Electronic ISBN: 978-3-319-44618-9

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-44618-9_23

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