Zero-Correlation Linear Cryptanalysis on SPARX-64

SPARX is a family of ARX-based block ciphers designed according to the long-trail strategy, which has 32-bit ARX-based SBoxes and has provable bounds against single-differential and single-linear cryptanalysis. Since its proposation, some third-party cryptanalysis methods have been presented. As far as we know, the best attacks against SPARX-64 covered 16 (out of 24) rounds. In this paper, we propose zero-correlation linear attacks on SPARX-64. At first, we construct some new zero-correlation linear distinguishers covering 14-round and 15-round SPARX-64. Then, 15,16,17 and 18-round versions can be attacked using multidimensional or multiple zero-correlation linear attack models, under DKP(distinct known plaintexts) settings. These are the best attacks against SPARX-64 up to now, regarding to the number of attacked rounds. Finally, we transform the zero-correlation distinguishers into integral ones using existing methods, which are also longer than the ones proposed by the designers.

Tips of tongues in the double standard family*

We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree two circle maps F λ : R / Z → R / Z defined by F λ ( x ) ≔ 2 x + a + b π sin ( 2 π x ) with λ ≔ ( a , b ) ∈ R / Z × ( 0 , 1 ) . We prove that if F λ ◦ n − i d has a zero of multiplicity three in R / Z , then there is a system of local coordinates ( α , β ) : W → R 2 defined in a neighborhood W of λ, such that α(λ) = β(λ) = 0 and F μ ◦ n − i d has a multiple zero with μ ∈ W if and only if β 3(μ) = α 2(μ). This shows that the tips of tongues are regular cusps.

Paradigm Structure in French Verbal Inflection

Verb inflectional morphology in French exhibits a range of complexities both in the structure of verb stems (stem-final latent consonant; vowel variation; stem-final nasal vowel ; suppletive forms ; etc.) and the organization of the inflectional system, marked for five grammatical categories: tense, aspect, mode, person and number, which in the majority of cases cannot be identified as a morphological or phonological unit. The main objective of this paper is to show that these morphosyntactic properties should be analyzed as a global affix, which operate within the same space, with no fixed order. This strategy has the advantage to 1) take into account all the verb syntactic properties, 2) avoid multiple zero suffixes, 3) avoid the use of different analyses depending on the verb class, 4) avoid non-productive and phonologically unmotivated rules of insertion of theme vowels as in [dorm-i-r-ons] dormirons, and epenthetic consonants as in [ku-d-r-ons] coudrons, 5) account for French verb inflectional system in a simple and more explanatory way than strictly segmental analyses without "motivated" processes, using massive suppletion and/or stems dependencies, where inflected verbal forms are related by arbitrary implicational associations or quantitative measures based on extensive memorization. This analysis also has the property of explaining by means of a very general principle (the Onset principle) the realization of a stem-final FC in front of the affixes 'ions' and 'iez' as in before any suffix beginning with an empty onset. The verb inflectional paradigmatic structures is captured within Construction Morphology (CxM) as stated in Booij, 2010.