Further Results of the Cryptographic Properties on the Butterfly Structures

Recently, a new structure called butterfly introduced by Perrin et at. is attractive for that it has very good cryptographic properties: the differential uniformity is at most equal to 4 and algebraic degree is also very high when exponent $e=3$. It is conjecture that the nonlinearity is also optimal for every odd $k$, which was proposed as a open problem. In this paper, we further study the butterfly structures and show that these structure with exponent $e=2^i+1$ have also very good cryptographic properties. More importantly, we prove in theory the nonlinearity is optimal for every odd $k$, which completely solve the open problem. Finally, we study the butter structures with trivial coefficient and show these butterflies have also optimal nonlinearity. Furthermore, we show that the closed butterflies with trivial coefficient are bijective as well, which also can be used to serve as a cryptographic primitive.Comment: 20 page

On the Derivative Imbalance and Ambiguity of Functions

In 2007, Carlet and Ding introduced two parameters, denoted by $Nb_F$ and $NB_F$, quantifying respectively the balancedness of general functions $F$ between finite Abelian groups and the (global) balancedness of their derivatives $D_a F(x)=F(x+a)-F(x)$, $a\in G\setminus\{0\}$ (providing an indicator of the nonlinearity of the functions). These authors studied the properties and cryptographic significance of these two measures. They provided for S-boxes inequalities relating the nonlinearity $\mathcal{NL}(F)$ to $NB_F$, and obtained in particular an upper bound on the nonlinearity which unifies Sidelnikov-Chabaud-Vaudenay's bound and the covering radius bound. At the Workshop WCC 2009 and in its postproceedings in 2011, a further study of these parameters was made; in particular, the first parameter was applied to the functions $F+L$ where $L$ is affine, providing more nonlinearity parameters. In 2010, motivated by the study of Costas arrays, two parameters called ambiguity and deficiency were introduced by Panario \emph{et al.} for permutations over finite Abelian groups to measure the injectivity and surjectivity of the derivatives respectively. These authors also studied some fundamental properties and cryptographic significance of these two measures. Further studies followed without that the second pair of parameters be compared to the first one. In the present paper, we observe that ambiguity is the same parameter as $NB_F$, up to additive and multiplicative constants (i.e. up to rescaling). We make the necessary work of comparison and unification of the results on $NB_F$, respectively on ambiguity, which have been obtained in the five papers devoted to these parameters. We generalize some known results to any Abelian groups and we more importantly derive many new results on these parameters

A Recursive Construction of Permutation Polynomials over Fq2\mathbb{F}_{q^2} with Odd Characteristic from R\'{e}dei Functions

In this paper, we construct two classes of permutation polynomials over $\mathbb{F}_{q^2}$ with odd characteristic from rational R\'{e}dei functions. A complete characterization of their compositional inverses is also given. These permutation polynomials can be generated recursively. As a consequence, we can generate recursively permutation polynomials with arbitrary number of terms. More importantly, the conditions of these polynomials being permutations are very easy to characterize. For wide applications in practice, several classes of permutation binomials and trinomials are given. With the help of a computer, we find that the number of permutation polynomials of these types is very large

Improved Constant-Sized Polynomial Commitment Schemes Without Trusted Setup

Argument systems are a fundamental ingredient in many cryptographic constructions. The best-performing argument systems to date largely rely on a trusted setup, which is undesirable in trust-minimized applications. While transparent argument systems avoid this trust assumption, they have historically been inefficient, typically exhibiting polylogarithmic proof sizes compared to their trusted counterparts. In 2023, Arun et al. (PKC 2023) constructed the first transparent constant-sized polynomial commitment scheme (PCS), leading to transparent constant-sized arguments. However, the evaluation proof still comprises 66 group elements in a group of unknown order (GUO), rendering it rather impractical. In this work, we address this challenge by presenting a set of novel batching and aggregation techniques tailored for proofs of knowledge of ranges in GUOs. These techniques may also be of independent interest and are readily applicable to enhance and shorten other existing schemes in GUOs. Consequently, by applying these techniques, we immediately achieve an improved PCS with an evaluation proof consisting of only 10 group elements---an impressive 85% reduction. To our knowledge, this represents the shortest PCS in the transparent setting. Thus compiling known information-theoretic proof systems using our improved PCS yields highly compact transparent argument systems when instantiated in a class group, which is more practical than prior constant-sized schemes

Involutory Differentially 4-Uniform Permutations from Known Constructions

Substitution box (S-box) is an important component of block ciphers for providing confusion into the cryptosystems. The functions used as S-boxes should have low differential uniformity, high nonlinearity and high algebraic degree. Due to the lack of knowledge on the existence of APN permutations over $\mathbb{F}_{2^{2k}}$, which have the lowest differential uniformity, when $k>3$, they are often constructed from differentially 4-uniform permutations. Up to now, many infinite families of such functions have been constructed. Besides, the less cost of hardware implementation of S-boxes is also an important criterion in the design of block ciphers. If the S-box is an involution, which means that the compositional inverse of the permutation is itself, then the implementation cost for its inverse is saved. The same hardware circuit can be used for both encryption and decryption, which is an advantage in hardware implementation. In this paper, we investigate all the differentially 4-uniform permutations that are known in the literature and determine whether they can be involutory. We found that some involutory differentially 4-uniform permutations with high nonlinearity and algebraic degree can be given from these known constructions

WristSketcher: Creating Dynamic Sketches in AR with a Sensing Wristband

Restricted by the limited interaction area of native AR glasses (e.g., touch bars), it is challenging to create sketches in AR glasses. Recent works have attempted to use mobile devices (e.g., tablets) or mid-air bare-hand gestures to expand the interactive spaces and can work as the 2D/3D sketching input interfaces for AR glasses. Between them, mobile devices allow for accurate sketching but are often heavy to carry, while sketching with bare hands is zero-burden but can be inaccurate due to arm instability. In addition, mid-air bare-hand sketching can easily lead to social misunderstandings and its prolonged use can cause arm fatigue. As a new attempt, in this work, we present WristSketcher, a new AR system based on a flexible sensing wristband for creating 2D dynamic sketches, featuring an almost zero-burden authoring model for accurate and comfortable sketch creation in real-world scenarios. Specifically, we have streamlined the interaction space from the mid-air to the surface of a lightweight sensing wristband, and implemented AR sketching and associated interaction commands by developing a gesture recognition method based on the sensing pressure points on the wristband. The set of interactive gestures used by our WristSketcher is determined by a heuristic study on user preferences. Moreover, we endow our WristSketcher with the ability of animation creation, allowing it to create dynamic and expressive sketches. Experimental results demonstrate that our WristSketcher i) faithfully recognizes users' gesture interactions with a high accuracy of 96.0%; ii) achieves higher sketching accuracy than Freehand sketching; iii) achieves high user satisfaction in ease of use, usability and functionality; and iv) shows innovation potentials in art creation, memory aids, and entertainment applications

WGCNA and molecular docking identify hub genes for cardiac aging

BackgroundCardiac aging and ageing-related cardiovascular diseases remain increase medical and social burden. Discovering the molecular mechanisms associated with cardiac aging is expected to provide new perspectives for delaying aging and related disease treatment.MethodsThe samples in GEO database were divided into older group and younger group based on age. Age-associated differentially expressed genes (DEGs) were identified by limma package. Gene modules significantly associated with age were mined using weighted gene co-expression network analysis (WGCNA). Protein-protein interaction networks (PPI) networks were developed using genes within modules, and topological analysis on the networks was performed to identify hub genes in cardiac aging. Pearson correlation was used to analyze the association among hub genes and immune and immune-related pathways. Molecular docking of hub genes and the anti-aging drug Sirolimus was performed to explore the potential role of hub genes in treating cardiac aging.ResultsWe found a generally negative correlation between age and immunity, with a significant negative correlation between age and b_cell_receptor_signaling_pathway, fc_gamma_r_mediated_phagocytosis, chemokine signaling pathway, t-cell receptor signaling pathway, toll_like_receptor_signaling_pathway, and jak_stat_signaling_pathway, respectively. Finally, 10 cardiac aging-related hub genes including LCP2, PTPRC, RAC2, CD48, CD68, CCR2, CCL2, IL10, CCL5 and IGF1 were identified. 10-hub genes were closely associated with age and immune-related pathways. There was a strong binding interaction between Sirolimus-CCR2. CCR2 may be a key target for Sirolimus in the treatment of cardiac aging.ConclusionThe 10 hub genes may be potential therapeutic targets for cardiac aging, and our study provided new ideas for the treatment of cardiac aging

Relationship between Central Arterial Stiffness and Insulin Resistance in Chinese Community-Dwelling Population without Diabetes Mellitus

Objective. Insulin resistance (IR) is a pathological condition present not only in patients with type 2 diabetes mellitus (DM), but also in community-dwelling population without DM. Both central arterial stiffness and IR are closely correlated with cardiovascular morbidity and mortality. The relationship between central arterial stiffness and IR has not been described in Chinese community-dwelling population without DM. The current analysis was designed to investigate the relationship between central arterial stiffness and IR in Chinese community-dwelling population without DM. Methods. There were 1150 participants fully assessed for not only homeostasis model assessment of insulin resistance (HOMA-IR) but also carotid-femoral pulse wave velocity (cfPWV). Results. Median age was 39 (18–80) years, and 69.7% were men. Bivariate correlation analysis showed that cfPWV was significantly related to HOMA-IR (P<0.05). Logistic regression analysis indicated that cfPWV was independently associated with HOMA-IR (P<0.05). Conclusions. This community-based analysis testified that the relationship between central arterial stiffness and IR was evident as early as during nondiabetic stage. Early interventions in Chinese community-dwelling population without DM to improve the IR are also important in the prevention of cardiovascular diseases