On Linear Complementary Pairs of Algebraic Geometry Codes over Finite Fields

Linear complementary dual (LCD) codes and linear complementary pairs (LCP) of codes have been proposed for new applications as countermeasures against side-channel attacks (SCA) and fault injection attacks (FIA) in the context of direct sum masking (DSM). The countermeasure against FIA may lead to a vulnerability for SCA when the whole algorithm needs to be masked (in environments like smart cards). This led to a variant of the LCD and LCP problems, where several results have been obtained intensively for LCD codes, but only partial results have been derived for LCP codes. Given the gap between the thin results and their particular importance, this paper aims to reduce this by further studying the LCP of codes in special code families and, precisely, the characterisation and construction mechanism of LCP codes of algebraic geometry codes over finite fields. Notably, we propose constructing explicit LCP of codes from elliptic curves. Besides, we also study the security parameters of the derived LCP of codes $(\mathcal{C}, \mathcal{D})$ (notably for cyclic codes), which are given by the minimum distances $d(\mathcal{C})$ and $d(\mathcal{D}^\perp)$. Further, we show that for LCP algebraic geometry codes $(\mathcal{C},\mathcal{D})$, the dual code $\mathcal{C}^\perp$ is equivalent to $\mathcal{D}$ under some specific conditions we exhibit. Finally, we investigate whether MDS LCP of algebraic geometry codes exist (MDS codes are among the most important in coding theory due to their theoretical significance and practical interests). Construction schemes for obtaining LCD codes from any algebraic curve were given in 2018 by Mesnager, Tang and Qi in [``Complementary dual algebraic geometry codes", IEEE Trans. Inform Theory, vol. 64(4), 2390--3297, 2018]. To our knowledge, it is the first time LCP of algebraic geometry codes has been studied

Results on Rotation Symmetric Bent Functions

In this paper we analyze the combinatorial properties related to the Walsh spectra of rotation symmetric Boolean functions on even number of variables. These results are then applied in studying rotation symmetric bent functions

Reducing the Number of Homogeneous Linear Equations in Finding Annihilators

Given a Boolean function $f$ on $n$-variables, we find a reduced set of homogeneous linear equations by solving which one can decide whether there exist annihilators at degree $d$ or not. Using our method the size of the associated matrix becomes $\nu_f \times (\sum_{i=0}^{d} \binom{n}{i} - \mu_f)$, where, $\nu_f = |\{x | wt(x) > d, f(x) = 1\}|$ and $\mu_f = |\{x | wt(x) \leq d, f(x) = 1\}|$ and the time required to construct the matrix is same as the size of the matrix. This is a preprocessing step before the exact solution strategy (to decide on the existence of the annihilators) that requires to solve the set of homogeneous linear equations (basically to calculate the rank) and this can be improved when the number of variables and the number of equations are minimized. As the linear transformation on the input variables of the Boolean function keeps the degree of the annihilators invariant, our preprocessing step can be more efficiently applied if one can find an affine transformation over $f(x)$ to get $h(x) = f(Bx+b)$ such that $\mu_h = |\{x | h(x) = 1, wt(x) \leq d\}|$ is maximized (and in turn $\nu_h$ is minimized too). We present an efficient heuristic towards this. Our study also shows for what kind of Boolean functions the asymptotic reduction in the size of the matrix is possible and when the reduction is not asymptotic but constant

Hash Chains Sensornet: A Key Predistribution Scheme for Distributed Sensor Networks Using Nets and Hash Chains

Key management is an essential functionality for a security protocol; particularly for implementations to low cost devices of a distributed sensor networks (DSN)–a prototype of Internet of Things (IoT). Constraints in resources of the constituent devices of a low cost IoT (sensors of DSN) restricts implementations of computationally heavy public key cryptosystems. This led to adaptation of the novel key predistribution technique in symmetric key platform to efficiently tackle the problem of key management for these resource starved networks. Initial proposals use random graphs, later key predistribution schemes (KPS) exploit combinatorial approaches to assure essential design properties. Combinatorial designs like a (v, b, r, k)– configuration which forms a µ–CID are effective schemes to design KPS. A net in a vector space is a set of cosets of certain kind of subspaces called partial spread. A µ(v, b, r, k)–CID can be formed from a net. In this paper, we propose a key predistribution scheme for DSN, named as Sensornet, using a net. We observe that any deterministic KPS suffer from “smart attack” and hence devise a generic method to eliminate it. Resilience of a KPS can be improved by clever Hash Chains technique introduced by Bechkit et al. We improve our Sensornet to achieve Hash Chains Sensornet (HC(Sensornet)) by the applications of these two generic methods. Effectiveness of Sensornet and HC(Sensornet) in term of crucial metrics in comparison to other prominent schemes has been theoretically established

Comparative Evaluation of the Complementary and Alternative Medicine Therapy and Conventional Therapy Use for Musculoskeletal Disorders Management and Its Association with Job Satisfaction among Dentists of West India

ABSTRACTMusculoskeletal problems have become a significant issue in the profession of dentistry. There are currently no recommended effective disease-preventing and modifying remedies. High prevalence rates for musculoskeletal disorders (MSDs) among dentists have been reported in the literature. Complementary and alternative medicine can be helpful in managing and preventing the MSDs. The purpose of this study was to determine if dentists in the western part of India are using complementary and alternative medicine therapies for MSDs, and also to find if those who use complementary and alternative medicine therapies have greater job/career satisfaction compared to conventional therapy (CT) users. Dentists of western India registered under the Dental Council of India (N=2166) were recruited for the study. Data were analyzed using univariate and bivariate analyses and logistic regression. A response rate of 73% (n=1581) was obtained, of which 79% (n=1249) was suffering from MSDs. The use of complementary and alternative medicine or CT was reported by 90% (n=1124) of dentists with MSDs. Dentists using complementary and alternative medicine reported greater health (P<0.001) and carrier satisfaction (P<0.001) and were able to work as many hours they wanted (P<0.001) compared to CT users. Complementary and alternative medicine therapies may improve the quality of life and enhance job satisfaction for a dentist who suffers from MSDs

Sensornet A Key Predistribution Scheme for Distributed Sensors using Nets

Key management is an essential functionality for developing secure cryptosystems; particularly for implementations to low cost devices of a distributed sensor networks (DSN)-a prototype of Internet of Things (IoT). Low cost leads to constraints in various resources of constituent devices of a IoT (sensors of a DSN); thereby restricting implementations of computationally heavy public key cryptosystems. This leads to adaptation of the novel key predistribution trick in symmetric key platform to efficiently tackle the problem of key management for these resource starved networks. After a few initial proposals based on random graphs, most key predistribution schemes (KPS) use deterministic (combinatorial) approaches to assure essential design properties. Combinatorial designs like a (v, b, r, k)-configuration which forms a mu(v, b, r, k)-CID are effective schemes to design KPS (Lee and Stinson, 2005). A net in a vector space is a set of cosets of certain kind of subspaces called partial spread. A mu(v, b, r, k)-CID can be formed from a net. In this paper, we propose a key predistribution scheme for DSN, named as sensornet, using net. Effectiveness of sensornet in term of crucial metrics in comparison to other prominent schemes has been theoretically established

Applied Statistics Unit, Indian Statistical Institute,

Abstract. Given a Boolean function f on n-variables, we find a reduced set of homogeneous linear equations by solving which one can decide whether there exist annihilators at degree d or not. Using our method the size of the associated matrix becomes νf × ( �d � � n i=0 − µf), where, i νf = |{x|wt(x)&gt; d, f(x) = 1} | and µf = |{x|wt(x) ≤ d, f(x) = 1}| and the time required to construct the matrix is same as the size of the matrix. This is a preprocessing step before the exact solution strategy (to decide on the existence of the annihilators) that requires to solve the set of homogeneous linear equations (basically to calculate the rank) and this can be improved when the number of variables and the number of equations are minimized. As the linear transformation on the input variables of the Boolean function keeps the degree of the annihilators invariant, our preprocessing step can be more efficiently applied if one can find an affine transformation over f(x) to get h(x) = f(Bx + b) such that µh = |{x|h(x) = 1, wt(x) ≤ d} | is maximized (and in turn νh is minimized too). We present an efficient heuristic towards this. Our study also shows for what kind of Boolean functions the asymptotic reduction in the size of the matrix is possible and when the reduction is not asymptotic but constant

Basic theory in construction of boolean functions with maximum possible annihilator immunity

So far there is no systematic attempt to construct Boolean functions with maximum annihilator immunity. In this paper we present a construction keeping in mind the basic theory of annihilator immunity. This construction provides functions with the maximum possible annihilator immunity and the weight, nonlinearity and algebraic degree of the functions can be properly calculated under certain cases. The basic construction is that of symmetric Boolean functions and applying linear transformation on the input variables of these functions, one can get a large class of non-symmetric functions too. Moreover, we also study several other modifications on the basic symmetric functions to identify interesting non symmetric functions with maximum annihilator immunity. In the process we also present an algorithm to compute the Walsh spectra of a symmetric Boolean function with O(n 2) time and O(n) space complexity

Notion of Algebraic Immunity and Its evaluation Related to Fast Algebraic Attacks

It has been noted recently that algebraic (annihilator) immunity alone does not provide sufficient resistance against algebraic attacks. In this regar