ACCELERATING THE SCALAR MULTIPLICATION ON GENUS 2 HYPERELLIPTIC CURVE CRYPTOSYSTEMS

Elliptic Curve Cryptography (ECC) was independently introduced by Koblitz and Miller in the eighties. ECC requires shorter sizes of underlying finite fields in com- parison to other public key cryptosystems such as RSA, introduced by Rivest, Shamir and Adleman. Hyperelliptic curves, a generalization of elliptic curves, require decreas- ing field size as genus increases. Hyperelliptic curves of genus g achieve equivalent security of ECC with field size 1/g times the size of field of ECC for g <= 4. Recently, a lot of research is being focused on increasing the efficiency of hyperelliptic curve cryptosystems (HECC). The most time consuming operation in HECC is the scalar multiplication. At present, scalar multiplication on HECC over prime fields under performs in terms of computational time compared to ECC of equivalent security. This thesis focuses on optimizing HECC scalar multiplication at the point arithmetic level. At the point arithmetic level we obtain more efficient doubling and mixed addi- tion operations to decrease the computational time in the scalar multiplication using binary expansions of scalars. In addition, we introduce tripling operations for the Jacobians of hyperelliptic curves to make use of multibase representations of scalars that are being used effectively in ECC. We also develop double-add operations for semi-affine coordinates and Lange’s new coordinates. We use these double-add opera- tions to improve the computational cost of precomputation for semi-affine coordinates and that of more important main phase of scalar multiplication for semi-affine coor- dinates and Lange’s new coordinates. We derive special addition to improve the cost of precomputation for Lange’s new coordinates and projective coordinates

Evaluation of Papaya (Carica papaya L.) Hybrids for Yield and Papain Recovery

Six papaya hybrids, viz., CO-1 × Pusa Nanha, CO-2 × Pusa Nanha, CO-4 × Pusa Nanha, CO-5 × Pusa Nanha, CO-6 × Pusa Nanha and CO-7 × Pusa Nanha, along with their respective parents, were evaluated for fruit yield and quality. Higher fruit yield was recorded in hybrids CO-2 × Pusa Nanha, CO-4 × Pusa Nanha and CO-5 × Pusa Nanha at first harvest. Higher papain recovery was seen in CO-2 × Pusa Nanha and CO-5 × Pusa Nanha and activity of this enzyme was highest in CO-5 × Pusa Nanha. For fruit yield at first harvest, hybrids CO-2 × Pusa Nanha, CO-4 × Pusa Nanha, CO-6 × Pusa Nanha and CO-5 × Pusa Nanha recorded higher heterosis over mid- and better parental values. Fruit yield at first harvest exhibited high genotypic and phenotypic coefficient of variation. Days to flowering had the least genotypic and phenotypic coefficient of variation. Highest heritability estimates were recorded for plant height at first flowering, ascorbic acid content and titrable acidity. Fruit yield at first harvest showed high genetic advance as percentage of mean and the least genetic advance was seen for days to flowering. CO-2 × Pusa Nanha, CO-4 × Pusa Nanha, CO-5 × Pusa Nanha and CO-6 × Pusa Nanha showed better yield and earliness, and are recommended for further evaluation

A fuzzy approach for unequal workers-task assignment with heptagonal fuzzy numbers

The problem of assigning n tasks to n workers with minimum assignment cost often arises in many practical applications. In real life, the cost of assignment may not be certain and also the number of tasks may not be always equal to the number of workers and an unbalanced situation may arise often. In this paper, the representation of the Heptagonal fuzzy number(HFN) and its arithmetic operations are reviewed and a fuzzy approach called as fuzzy row penalty method is extended within the context of Heptagonal fuzzy numbers to deal with the unbalanced Fuzzy Assignment Problems. The cost of assignment is represented by Heptagonal fuzzy numbers which are capable of incorporating the degree of satisfaction about the assignment cost. So the use of HFN is more suitable. The proposed method overcomes the limitations of existing methods and it is illustrated through numerical example

Standardization of Stage-Wise Requirement of Nutrients in Banana Cv. Grande Naine (AAA)

A field trial was conducted during 2009-2010 at College Orchard, Horticultural College and Research Institute, Tamil Nadu Agricultural University, Coimbatore, to standardize stage-wise requirement of nutrients in banana cv. Grand Naine (AAA). Treatment T16&nbsp;where application of 100% RDF (165:52.5:495g NPK plant-1) at 4 critical growth stages, i.e., 40:52.5:25, 30:0:35, 30:0:25 and 0:0:15% at the 3rd, 5th, 7th&nbsp;and 9thmonths after planting (MAP), respectively, recorded maximum plant height, pseudostem girth and leaf area index. Maximum bunch weight of 32.15kg was recorded in T16. Higher yield was attributed to more number of (i) hands per bunch, (ii) fingers per hand and (iii) per bunch, besides the higher average weight of the finger. Better quality fruits, with higher TSS, total sugars, low acidity and better sugar:acid blend, were obtained in T16. In treatment T16, where 100% RDF was applied, increased N, P, and K content were seen in the index leaf of the crop. Lower soil-available nutrients, viz., N, P, K, at the higher level of split-application at critical stages of the crop revealed, that, the nutrients applied were utilized efficiently. This was reflected in the better yield and quality obtained. Economics were worked out which indicated T16&nbsp;as giving the highest cost:benefit ratio (1:3.97)

Effect of Foliar Spray of Nitrogenous Chemicals on Flowering, Fruit Set and Yield in Mango (Mangifera indica L.) Cv. Alphonso

Effect of foliar application of various nitrogenous chemicals on flowering, fruit set and yield of mango cv. Alphonso was studied at the orchard of Horticultural College and Research Institute, Coimbatore, during 2010 - 2011. Maximum number of flowering shoots (68.7%), number of panicles (7.5/m2), panicle length (31.4cm), number of hermaphrodite flowers (282.5/panicle), fruit set (17.0%), number of fruits (146.0/tree) and fruit yield (43.8 kg/tree) was obtained with foliar spray of KNO3&nbsp;at 2% concentration. Higher content of chlorophyll (1.7g mg-1), carbohydrate (14.5g 100g-1) and nitrogen (1.43%) and higher C/N ratio (10.18) were also recorded in plants sprayed with 2% KNO3, followed by 1% KNO3

Synergistic Effect of Leaf Count for Flower Induction in Mango cv. \u27Himampasand\u27

The synergistic effect of leaf count for flower induction was investigated in mango cv. \u27Himampasand\u27 under Ultra High Density Plantation. The trees are grown in tropical conditions in Tamil Nadu, India, and the trial was conducted by adopting a Factorial Randomized Block Design (FRBD) with three replications and two factors: leaf pruning and month. The experiment was set up in a five-year old orchard with uniform-sized \u27Himampasand\u27 trees planted at 3 x 2 m spacing. The treatments were imposed during the middle of October, November and December. Treatments consisted of 0 (no leaves), 1/8, 1/4, 1/2, 1, 2, 3, 4, 5, 6, and control (without leaf removal) leaves remaining on each stem of every treated branch. Under tropical, warm weather, the fractions of leaves / stem are able to induce minimal quantity of flowering without leaves in the shoot. Leaf pruning in different months from October to December had varied effects. However, in a tropical climate, six leaves per shoot and December pruning resulted in 100 per cent flowering in mango cv. \u27Himampasand\u27

Properties of concrete containing high volume fly ash

The utilization of waste materials in concrete is one of the best value added solutions can be provided to the construction industry. To realize this aim, waste of coal combustion from power plant, known as fly ash is used. Although various researches conducted on the properties of fly ash concrete with fly ash, very little is known on high volume substitution of cement with Class F fly ash particularly for concrete with common water to cement ratio and strength in the concrete application in Malaysia. This research was dedicated to investigate various fresh and hardened state properties of concrete containing high volume fly ash (HVFA). In this investigation, the HVFA were tested in mortar and concrete, and both specimens were tested by substituting 40 to 60% of OPC with fly ash. Properties studied in this research includes fresh concrete properties, mechanical properties and durability properties of concrete exposed to chloride, acid and sulphate solutions. The test result indicates that HVFA positively influenced the workability; however the setting times of the concrete were retarded. The development of strength of HVFA concrete was relatively slower, but the strength development of HVFA concrete after 28 days was greater than concrete with OPC cement. In-terms of durability, the HVFA concrete demonstrated better resistance to destructive chemical penetration and attacks such as chloride, acid and sulphate. Additionally, the test results on the concrete temperature rise suggests that the replacement of cement with HVFA is advantageous, particularly for mass concrete where thermal cracking is of a major concern. However, the performance of concrete at elevated temperatures reveals that concrete without any fly ash has better resistance than HVFA concrete at high temperature. Conclusively, high volume fly ash integration as partial cement replacement increases the resistance of concrete towards chloride penetration, acid and sulphate attack and reduces the temperature rise while obtaining good strength and modulus properties

Nested recursions with ceiling function solutions

Consider a nested, non-homogeneous recursion R(n) defined by R(n) = \sum_{i=1}^k R(n-s_i-\sum_{j=1}^{p_i} R(n-a_ij)) + nu, with c initial conditions R(1) = xi_1 > 0,R(2)=xi_2 > 0, ..., R(c)=xi_c > 0, where the parameters are integers satisfying k > 0, p_i > 0 and a_ij > 0. We develop an algorithm to answer the following question: for an arbitrary rational number r/q, is there any set of values for k, p_i, s_i, a_ij and nu such that the ceiling function ceiling{rn/q} is the unique solution generated by R(n) with appropriate initial conditions? We apply this algorithm to explore those ceiling functions that appear as solutions to R(n). The pattern that emerges from this empirical investigation leads us to the following general result: every ceiling function of the form ceiling{n/q}$ is the solution of infinitely many such recursions. Further, the empirical evidence suggests that the converse conjecture is true: if ceiling{rn/q} is the solution generated by any recursion R(n) of the form above, then r=1. We also use our ceiling function methodology to derive the first known connection between the recursion R(n) and a natural generalization of Conway's recursion.Comment: Published in Journal of Difference Equations and Applications, 2010. 11 pages, 1 tabl

Molecular Diversity Analysis in F3 Intergeneric Population of Papaya (Carica papaya L.)

Attempts were made to estimate molecular diversity present in F3&nbsp;populations of intergeneric crosses between&nbsp;Carica papaya&nbsp;L. (Var. Pusa Nanha and CP 50) and&nbsp;Vasconcellea cauliflora. Molecular studies revealed that PCR amplification using five ISSR primers in 40 F3&nbsp;progenies yielded 53 reproducible amplified bands. Of the 53 bands, 44 were polymorphic (83.02%). Polymorphic Information Content (PIC) value ranged between 0.90 (ISSR 807 x 810) and 0.66 (ISSR 834 x 810). Similarity coefficients based on five ISSR markers ranged from 0.05 to 0.96. Maximum similarity was observed for genotypes 1, 4 and 6 of Pusa Nanha x&nbsp;Vasconcellea cauliflora&nbsp;(0.96). Minimum similarity was observed between genotypes 3 and 14 of CP 50 x&nbsp;Vasconcellea cauliflora&nbsp;(0.04). This higher genetic diversity of papaya progenies stands to contribute to development of new varieties and, using the data, further hybridization and selection can be planned