New minimal weight representations for left-to-right window methods

Abstract. For an integer w ≥ 2, a radix 2 representation is called a width-w nonadjacent form (w-NAF, for short) if each nonzero digit is an odd integer with absolute value less than 2 w−1, and of any w consecutive digits, at most one is nonzero. In elliptic curve cryptography, the w-NAF window method is used to efficiently compute nP where n is an integer and P is an elliptic curve point. We introduce a new family of radix 2 representations which use the same digits as the w-NAF but have the advantage that they result in a window method which uses less memory. This memory savings results from the fact that these new representations can be deduced using a very simple left-to-right algorithm. Further, we show that like the w-NAF, these new representations have a minimal number of nonzero digits. 1 Window Methods An operation fundamental to elliptic curve cryptography is scalar multiplication; that is, computing nP for an integer, n, and an elliptic curve point, P. A number of different algorithms have been proposed to perform this operation efficiently (see Ch. 3 of [4] for a recent survey). A variety of these algorithms, known as window methods, use the approach described in Algorithm 1.1. For example, suppose D = {0, 1, 3, 5, 7}. Using this digit set, Algorithm 1.1 first computes and stores P, 3P, 5P and 7P. After a D-radix 2 representation of n is computed its digits are read from left to right by the “for ” loop and nP is computed using doubling and addition operations (and no subtractions). One way to compute a D-radix 2 representation of n is to slide a 3-digit window from right to left across the {0, 1}-radix 2 representation of n (see Section 4). Using negative digits takes advantage of the fact that subtracting an elliptic curve point can be done just as efficiently as adding it. Suppose now that D

Teaching them all: An exploratory mixed methods study of African American students\u27 perceptions of their middle school\u27s culture

Research indicates school culture impacts student achievement. At Teach Them All Middle School (TTA), an achievement gap exists between African American and White students. The purpose of the current study was to examine the perceptions of African American students concerning the school culture at TTA. The research questions explored the perceptions of these students regarding the role of school leaders in shaping a school culture that is academically supportive, as well as their perceptions of the actual academic support, academic rigor, and encouragement they received from administrators and faculty. A sequential exploratory mixed methods strategy was used to quantify and describe the perceptions of 8th-grade African American students at TTA. Participants (36 students) completed a school culture survey and individual in-depth interviews. Descriptive statistical analysis of survey results revealed students have an overall positive perception of the school culture at TTA. Triangulation of results showed a strong view by students of the school administrators\u27 influence in establishing the school culture present at TTA. Constant comparison analysis of coded interview data revealed two themes: (a) the willingness and availability of teachers to help students even after school, and (b) the students\u27 belief that problems can be brought to the attention of administrators and/or teachers for resolution. The study\u27s key recommendation is for TTA to ensure its school culture exhibits high academic expectations for every student, especially African American males. The study contributes to positive social change by giving voice to a stakeholder group, African American students, who research shows have had a limited one in school improvement efforts. The study also guides schools in utilizing insight from these stakeholders to establish school cultures with high quality teaching and learning

Black Voices Matter

This article examines the role of voice in the writing of African American students from the African American Language (AAL)-speaking culture. Drawing on data from a qualitative study, this article presents empirical evidence that is likely to inform existing and new initiatives to support the voice and writing practices of AAL-speaking students, and by extension, all culturally and linguistically diverse students. This rarely considered insight, I argue, is important as in recent decades there have been a growing number of calls for instructional material that meets the language and literacy development needs of second language speakers and writers. By generating implications that offer rich insight into the nature of teaching voice in writing to African American Language (AAL)-speaking students, and by extension all culturally and linguistically diverse students, this article addresses this call

Secure Data Aggregation in Wireless Sensor Networks. Homomorphism versus Watermarking Approach

International audienceWireless sensor networks are now in widespread use to monitor regions, detect events and acquire information. Since the deployed nodes are separated, they need to cooperatively communicate sensed data to the base station. Hence, transmissions are a very energy consuming operation. To reduce the amount of sending data, an aggregation approach can be applied along the path from sensors to the sink. However, usually the carried information contains confidential data. Therefore, an end-to-end secure aggregation approach is required to ensure a healthy data reception. End-to-end encryption schemes that support operations over cypher-text have been proved important for private party sensor network implementations. These schemes offer two main advantages: end-to-end concealment of data and ability to operate on cipher text, then no more decryption is required for aggregation. Unfortunately, nowadays these methods are very complex and not suitable for sensor nodes having limited resources. In this paper, we propose a secure end-to-end encrypted-data aggregation scheme. It is based on elliptic curve cryptography that exploits a smaller key size. Additionally, it allows the use of higher number of operations on cypher-texts and prevents the distinction between two identical texts from their cryptograms. These properties permit to our approach to achieve higher security levels than existing cryptosystems in sensor networks. Our experiments show that our proposed secure aggregation method significantly reduces computation and communication overhead and can be practically implemented in on-the-shelf sensor platforms. By using homomorphic encryption on elliptic curves, we thus have realized an efficient and secure data aggregation in sensor networks. Lastly, to enlarge the aggregation functions that can be used in a secure wireless sensor network, a watermarking-based authentication scheme is finally proposed

Facies Analysis of Terrebonne Basin Using Vibracores and CHIRP Seismic Data

This study was conducted in upper and lower Madison Bay as well as Lake Boudreaux in Terrebonne basin located in southcentral Louisiana. This region is part of the recently abandoned Lafourche delta complex (0.6-0.8 kyr). Much of coastal Louisiana is comprised of formerly active delta complexes of the Mississippi River that have undergone subsequent reworking. As more restoration actions are being considered to combat land loss in coastal Louisiana, exploring the framework of a recently abandoned delta complex could aid in these plans. Utilizing core descriptions and CHIRP seismic data, facies analysis was performed to produce cross sections that display the recent depositional history within the region. The facies described construct the profile of a regionally transgressive abandoned delta complex. Growth fault interaction with the shallow stratigraphy was not noted within these three study areas, however, the morphological effects of an abandoned delta complex were observed in each study area