There is a growing body of research that suggests that video-based interventions, such as video modeling and video prompting, are effective tools for teaching academic skills to students with disabilities. This study used a single subject, multiple-baseline-across-subjects design to evaluate whether a video-prompting intervention could effectively assist second grade students who had been identified by their teachers as "struggling"in mathematics to better solve multiplication story problems. Five second grade students (one female and four males) ages 7 to 8 viewed the intervention videos on an iPad that modeled how to solve multiplication word problems. To evaluate the effectiveness of the videos, a rubric was used as the primary measure to assess the domains of problem-solving, communicating, and representing with numbers. Based on visual analysis between baseline and intervention, there was a functional relationship between the introduction of the intervention and the performance on the math problems. In addition, a visual analysis between intervention and maintenance appeared stable for all participants. These results indicate that technology can be used to implement interventions for struggling learners and may be utilized in regular classrooms. Results also demonstrate that video modeling can be a useful instructional tool for helping many individuals, not just those with an identified disability, to learn complex tasks. Implementing video models in a classroom setting could enable teachers to consistently provide interventions to students that work more independently, allowing teachers to work on a more one-on-one or small group basis with their students.

Large integers are used in several key areas such as RSA (Rivest-Shamir-Adleman) public-key cryptographic system and elliptic curve public-key cryptographic system. To achieve higher levels of security requires larger key size and this becomes a limiting factor in prime finite field GF(p) arithmetic using large integers because operations on large integers suffer from the long carry propagation problem. Large integer representation has direct impact on the efficiency of the calculations and the hardware and software implementations. Attempts to use different representations such as residue number systems suffer from their own problems. In this dissertation, we propose a novel and efficient attribute-based large integer representation scheme capable of efficiently representing the large integers that are commonly used in cryptography such as the five NIST primes and the Pierpont primes used in supersingular isogeny Diffie-Hellman (SIDH) used in post-quantum cryptography. Moreover, we propose algorithms for this new representation to perform arithmetic operations such as conversions from and to binary representation, two’s complement, left-shift, numbers comparison, addition/subtraction, modular addition/subtraction, modular reduction, multiplication, and modular multiplication. Extensive numerical simulations and software implementations are done to verify the performance of the new number representation. Results show that the attribute-based large integer arithmetic operations are done faster in our proposed representation when compared with binary and residue number representations. This makes the proposed representation suitable for cryptographic applications on embedded systems and IoT devices with limited resources for better security level. / Graduate / 2020-07-04

Telemetry system, Optimisation, Sensoric networks, Smart Grid, Internet of Things, Sensors, Information security, Cryptography, Cryptography algorithms, Cryptosystem, Confidentiality, Integrity, Authentication, Data freshness, Non-Repudiation.