The Performance of Elliptic Curve Based Group Diffie-Hellman Protocols for Secure Group Communication over Ad Hoc Networks

The security of the two party Diffie-Hellman key exchange protocol is currently based on the discrete logarithm problem (DLP). However, it can also be built upon the elliptic curve discrete logarithm problem (ECDLP). Most proposed secure group communication schemes employ the DLP-based Diffie-Hellman protocol. This paper proposes the ECDLP-based Diffie-Hellman protocols for secure group communication and evaluates their performance on wireless ad hoc networks. The proposed schemes are compared at the same security level with DLP-based group protocols under different channel conditions. Our experiments and analysis show that the Tree-based Group Elliptic Curve Diffie-Hellman (TGECDH) protocol is the best in overall performance for secure group communication among the four schemes discussed in the paper. Low communication overhead, relatively low computation load and short packets are the main reasons for the good performance of the TGECDH protocol.

The Use of Think-Aloud Strategies to Solve Word Problems

In this action research study of my sixth grade mathematics class, I investigated how students’ use of think-aloud strategies impacts their success in solving word problems. My research reveals that the use of think-aloud strategies can play an important role in the students’ abilities to understand and solve word problems. Direct instruction and modeling of think-aloud strategies increased my students’ confidence levels and the likelihood that they would use the strategies on their own. Providing students with a template to use as they solve a word problem helps students to better focus in on the think-aloud strategies I had been modeling for them.