6,389 research outputs found
A Machine-Checked Formalization of the Generic Model and the Random Oracle Model
Most approaches to the formal analyses of cryptographic protocols make the perfect cryptography assumption, i.e. the hypothese that there is no way to obtain knowledge about the plaintext pertaining to a ciphertext without knowing the key. Ideally, one would prefer to rely on a weaker hypothesis on the computational cost of gaining information about the plaintext pertaining to a ciphertext without knowing the key. Such a view is permitted by the Generic Model and the Random Oracle Model which provide non-standard computational models in which one may reason about the computational cost of breaking a cryptographic scheme. Using the proof assistant Coq, we provide a machine-checked account of the Generic Model and the Random Oracle Mode
Developing further support for in-service teachersâ implementation of a reasoning-and-proving activity and their identification of studentsâ level of mathematical argumentation
This is the third in a series of papers focusing reasoning-and-proving. Participants were in-service teachers enrolled in a continuing university education programme in teaching mathematics for grades 5â10. Data were collected from a course assignment in 2018 and 2019, where the in-service teachers reported about their studentsâ work with a reasoning-and-proving task. Their reports included an identification of the levels the studentsâ written argumentation reached, based on Balacheffâs taxonomy of proofs. The course assignmentâs instructions were expanded for the 2019-cohort. Comparing in-service teachersâ proof level identifications to the researchersâ by statistical analyses, indicated an improvement of the general quality from 2018 to 2019. A higher consensus in 2019 included identifying generic arguments and an understanding that there might be examples falling outside of the taxonomy levels. Qualitative content analysis of the two cohortsâ justifications of their identifications revealed an improved understanding of what is considered generic argumentation. The results encourage and contribute to further developments of the concept.publishedVersio
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