Subtypes of mathematical difficulties and their stability.

AbstractMontgomery’s and Barrett’s modular multiplication algorithms are widely used in modular exponentiation algorithms, e.g. to compute RSA or ECC operations. While Montgomery’s multiplication algorithm has been studied extensively in the literature and many side-channel attacks have been detected, to our best knowledge no thorough analysis exists for Barrett’s multiplication algorithm. This article closes this gap. For both Montgomery’s and Barrett’s multiplication algorithm, differences of the execution times are caused by conditional integer subtractions, so-called extra reductions. Barrett’s multiplication algorithm allows even two extra reductions, and this feature increases the mathematical difficulties significantly. We formulate and analyse a two-dimensional Markov process, from which we deduce relevant stochastic properties of Barrett’s multiplication algorithm within modular exponentiation algorithms. This allows to transfer the timing attacks and local timing attacks (where a second side-channel attack exhibits the execution times of the particular modular squarings and multiplications) on Montgomery’s multiplication algorithm to attacks on Barrett’s algorithm. However, there are also differences. Barrett’s multiplication algorithm requires additional attack substeps, and the attack efficiency is much more sensitive to variations of the parameters. We treat timing attacks on RSA with CRT, on RSA without CRT, and on Diffie–Hellman, as well as local timing attacks against these algorithms in the presence of basis blinding. Experiments confirm our theoretical results.

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Investigating EEG Based Marker for Diagnosis of Mathematical Difficulties

2020 28th Signal Processing and Communications Applications Conference (SIU) ◽

10.1109/siu49456.2020.9302409 ◽

2020 ◽

Author(s):

Farhad Nassehi ◽

Mertcan Ozdemir ◽

Osman Erogul

Keyword(s):

Mathematical Difficulties

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Αποτελεσματική διδασκαλία γνωστικού σχήματος προβλημάτων αφαίρεσης σε μαθητές με ειδικές μαθησιακές δυσκολίες με τη χρήση πολλαπλών τρόπων αναπαράστασης της γνώσης

Psychology: the Journal of the Hellenic Psychological Society ◽

10.12681/psy_hps.26235 ◽

2021 ◽

Vol 26 (1) ◽

pp. 160

Author(s):

Στέργιος Αγγελόπουλος ◽

Ιωάννης Αγαλιώτης

Keyword(s):

Learning Disabilities ◽

Problem Solving ◽

Effective Instruction ◽

Specific Learning Disabilities ◽

Primary School Students ◽

School Students ◽

Cognitive Schemata ◽

Mathematical Difficulties ◽

Specific Learning

The present research examines the construction and activation of cognitive schemata corresponding to subtraction-compare and subtraction-equalize math word problems by primary school students with specific learning disabilities. In order to facilitate the participants in developing their cognitive schemata, we utilized multiple ways of knowledge representation (manipulatives, pictures, and arithmetic symbols) in the context of an intervention based on the principles of effective instruction. In order to evaluate the results, assessments were conducted prior and immediately after the implementation of the intervention, as well as three weeks after its completion. It was found that participants performed significantly better in problem solving both after the intervention and at follow-up, proving that they benefited from the instruction they had received. Results are discussed in regard to organizing appropriate instruction for students with mathematical difficulties and disabilities.

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