New Candidates for Multivariate Trapdoor Functions

Porras, Jaiberth; Baena, John B.; Ding, Jíntai

doi:10.15446/recolma.v49n1.54163

Cited by 8 publications

(5 citation statements)

References 11 publications

(16 reference statements)

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“…Subsequently, they had to make a reasoned judgement on the suitability of the lesson in each facet and overall, taking into account the assessment of the indicators and the conflicts (epistemic, cognitive and interactional) encountered. Finally, they were asked to re-evaluate the lesson by Porras et al (2013) using the Doodle survey and explain whether and why they had changed their opinion regarding the degree of appropriateness assigned in the initial task.…”

Section: Session 3 Tlag-proportionality and Didactical-mathematical K...mentioning

confidence: 99%

Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons

Castillo¹,

Burgos

2022

EURASIA J Math Sci Tech Ed

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Achieving the competence to reflect on the degree of suitability of textbooks is not easy, so it is necessary to train prospective professionals in the knowledge and use of analytical tools to guide them in critically analyzing these curricular materials. In response to this research problem, this paper describes and analyses the implementation of a training intervention that aims to promote reflective competence in prospective Costa Rican teachers through the analysis of textbook lessons. The content of proportionality is chosen because of its central in the curriculum. The training activity was motivating for the participants and helped them to progress in the competence of lesson analysis. However, it is noted that the design needs to be improved in terms of time dedication, as well as attention to the necessary didactical-mathematical background knowledge on proportionality to achieve better results.

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Section: Session 3 Tlag-proportionality and Didactical-mathematical K...mentioning

confidence: 99%

Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons

Castillo¹,

Burgos

2022

EURASIA J Math Sci Tech Ed

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“…The survey on various modifications of this algorithm and corresponding cryptanalysis the reader can find in [1]. Various attempts to build secure multivariate public key were unsuccessful, but the research of the development of new candidates for secure multivariate public keys is going on (see for instance [2] and further references).…”

Section: On Post Quantum and Multivariate Cryptographymentioning

confidence: 99%

On computations with double Schubert automaton and stable maps of multivariate cryptography

Ustimenko¹

2021

Мiждисциплiнарнi дослiдження складних систем

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The families of bijective transformations Gn of affine space K n over general commutative ring K of increasing order with the property of stability will be constructed. Stability means that maximal degree of elements of cyclic subgroup generated by the transformation of degree d is bounded by d. In the case K = Fq these transformations of K n can be of an exponential order. We introduce large groups formed by quadratic transformations and numerical encryption algorithm protected by secure protocol of Noncommutative Cryptography. The construction of transformations is presented in terms of walks on Double Schubert Graphs.

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Section: On Post Quantum and Multivariate Cryptographymentioning

confidence: 99%

On multivariate public keys based on a pair of transformations with density gap

Ustimenko¹

2018

Dopov. Nac. akad. nauk Ukr.

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Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces K n over general commutative ring K of increasing with n order can be used in the key exchange protocols and related to them El Gamal multivariate cryptosystems. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via the usage of conjugations for two polynomials of kind g k and g −1 given by key holder (Alice) or giving them as elements of different transformation groups. We present key exchange protocols based on twisted discrete logarithms problem which uses noncommutativity of semigroup. Recent results on the existence of families of stable transformations of prescribed degree and density and exponential order over finite fields can be used for the implementation of schemes as above with feasible computational complexity. We introduce an example of a new implemented quadratic multivariate cryptosystem based on the above mentioned ideas.

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New Candidates for Multivariate Trapdoor Functions

Cited by 8 publications

References 11 publications

Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons

Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons

On computations with double Schubert automaton and stable maps of multivariate cryptography

On multivariate public keys based on a pair of transformations with density gap

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