## Verification of the RSA Algorithm

During the course of this year the Crypto Giants have been looking at the RSA Algorithm. They were required to make use of MATHEMATICA software in order to verify the mechanics of the RSA public key crypto system, that decryption of a message produces the original message. The project was supervised by Dr Gaza Maluleka. Below are 2 reports from their members, Ntombifuthi Khoza and Pilane Koma, in which they describe how they carried out the task.

CRYPTO GIANTS PROJECT

Verification of RSA Algorithm.

N Khoza

30 October 2015

Project Supervisor:Dr Gaza Maluleka

Contents

1 Historic Background on the

RSA Algorithm ………………………………………………………………………….. 3

2 Introduction …………………………………………………………………………….. 4

3 Task procedure …………………………………………………………………… 4

3.1 Prime numbers……………………………………………………………………………………………… 4

3.2 Computing n…………………………………………………………………………………………………… 4

3.3 Phi φ………………………………………………………………………………………………………………… 5

3.4 Public Key(e)………………………………………………………………………………………………….. 5

3.5 Private Key(d)……………………………………………………………………………………………….. 5

3.6 Encryption……………………………………………………………………………………………………… 5

3.7 Decryption……………………………………………………………………………………………………… 6

4 Conclusion …………………………………………………………………………………… 7

5 Reference ……………………………………………………………………………………… 8

1 Historic Background on the RSA

## Algorithm

The RSA algorithm was developed by professor Ron River, Adi Shamir and Leonard Adlemen in 1977 at MIT.…

## Use your machine learning powers to solve the stock market on numer.ai

Home-grown South African mathematics, statistics and computer science have come together to give us numer.ai, founded by Richard Craib. This site which has come up with a seemingly brilliant idea, allowing anyone free access to otherwise very expensive data, but in such an encrypted form that you don’t know what the data means, but its patterns are preserved. This data is stock market data which you can use to make predictions. The predictions on their own don’t mean anything, so you send these predictions back to numer.ai, and they can apply it to the unencrypted data and make purchases on the stock market based on the most accurate models on their test data.

It’s simple but brilliant. They give you something very expensive for free, and you give them something very valuable for free. The brightest minds in machine learning can then potentially earn big money which would be impossible if it weren’t for the beauty of homomorphic encryption.…

## Elephant Delta Day 3 – Renee LaRue from West Virginia University on Optimization in first semester calculus: A look at a classic problem

Photo of Renee LaRue available here.

Co-author Nicole Engelke Infante

Classic problem: Fence along a barn. Minimize amount of fencing given a fixed amount of fencing.

Literature: 4 versions of this problem. More difficult when students have to set up problem from words.

Carlson and Bloom (2005) Problem-Solving Framework

Tall and Vinner (1981) Concept image

7 students (pilot with 3 students), just before final exam involving optimization.

Recordings of students thinking aloud.

Questions about rectangles – what happens to perimeter if area changes?

5 students solved without intervention, 3 perfectly, 2 forgot about barn. Other 2 needed much help.

Responses showed gaps in reasoning.

Six key maths concepts that played a role:

1. Use 2x + y or 2y + x? 2l + 2w = 2y + 2x (matching variables to what they think they must mean).
2. Function notation. Haphazard use of equal signs. Student said you can’t write 2x + y as f(x) because y = f(x).

## Johann Engelbrecht from University of Pretoria on Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries

Opening photo of co-author Owe’s colourful toenails – a different colour for each of the 10 Delta conferences!

Photo available here

Paper available here

Traditionally, engineers demand from mathematics fluent use of techniques.

With technology, is this as important as conceptual insight?

Procedural (mechanical) knowledge in mathematics, e.g. ‘For this function, what is the equation of the tangent line at this point?’

Conceptual knowledge link relationships between verbal, visual, symbolic representations. E.g. Match graph of derivative to a written description.

SA – Sweden project.

Quantitative analysis: Junior students in 3rd semester; senior students in 7th semester.

Qualitative analysis: interviews with Swedish and SA engineers.

Swedish engineer

• Procedural maths needed as a basis for mathematics (concerns that he understood procedural knowledge as basic maths background for applications, equivalent to learning the language of maths).
• Conceptual understanding = engineering judgement, broader than maths.
• New engineers should be able to be independent, deal with a whole problem, be self-confident.

## Elephant Delta day 3 – Emilie Naccarato from University of Northern Colorado on Expectations and implementations of the flipped classroom model in mathematics courses

Emilie Naccarato presenting, co-author Gulden Karakok

Goal: talk about themes occurring in flipped classrooms in tertiary maths in USA

Flipped class:

• Some course content on technology accessed outside class
• More time in class for related, meaningful activities
• Same contact, face-to-face hours
• (notice the loose way a flipped class can be arranged – many ways to arrange)

Existing studies

Descriptions of implementation and student perceptions.

Looking at student performance in flipped vs traditional courses. Big differences in studies – no consensus on what works best (but implementations vary a lot).

Need to link expectation and goals of a flipped class to the implementation – can’t simply compare all versions of a flipped class.

How do you assess differences when learning goals and implementations are so different?

You need alignment. Schoenfeld (2000) emphasized “identifying important topics and specifying what it means to have a conceptual understanding of them. With this kind of information … [they] could then decide which aspects of understanding were most important, which they wanted to assess, and how.” (p.…