• Class Number 6060
• Term Code 3260
• Class Info
• Unit Value 6 units
• Mode of Delivery In Person
• COURSE CONVENER
• Dr Dom Verity
• LECTURER
• Dr Dom Verity
• Class Dates
• Class Start Date 25/07/2022
• Class End Date 28/10/2022
• Census Date 31/08/2022
• Last Date to Enrol 01/08/2022
SELT Survey Results

Number Theory and Cryptography (MATH6114)

The need to protect information being transmitted electronically, such as the widespread use of electronic payment, has transformed the importance of cryptography. Most of the modern types of cryptosystems rely on number theory for their theoretical background. This course introduces elementary number theory, with an emphasis on those parts that have applications to cryptography, and shows how the theory can be applied to cryptography.

Number theory topics will be chosen from: the Euclidean algorithm, greatest common divisor, prime numbers, prime factorisation, primality testing, modular arithmetic, the Chinese remainder theorem, diophantine equations, sums of squares, Euler's function, Fermat's little theorem, primitive roots, quadratic residues, quadratic reciprocity, Pell's equation, continued fractions, Diophantine approximation.

Cryptography topics will be chosen from: symmetric key cryptosystems, including classical examples and a brief discussion of modern systems such as DES and AES, public key systems such as RSA and discrete logarithm systems, cryptanalysis (code breaking) using some of the number theory developed.

Note: Graduate students attend joint classes with undergraduates but are assessed separately. The additional assessment will consist of assignments requiring deeper conceptual understanding and/or a project, and the final exam will contain alternative questions requiring deeper conceptual understanding.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Solve problems in elementary number theory.
2. Apply elementary number theory to cryptography.
3. Develop a deeper conceptual understanding of the theoretical basis of number theory and cryptography.

Recommended student system requirements

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

## Staff Feedback

Students will be given feedback in the following forms in this course:

• feedback to whole class, groups, individuals, focus group etc

## Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

## Class Schedule

Week/Session Summary of Activities Assessment
1 Prime numbers, uniqueness of factorization, Euclid's algorithm
2 Diophantine equations, arithmetic modulo N
3 Linear Diophantine equations, modular inverses, Chinese remainder theorem
4 Wilson's theorem, Fermat's Little Theorem, Pollard's algorithm, Euler's theorem Assignment 1 due (on Week 1 to 3 material)
5 Primality testing, pseudoprimes, Miller's test, Rabin's test, cryptosystems
6 Public key cryptography, RSA, primitive roots, multiplicative functions Assignment 2 due (on Week 4 to 5 material)
7 Existence of primitive roots modulo primes and odd prime powers Graduate/HPO Assignment due
8 Discrete logarithms, primality test and Miller's test revisited Assignment 3 due (on Week 6 to 7 material)
9 Continued fractions, Diophantine approximation
10 Applications of Dirichlet's theorem, continued fractions and Diophantine equations, solutions to Pell's equation Assignment 4 due (on Week 8 to 9 material)
11 quadratic residues, Legendre symbol, quadratic reciprocity Assignment 5 due (on Week 10 to 11 material)
12 Guest lectures and supplementary topics Graduate/HPO mini-project presentations and reports due

## Tutorial Registration

Workshop registration will be via MyTimetable. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage. See Wattle for more information about workshops in this class.

## Assessment Summary

Assessment task Value Due Date Return of assessment Learning Outcomes
Assignment 1 7 % 19/08/2022 26/08/2022 1,2
Assignment 2 8 % 02/09/2022 09/09/2022 1,2
Assignment 3 7 % 30/09/2022 07/10/2022 1,2
Assignment 4 8 % 14/10/2022 21/10/2022 1,2
Assignment 5 7 % 28/10/2022 04/11/2022 1,2
Final examination 38 % 03/11/2022 01/12/2022 1,2,3
Graduate/HPO Assignment 10 % 23/09/2022 07/10/2022 1,2,3
Graduate/HPO Mini Project 15 % 24/10/2022 11/11/2022 1,2,3

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

## Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

## Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

## Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

## Participation

Students are expected to attend lectures and contribute to discussions. When this is not possible students are expected to listen to the audio recording(s) of all lectures.

This course has been adjusted for remote participants, there will be separate workshops allocated for in person and on campus students. Remote students are encouraged to identify themselves to the course convener before the start of semester

## Examination(s)

Final examination, 3 hours, no permitted materials. Please check the ANU final Examination Timetable to confirm the date, time and mode of the end of semester exam.

Value: 7 %
Due Date: 19/08/2022
Return of Assessment: 26/08/2022
Learning Outcomes: 1,2

Assignment 1

Questions on the material presented in lecture in weeks 1-3. The exact value of this assignment is 7.5% towards the total grade.

Value: 8 %
Due Date: 02/09/2022
Return of Assessment: 09/09/2022
Learning Outcomes: 1,2

Assignment 2

Questions on the material presented in lecture in weeks 4-5. The exact value of this assignment is 7.5% towards the total grade.

Value: 7 %
Due Date: 30/09/2022
Return of Assessment: 07/10/2022
Learning Outcomes: 1,2

Assignment 3

Questions on the material presented in lecture in weeks 6-7. The exact value of this assignment is 7.5% towards the total grade.

Value: 8 %
Due Date: 14/10/2022
Return of Assessment: 21/10/2022
Learning Outcomes: 1,2

Assignment 4

Questions on the material presented in lecture in weeks 8-9. The exact value of this assignment is 7.5% towards the total grade.

Value: 7 %
Due Date: 28/10/2022
Return of Assessment: 04/11/2022
Learning Outcomes: 1,2

Assignment 5

Questions on the material presented in lecture in weeks 10-11. The exact value of this assignment is 7.5% towards the total grade.

Value: 38 %
Due Date: 03/11/2022
Return of Assessment: 01/12/2022
Learning Outcomes: 1,2,3

Final examination

The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location exam. The exact value of this exam is 37.5% towards the total grade.

Value: 10 %
Due Date: 23/09/2022
Return of Assessment: 07/10/2022
Learning Outcomes: 1,2,3

This assignment will relate to the graduate/HPO content given in the add-on module.

Value: 15 %
Due Date: 24/10/2022
Return of Assessment: 11/11/2022
Learning Outcomes: 1,2,3

The mini project will involve an investigation of a more advanced topic related to the content of the add-on module. Assessment of the mini project will be based on a presentation and a written report, due in Week 12.

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

## Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Assignment submission will be via Wattle. MATH6114 does not use Turnitin, having been granted an exemption.

## Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

## Late Submission

Individual assessment tasks may or may not allow for late submission. Policy regarding late submission is detailed below:

• Late submission permitted. Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.

## Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

## Returning Assignments

Assignments will be returned electronically.

## Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

## Resubmission of Assignments

No resubmission is allowed.

## Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

## Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

## Convener

 Dr Dom Verity Dominic.Verity@anu.edu.au

### Dr Dom Verity

 By Appointment By Appointment

## Instructor

 Dr Dom Verity 61252908 Dominic.Verity@anu.edu.au

### Dr Dom Verity

 By Appointment By Appointment