“[Summer School] has reinforced my decision to do Honours
in mathematics and it has strengthened my interest in
mathematical modelling.”

Dylan Maher, University of Wollongong

Cryptography for Cybersecurity


Dr. Arathi Arakala, RMIT


Cryptography, the science and art of confidential communication between two parties has been in existence for 1000s of years. From protecting handwritten secrets to military radio communication during the World Wars, many ciphers (algorithms to protect data) have played pivotal roles in history. With the advent of the internet and e-commerce, the number of applications like emails, credit card information and digital media, that need secure data transmission has skyrocketed. In fact every person today needs cryptography to not only keep information secure, but to check its integrity and validate its source.

This course will provide look at the mathematical structures that underpin classical and modern cryptosystems. Topics covered include the concept of perfect secrecy and one-time pads; symmetric ciphers; shift registers and stream ciphers; block ciphers like DES and AES; asymmetric ciphers like the RSA and ElGamal cryptosystems; digital signatures; hash functions and their applications.

Course Overview

Topics covered in this course include:

  1. Introduction to Private-Key Cryptosystems, Security Objectives and Cryptographic Primitives.
  2. Background Mathematics – Finite Fields and Primitive Polynomials, Number Theory
  3. Linear Recurrence Sequences (LRS), Linear Feedback Shift Registers (LFSR), Stream Ciphers.
  4. Levels of security, Perfect Secrecy, Introduction to Complexity Theory, Computational Security
  5. Block Ciphers and Modes of Operation, DES, AES
  6. Introduction to Public-Key Cryptosystems, Knapsack (Merkle Hellman) cryptosystem, RSA cryptosystem, El Gamal cryptosystem.
  7. Hash Functions, Message Authentication and Digital Signatures.
  8. Introduction to the technology of Bitcoin and Blockchain. Introduction to post-quantum cryptography.


  • The students taking this course should have an understanding of Discrete Mathematics. This includes modular arithmetic with an understanding of Groups and Fields.


  • 4 quizzes due at the end of each week 5% each (20% total)
  • 2 R-based assignments due at the end of week 2 and week 4 15% each (30% total)
  • Final exam 50%

Attendance requrements

  • For those completing the subject for their own knowledge/interest, quizzes must be completed as an attendance requirement

Resources/pre-reading (if available)

There is no set text book for this course, and full lecture notes will be provided. However similar material to that covered can be found in:

  • Handbook of Applied Cryptography, Menezes et al., CRC Press, 2018.
  • Cryptography : Theory and Practice, Stinson, D. R., Paterson, M. B., 4th ed., Chapman Hall, CRC, 2018.
  • R (programming software package) will be required for this course. Details on how to download this will be provided to students on the Canvas LMS after subject enrollments are confirmed.

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Dr. Arathi Arakala, RMIT

Dr. Arathi Arakala got her PhD from RMIT University in 2008. After a series of post doctoral positions at RMIT University and Monash University, she is now an Early Career Development Fellow in Cybersecurity at RMIT University’s STEM College. Arathi’s area of interest is Cybersecurity. In particular, the security of Biometric Authentication Systems and user behaviour in online social networks.