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Introduction to Cryptography
March 31, 2025
Individual Assessment
Cryptography, the art of securing communication, is paramount in our digital age. Traditional encryption techniques such as RSA or Diffie-Hellman rely on the difficulty of factoring large numbers or solving the discrete logarithm problem. However, the looming threat of quantum computers poses a significant challenge. These powerful machines could theoretically break these traditional methods, rendering our current encryption schemes vulnerable. This is where post-quantum cryptography (PQC) steps in.
In this assignment you will produce a report that introduces and discusses Kyber [2], the post-quantum secure key encapsulation mechanism that was recently chosen as a finalist for the NIST Post-Quantum Cryptography Standardization Process [3]. The report should be 1000-2000 words, and should show evidence of independent research, be academically rigorous (with citations and references provided as required), read well, and address the following topics:
(a) Motivation for Post-Quantum Cryptography.
Begin your assignment by explaining the vulnerability of classical encryption algorithms to quantum computers. Briefly discuss Shor’s Algorithm, a quantum algorithm that can efficiently factor large numbers and solve the discrete logarithm problem. Explain how this capability would render current public-key cryptography (e.g., RSA, Diffie-Hellman) ineffective. Introduce and motivate the need for the concept of post-quantum cryptography.
(b) Introducing Kyber: A Post-Quantum Key Encapsulation Mechanism.
(c) Kyber’s Algorithmic Core.
Delve into the core algorithms of Kyber [1]. Describe the key generation, encapsulation, and decapsulation processes within Kyber, mapping them to the KEM algorithms we have discussed in class. Briefly explain the usage of pseudorandom number generators and hashing functions like Keccak (SHA-3) within the algorithms.
Discuss the security properties of Kyber by first explaining the security notion (IND-CCA2) that Kyber achieves. Briefly explain what IND-CCA2 security entails and its importance in secure communication. Briefly explain how the security of Kyber relates to the Learning With Error problem over module lattices. You should also discuss the parameter sets offered by Kyber (e.g., Kyber-512, Kyber-768, Kyber-1024) and how they provide different security levels, discussing the trade-off between security level, key/ciphertext size, and performance.
Finally, explore the potential applications of Kyber. Discuss where post-quantum cryptography has already been implemented, and how Kyber can be used to establish secure communication channels in various scenarios.
- It would be helpful to include diagrams or flowcharts to illustrate Kyber’s algorithms and how users process and exchange messages from Kyber in practice.
- Part of this assessment requires you to read research papers. You are required to cite your sources appropriately.
- The resources provided by NIST and the creators of Kyber will be useful to you. Cite your sources appropriately.
- When describing the algorithms of Kyber, it will be useful to provide pseudocode descriptions of their algorithms. This will not contribute towards your word count.
- Aim for a clear and concise explanation, avoiding excessive technical jargon outside of the algorithm descriptions, security definitions and mathematical problems. Maintain a wellstructured format with headings and subheadings for easy navigation.
Acknowledgements. This exercise is in part inspired by the problems designed by Dr. Benjamin Dowling.
|
Percentage |
Marking Criteria |
|
80-100% |
Evidence of significant independent research. The student has clearly demonstrated their insight and understanding of the topic. Algorithmic descriptions, security definitions contain no errors, and are given intuitive explanations. The report reads well, with clear structure and with no grammatical errors or awkward wording. |
|
70-79% |
Evidence of independent research. Demonstration of understanding of the topic. Algorithmic descriptions, security definitions contain few errors, and explanations/motivations given are reasonably clear. Overall, the report reads well, with clear structure, but perhaps some grammatical errors or awkward wording. |
|
60-69% |
Evidence of independent research, but missing some supporting evidence or references. Student demonstrates understanding of the topic, but some aspects aren’t explained well. Algorithmic descriptions, security definitions contain minor errors, and explanations are given, but occasionally unclear. The report is structured unclearly, with difficult transitions and grammatical errors or awkward wording. |
|
50-59% |
Some evidence of research, but missing supporting evidence or references. Student demonstrates understanding of the topic, but frequently fails to explain intuition or understanding. Algorithmic descriptions, security definitions contain errors, and explanations are sometimes unclear. The report is understandable but difficult to parse. |
|
40-49% |
Some evidence of research, but missing core supporting evidence or references. Student fails to consistently display understanding of the topic. Algorithmic descriptions, security definitions contain errors, and explanations are unclear. The report is difficult to parse. |