Principles of information security and relevant mathematical concepts. Classical ciphers, relevant abstract algebra and number theory, symmetric-key ciphers, cipher modes of operation, and asymmetric-key ciphers. Cryptographic hash functions and message authentication codes. Elliptic curve cryptography and cryptosystems. Applications and standards relevant to network and computer security.
Past experiences have shown us that security mechanisms of a given system or network must be properly designed from the very beginning, and not added on as an afterthought. If the required security mechanisms are not carefully integrated into the target system/network a priori to deployment, potential security breaches can inflict enormous damage. This issue is becoming more critical than ever as we see an increase in the exchange of sensitive information (e.g., medical records, financial data, etc.) over insecure network links. the design, deployment, and management of secure systems or networks require the ability to understand core security concepts, analyze the security vulnerabilities of a target system, and design necessary cryptosystems for the target system. This course provides requisite knowledge of fundamental security concepts and a brief introduction to their applications that are need3ed by students who are conducting research in security-related topics.
Percentage of Course
|1. Introduction to basic security concepts||5%|
|2. Classical ciphers||5%|
|3. Abstract algebra: a) Groups, rings, fields, and finite fields; b) Modular arithmetic and arithmetic in finite fields; c) The Euclidean algorithm||10%|
|4. Symmetric-key cryptosystems and Advanced Encryption Standard (AES)||20%|
|5. Cipher modes of operation||5%|
|6. Number theory: a) Primality testing algorithms, the Chinese remainder theorem; b) Fermat's little theorem, Euler's theorem; c) Euler's totient function, the discrete logarithm problem||10%|
|7. Asymmetric-key cryptosystems||20%|
|8. Cryptographic hash functions and message authentication codes||5%|
|9. Elliptic Curve Cryptography (ECC) and ECC-based cryptosystems||5%|
|10. Applications of cryptographic algorithms and protocols||15%|