TAILIEUCHUNG - Lecture Data security and encryption - Lecture 11: Number Theory and Finite Fields

This chapter presents the following content: Number theory, divisibility & GCD, modular arithmetic with integers, Euclid’s algorithm for GCD & inverse, the AES selection process, the details of Rijndael – the AES cipher, looked at the steps in each round out of four AES stages, last two are discussed: MixColumns, AddRoundKey. | Data Security and Encryption (CSE348) Lecture slides by Lawrie Brown for “Cryptography and Network Security”, 5/e, by William Stallings, briefly reviewing the text outline from Ch 0, and then presenting the content from Chapter 1 – “Introduction”. Lecture # 11 Review The AES selection process The details of Rijndael – the AES cipher Looked at the steps in each round Out of four AES stages, last two are discussed MixColumns AddRoundKey The key expansion Implementation aspects Chapter 5 summary. Chapter 4 Basic Concepts in Number Theory and Finite Fields Intro quote. The next morning at daybreak, Star flew indoors, seemingly keen for a lesson. I said, "Tap eight." She did a brilliant exhibition, first tapping it in 4, 4, then giving me a hasty glance and doing it in 2, 2, 2, 2, before coming for her nut. It is astonishing that Star learned to count up to 8 with no difficulty, and of her own accord discovered that each number could be given with various different divisions, this leaving no doubt that she was consciously thinking each number. In fact, she did mental arithmetic, although unable, like humans, to name the numbers. But she learned to recognize their spoken names almost immediately and was able to remember the sounds of the names. Star is unique as a wild bird, who of her own free will pursued the science of numbers with keen interest and astonishing intelligence. — Living with Birds, Len Howard Intro quote. Introduction Finite fields have become increasingly important in cryptography A number of cryptographic algorithms rely heavily on properties of finite fields Notably the Advanced Encryption Standard (AES) and elliptic curve cryptography Finite fields have become increasingly important in cryptography. A number of cryptographic algorithms rely heavily on properties of finite fields, notably the Advanced Encryption Standard (AES) and elliptic curve cryptography. The main purpose of this chapter is to .

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• Data security
• Data security and encryption
• Network security
• Symmetric ciphers
• Asymmetric ciphers
• Cryptographic data integrity algorithms
• Mutual trust
• Lecture Data security and encryption
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• IPSec security framework
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• Wireless Network Security
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