John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Abstract Algebra

Understanding Modular Arithmetic: Residues and Additive Inverses.

Unlike ordinary addition, there is not an additive inverse to each integer in modular arithmetic 1 In modular arithmetic, we work with numbers that are taken modulo...

John Rhodes
June 21, 2023
Abstract Algebra

Math Made Simple: Understanding Congruence Modulo n

Two integers a and b are said to be congruent modulo n, if (a mod n) = (b mod n). Fermat’s Little Theorem. This means that when...

John Rhodes
June 21, 2023
Abstract Algebra

Exploring the Crucial Role of Finite Fields in Cryptographic Algorithms.

Cryptographic algorithms do not rely on properties of finite fields. 0 This statement is not entirely accurate. Cryptographic algorithms make use of finite fields in various ways....

John Rhodes
June 21, 2023
Abstract Algebra

Understanding Finite Fields of Order p and their Applications in Cryptography and Coding Theory.

Finite fields of order p can be defined using arithmetic mod p. 1 Yes, that is correct. A finite field of order p is a mathematical structure...

John Rhodes
June 21, 2023
Abstract Algebra

Understanding AES Encryption: The Role of Finite Fields in Secure Data Transmission

The Advanced Encryption Standard uses infinite fields. 0 This is not entirely correct. The Advanced Encryption Standard (AES) is a symmetric encryption algorithm that uses a finite...

John Rhodes
June 21, 2023
Abstract Algebra

Mastering Modular Arithmetic: A Guide to Addition, Subtraction, and Multiplication Rules

The rules for ordinary arithmetic involving addition, subtraction, and multiplication carry over into modular arithmetic. 1 Modular arithmetic is a branch of arithmetic that deals with the...

John Rhodes
June 21, 2023
Abstract Algebra

Understanding Cyclic Groups: Properties and Examples.

A cyclic group is always commutative and may be finite or infinite. Z4 is a cyclic group generated by 1, and it is also abelian or commutative....

John Rhodes
June 21, 2023
Abstract Algebra

Understanding Fields in Mathematics: Definition and Properties

A field is a set in which we can do addition, subtraction, multiplication and division without leaving the set. 1 True. A field is a set of...