Lectures related to Arithmetic with Base 2 Expansions

Covers binary addition, multiplication, and modular exponentiation in cryptography.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Covers the fast exponentiation algorithm and its time complexity, prime number properties, and the El-Gamal encryption scheme.

Computer Arithmetic (Integers)

Covers binary representation, two's complement, overflow detection, and operations in MIPS for computer arithmetic with integers.

Binary Counting

Covers the process of counting in binary and performing addition and multiplication operations.

Quantum Random Number Generation

Explores quantum random number generation, discussing the challenges and implementations of generating good randomness using quantum devices.

Vector Spaces: Definition, R2 MOOC: Linear Algebra (Part 1)

Introduces vector spaces with binary addition and scalar multiplication, exploring geometric examples in R2.

Modular Arithmetic: Introducing Z/mZ

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Number Theory: Fundamental Concepts

Covers binary addition, prime numbers, and the sieve of Eratosthenes in number theory.

Binary Operations: Addition and Multiplication

Covers binary operations, including addition and multiplication of integers represented in binary form.

Cryptography and Information Theory

Explores cryptography, perfect secrecy, group theory, and modern cryptographic milestones, emphasizing the trade-off between security and cost.

Diffie-Hellman Cryptography: Basics

Introduces the basics of Diffie-Hellman cryptography, covering algorithms, monoids, and key agreement protocols.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Number Theory: Foundations and Applications in Cryptography

Introduces number theory and its essential applications in cryptography.

Computer Arithmetic: Floating Point Numbers

Explores computer arithmetic, emphasizing fixed-point and floating-point numbers, IEEE 754 standard, dynamic range, and floating-point operations in MIPS architecture.

Polynomial Applications: Combinatorial Computations

Delves into using polynomials for combinatorial computations and explores operations and identities with binomial coefficients.

Elliptic Curve Cryptography: Galois Fields

Explores Galois fields, elliptic curve cryptography, arithmetic operations, group structure, and practical examples in cryptography.

Integer Representations: Magnitude & Complement Log in to Mediaspace to watch this video

Explores integer representations, focusing on sign-and-magnitude, one's complement, two's complement, Excess-N, overflow, underflow, and binary multiplication.

Computation: information representation Log in to Mediaspace to watch this video

Covers the conversion between binary and decimal numbers, addition, subtraction, multiplication, and division operations.

Integers Representation: Sign vs. Two's Complement Log in to Mediaspace to watch this video

Explores integer representation methods, comparing sign-and-magnitude with two's complement, and introduces fixed-point and floating-point representations.