Lecture

Arithmetic with Base 2 Expansions

Related lectures (27)

Covers binary addition, multiplication, and modular exponentiation of integers.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Integer Representations: Magnitude & Complement

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

Binary Counting

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

Computation: information representation

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

Exponentiation: Time Complexity

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

Vector Spaces: Definition, R2

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

Computer Arithmetic (Integers)

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

Integers Representation: Sign vs. Two's Complement

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

Cryptography and Information Theory

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

Algorithms for Big Numbers: Z_n and Orders

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Quantum Random Number Generation

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

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Diffie-Hellman Cryptography: Basics

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

Logic Systems: Arithmetic Operations

Covers classic pen-and-paper methods for arithmetic operations and binary representations of numbers.

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.

Public Key Cryptography: RSA

Explores public key cryptography, focusing on RSA, key generation, encryption, decryption, security challenges, and vulnerabilities.

Binary Operations: Addition and Multiplication

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

Number Theory: Fundamental Concepts

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

Introduction to Cryptography: Fundamentals and Applications

Covers the fundamentals of cryptography, including symmetric encryption, digital signatures, and secure communication standards.