RSA public key cryptography

This comprehensive guide is structured to build your knowledge step-by-step. 1. Introduction to RSA Public Key Cryptography Start with the core principles of asymmetric encryption and the geniuses behind the algorithm. - The RSA Algorithm: Named after its creators—Rivest, Shamir, and Adleman. - Public and Private Keys: Learn how RSA uses a public key (K) that is freely available and a private key (G) that is hidden. - One-Way Functions: Grasp the fundamental concept that makes RSA secure: functions that are easy to compute in one direction but incredibly hard to reverse. The notes use the analogy of multiplying two large prime numbers (p,q), which is easy, versus factoring their product (pq), which is hard. - Core Use Cases: Understand how RSA is used for both confidentiality (encrypting a message with someone's public key) and authentication (signing a message with your own private key). 2. The Mathematical Foundations Dive into the essential mathematics that makes RSA possible. - Prime Numbers & Co-primes: Get clear definitions of prime numbers and co-prime numbers (two numbers whose greatest common divisor is 1). - Euler's Phi Function ϕ(n): A crucial component of RSA, this function counts the number of positive integers less than n that are co-prime to n. The notes explain key properties. - Modular Arithmetic: Learn the "remainder" operation (e.g., 13(mod6)=1) and why it's a perfect one-way function for cryptography. 3. Generating RSA Keys Discover the step-by-step process for creating the public and private keys. 4. The Proof That RSA Works For the advanced student, this section provides a mathematical proof of RSA's effectiveness, grounded in established number theory. - The Fermat's Little Theorem 5. Practice Assignments & Quizzes Test your understanding and reinforce your learning with integrated quizzes covering all key areas. - Practice questions on the properties of public/private keys and one-way functions. - Mathematical challenges involving modular arithmetic