The Mathematics behind Cryptography: Understanding Encryption

Welcome to this tutorial on the mathematics behind cryptography. Encryption is the process of converting plain text into a code that can be read only by the intended receiver. This is done using mathematical algorithms that are designed to be secure and unbreakable. In this video, we will explore the concepts of encryption, and how the mathematics behind cryptography makes it possible. To understand how encryption works, we need to first understand a little about modern cryptography and the different types of encryption technologies that are commonly used. In the modern digital age, cryptography is used in almost every aspect of online security, from email communications to online banking. Cryptography can be divided into two main types of encryption: symmetric and asymmetric encryption. Symmetric encryption uses a single key to encrypt and decrypt data, while asymmetric encryption (also known as public-key cryptography) uses two keys: one key to encrypt the data and another key to decrypt it. One of the most widely used encryption algorithms, Advanced Encryption Standard (AES), is a symmetric encryption algorithm. It uses a 128-bit key to encrypt data, which makes it virtually impossible to break. Asymmetric encryption, on the other hand, uses two keys – a public key and a private key – to encrypt and decrypt data. The public key is used to encrypt the data, while the private key is used to decrypt it. This is considered to be more secure than symmetric encryption since the private key is only known to the receiver, making it virtually impossible for anyone else to intercept the message. To better understand how encryption algorithms work, we need to look at some basic mathematical concepts. One such concept is modular arithmetic, which is used in many encryption algorithms such as RSA. Modular arithmetic is the process of performing mathematical operations on remainders, rather than only on whole numbers. This makes it possible to create complex algorithms that are more secure. Another mathematical concept used in encryption algorithms is prime numbers. Prime numbers are unique in that they can only be divided by the number one and themselves. This makes them ideal for use in encryption algorithms, as they are very difficult to factorise. A popular encryption algorithm that uses prime numbers is Rivest-Shamir-Adleman (RSA) encryption. RSA encryption is widely used in digital certificates, SSL/TLS, and SSH security protocols. It involves selecting two prime numbers, multiplying them together, and using the product as the public key. The security of encryption algorithms depends on the strength of the keys used. The stronger the key, the more secure the encryption. Key length is measured in bits, and longer keys provide more security. For example, a 128-bit key is more secure than a 64-bit key. In conclusion, cryptography is an essential tool for securing online communications in the modern digital age. Encryption algorithms use mathematical concepts such as modular arithmetic and prime numbers to keep data safe. Understanding the mathematics behind cryptography is essential for anyone who wants to study or work in the field of cyber security.