Cryptographic systems are methods used to secure information by transforming it into a format that is unreadable to unauthorized users. This process involves algorithms and keys, which are essential for both encrypting (scrambling) and decrypting (unscrambling) data. Common applications include securing online communications, protecting sensitive data, and ensuring the integrity of digital signatures. These systems rely on various techniques, such as symmetric encryption, where the same key is used for both encryption and decryption, and asymmetric encryption, which uses a pair of keys: a public key for encryption and a private key for decryption. Cryptographic systems are fundamental to modern cybersecurity.