5.4 Asymmetric Cryptography

Topic 5.4: Asymmetric Cryptography

Asymmetric encryption, also known as public-key cryptography, is a revolutionary system that allows for secure communication between two parties without the need for them to pre-share a secret key. This is achieved through the use of a mathematically linked key pair: a public key and a private key.

When an individual wishes to receive encrypted data, they first generate this key pair. The private key must be kept secret and secure at all times; its compromise would break the security of all communications. The public key, as its name suggests, is made available to anyone who wants to send an encrypted message to the key pair's owner.

The two keys are mathematical inverses. Information encrypted with the public key can only be decrypted by its corresponding private key. This one-way relationship is the foundation of confidentiality in asymmetric cryptography. To send a secure message, the sender obtains the receiver's public key. The sender then uses this public key to encrypt the plaintext message, creating ciphertext. This ciphertext can be sent over an unsecure channel. Upon receipt, the receiver uses their own private key to decrypt the ciphertext, restoring it to the original plaintext. Because only the receiver possesses the necessary private key, no one else can read the message.

The security of an encrypted message is directly related to the length of the key. A longer key creates a larger keyspace (the total number of possible keys), making it exponentially more difficult for an adversary to guess the key through a brute-force attack. For a key of n bits, there are 2^n possible keys. As computational power increases over time, the recommended minimum key lengths for cryptographic algorithms are periodically increased to maintain security. It is important to note that key lengths can only be compared within the same algorithm family. For example, a 2048-bit key for the RSA algorithm is more secure than a 1024-bit RSA key, but this cannot be directly compared to the security of a 256-bit AES key, as they are different types of algorithms with different mathematical properties.

Common asymmetric encryption algorithms include RSA and Elliptic Curve Cryptography (ECC). These algorithms can be used to encrypt and decrypt data using command-line tools like OpenSSL, specialized software, or web-based applications. The process involves first generating a key pair, then extracting the public key to share with others, and finally using the appropriate keys for encryption and decryption.