What is public key?
In the world of modern cryptography, the concept of public key encryption is essential. Public key encryption enables secure communication over insecure channels, ensuring the privacy and authenticity of the messages sent between parties. But what exactly is a public key, and how does it work?
At a high level, a public key is a component of a public key cryptosystem that enables secure communication between two parties. The public key is a mathematical function that can be used to encrypt messages, but cannot be used to decrypt them. The counterpart to the public key is the private key, which is kept secret by its owner and can be used to decrypt messages encrypted with the public key.
Public key cryptography was first proposed by Whitfield Diffie and Martin Hellman in 1976. Their proposal was a significant advancement over traditional symmetric-key cryptography, which required both parties to share a secret key before they could communicate securely. With public key cryptography, only one party needs to generate and distribute a public key, which can then be used by anyone to encrypt messages that only the owner of the corresponding private key can decrypt.
One of the most widely used public key cryptosystems is the RSA algorithm, named after its inventors Ron Rivest, Adi Shamir, and Leonard Adleman. The RSA algorithm is based on the difficulty of factoring large numbers, which means that it is very difficult to determine the private key from the public key. To generate an RSA key pair, one selects two large prime numbers, computes their product (which is used as the modulus), and then selects an exponent that is relatively prime to the product. The public key is the modulus and exponent, while the private key is the modulus and a different exponent that satisfies a specific mathematical relationship with the public exponent.
To use public key encryption, the sender of a message encrypts it using the recipient’s public key. The recipient then uses their private key to decrypt the message. This provides confidentiality, as only the recipient with the corresponding private key can read the message. Public key encryption also provides authenticity, as the sender can sign the message using their private key, which the recipient can verify using the sender’s public key.
In addition to encryption and digital signatures, public key cryptography has many other applications, including key exchange, secure hash functions, and digital certificates. Public key encryption is widely used in modern communications protocols, such as SSL/TLS for secure web browsing and SSH for secure remote access.
In conclusion, public key encryption is an essential concept in modern cryptography. The public key is a mathematical function that can be used to encrypt messages, but cannot be used to decrypt them. Public key cryptography enables secure communication between parties without requiring a shared secret key, providing confidentiality and authenticity. The RSA algorithm is one of the most widely used public key cryptosystems, and public key encryption has many other applications beyond secure communication.