Introduction to Public key Cryptography

Public-key algorithms are asymmetric algorithms and, therefore, are based on the sue of two different keys, instead of just one. In public-key cryptography, the two keys are called the Private key and the Public key.

• Private key: This key must be known only by its owner.
• Public key:This key is known to everyone (it is public).
• Relation between both keys: What one key encrypts, the other one decrypts, and vice versa. It means that if A encrypts something with B’s public key (which A would know, because it's public), B would need his private key to decrypt the message.
  

Secure conversation using public-key cryptography:

In a basic secure conversation using public-key cryptography, the sender encrypts the message using the receiver's public key. The encrypted message is sent to the receiving end, who will decrypt the message with his private key. Only the receiver can decrypt the message because no one else has the private key. Also, the encryption algorithm is the same at both ends: what is encrypted with one key is decrypted with the other key using the same algorithm.


Key-pair Generation:

A public key cryptosystem is based on a “trap door one-way function,” that is, a function that is easy to compute in one direction and hard to compute in other direction. The purpose of the trap door is to ensure that an attacker cannot use the public information to recover the secret information.

Figure 5. Public key generation

Symmetric and Asymmetric key-based algorithms

Symmetric key-based algorithms use a single secret key for both encryption and decryption. To use a symmetric encryption scheme, the sender and receiver must share a key in advance. Because symmetric encryption is less computationally intensive and requires less bandwidth, it is common to exchange a key using a key-exchange algorithm and transmit data using an enciphering scheme.

Figure 3. Key-based Symmetric algorithm

Asymmetric key-based algorithm uses two keys - the key used to encrypt a message differs from the key used to decrypt it. In this, a user has a pair of cryptographic keys — a public key and a private key. The private key is kept secret, while the public key may be widely distributed. Messages are encrypted with the recipient's public key and can only be decrypted with the corresponding private key. The keys are related mathematically, but the private key cannot be feasibly (i.e., in actual or projected practice) derived from the public key.

Figure 4. Key-based asymmetric algorithm