Public Key Cryptography

In computer science, public key cryptography is used for following purposes:

• Encrypt valuable information so that no one can read it.
• Identify source of publisher i.e. Digital Signatures.
• Cryptography private keys exchange.

How it works
To do this a key pair is generated i.e. a public key and a private key. Let suppose a user A generated his key pair then A will broadcast his public key. Now any one, let suppose B, who wants to communicate with A can get public key of A. Now they can communicate securely.

Encryption and Decryption Process
Suppose A and B wants to communicate securely. Then A and B will exchange their public keys to each let me explain it with an example:

Lets suppose

• A's key pair is Pa (Public Key) and Sa (Secret Key)
• B's key pair is Pb (Public Key) and Sb (Secret Key)

Now A wants to send a message to B such that no one can read it then

A will encrypt the message with public key of B and send it over network. The message payload will be received by B then B decrypt it by his private key. i.e if M is message, Pb is public key of B, Sb is secret or private key of B and C is cipher text which will be send over network then:

• A:   Encrypt  (M, Pb) = C
• B:   Decrypt  (C, Sb) = M

Do you know about man in the middle attack? this Encryption and Decryption process is vulnerable to man in middle Attack. For Example:

• A encrypt message M with public key of B which produce cipher text C and send C to network.
• An attacker capture the C which was send to B. Attacker know the public key of B then attacker can change the message and encrypt it with public key of B and send it to B. i.e Encrypt (FakeMessage, Pb) = FakeCipher  and send FakeCipher to B.
• Now when B decrypt it i.e Decrypt  (FakeCipher, Sb) = FakeMessage

What is solution of this such that no one can see message and also source of message is identified too. Answer is use of Digital Signatures.

Digital Signatures 
In public key cryptography digital signatures are widely used for source identification. who they works let me explain it by example:

Suppose A want to send A message to B and Also wants to identify him self then.

• A will encrypt the message with public key of B. i.e Encrypt  (M, Pb) = C
• Now A will use any hashing function SHA or MD5 and generate hash of message. i.e SHA (M) = hash. 
• Now A will encrypt whole package, cipher C and hash, with its own secret key Sa. i.e. Encrypt  (C+hash, Sa) = SignedCipher
• Now A send SignedCipher over the network.
• B recive the Signed Cipher and then decrypt it with public key of A this will give B orignal cipher and i.e. Decrypt  (SignedCipher, Pa) = C + hash
• Then B will decrypt the cipher i.e. Decrypt  (C, Sb) = M1
• Now B will generate a hash of M1 i.e. SHA (M1)
• If hash of M1 is equal to hash which was send previously then message is same which was send by A, also source of A is identified.

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