Is message sent by you is secure?

The words encryption and decryption are familiar to us. You have countered these words in your in digital field as well as in daily life. What is encryption and why do we need it?

Let’s find.

How does our message travels through internet? 

A local internet service provider communicates with a regional service provider along with network service provider and at last destination. We know that the data transfer takes place in form of packets and it can take any route to reach destination via router. Normally we thought ISP and NSP don’t track us. When we connect our smart phone with public Wi-Fi or restaurant hotspot, we need to keep security in mind. The agency/person who installed the Wi-Fi cannot know that what we are accessing. Many of you have noticed the words HTTP or HTTPS in URL which you are accessing, these are protocols for internet communication. The letter ‘s’ in HTTPS represents communication is secured. Access point providers can only access the site. They cannot use our logins or the webpage which we are accessing. All these are connections are encrypted. In the cellular communication data is encrypted between communication tower and mobile phone. 

Encryption & Decryption

Let understand how this important encryption is done?

Encryption is a process to convert plaintext into cipher text. For example word ‘HELLO’ in ASCII code will be 072 069 076 076 079 (Message) and its encryption can be done by adding +1 to the code which will result in 073 070 077 077 080 (Encrypted Message). Here +1 is called as encryption key. Only the receiver who knows the key can decrypt the message by -1 to 072 069 076 076 079 (Decrypted Message). An intruder cannot decrypt the message. It can be understood as a confidential message locked in a briefcase and only the person who has key can access the briefcase. A responsible ‘key distribution center’ takes responsibility to transfer key from center to receiver and if the receiver uses same key to access data the encryption is called symmetrical encryption and if opening key is different from locking the key the encryption will be called asymmetrical key. What happens if key has stolen?

Let design an intelligent locking system to solve the issue.

In intelligent system every user will have two keys and the users will submit one key to the key distribution center means these keys are available in public and let name it as ‘public key’, and the second key which is held by users are kept private and no one shares and we called it private key. Interesting part of this intelligent system is a lock. This lock can be locked with any public key and the same key cannot open the lock, to unlock the lock you will need use private key corresponding to lock. Private or public key of other users cannot unlock. With this system data is transfer is highly secured.

Let see how data transfer is safe?

Suppose your friend wants to send you some confidential documents. He will demand your public key from key distribution center and will lock the briefcase with your public key, when the briefcase will sent to you only you can open the briefcase with the private key you have. You can relate this example with  digital communication, here the message ‘hello’ is encrypted with your public key and only the private key of you  will decrypt the message ‘hello’. 

Security

Let take a look at peculiar properties of this lock.

We have already seen that this lock is locked with a public key and opened with corresponding private key. In this digital world relation between used keys should be kept in mind otherwise algorithm will not do anything at all. The secure connection between these keys is prime numbers. Public and private keys are obtained by product of two prime numbers. These example is only representative. In real world prime numbers are not used to generate these keys. A popular algorithm used in generation of Public/Private key is RSA (Rivest-Shamir-Adleman). How RSA uses two prime numbers to generate public and private key. Look below.

Public key generation

Let us take prime numbers be p=3 and q=11

Product n = pq = 33

Euler Totient Function = (p-1) x (q-1) = 2 x 10 = 20 = φ(n)

Choose an encryption key e, such that gcd(e, φ(n))=1 gcd (3,20)=1

Public Key = 3

Private key generation

Such that ( 3 x d) modulus 20 = 1

3xd = minimum (21)

 d = 21/3 = 7

Private key = 7

Let  take prime numbers p = 3 and q = 11 to encrypt and decrypt ‘H’

ASCII for H is 104.

Encryption

Cipher text = (104)³ mod 33

                     = (104 x104 x 104) mod 33

                     = (5 x 5 x 5 ) mod 33

                     = (125) mod 33

                     = 26 (Encrypted)

Decryption

= (26)⁷ mod 33

= (26 x 26 x 26 x26 x 26 x 26 x 26) mod 33

= ( -7 x -7 x -7 x -7 x -7 x-7 x -7) mod 33

= ( 49 x 49 x 49 x – 7 ) mod 33

= (-17 x-17 x 17 x -7) mod 33

= ( 289 x 119 ) mod 33

= (-8 x -13) mod 33

= 104 (Decrypted message)

The detailed explanation to the above algorithm is beyond this article.

Why we use only prime numbers and why not other numbers?

The process of finding the factors of any number is called factorization. A hacker always tries to factorize present numbers in encryption, he can succeed to get private key. When prime numbers are not included to encrypt, factorization method works very fast and if prime numbers are used the method is slow especially when prime number used are greater. By this method hacker will try to steal your private key using RSA method. 

Asymmetric encryption has replaced symmetric encryption method. The problem with asymmetric encryption is that it is computationally intensive. RSA will stop hacking only if prime numbers used are very large, means if we directly use RSA, time taken to data transfer will be large. To overcome this problem a smart solution is taken in use called Advance Encryption Standard. In using private and public key cryptography one key is exchanged in form of message this key is called session key and this key will be a symmetric key. By using this symmetric key, two parties can exchange data without any further key transfer. Session is updated on basis of communication protocols.

For example in whatsApp for every message there is a new session key. In https it is valid only for a session. Key size for private and public key is 2048 Bits and it takes great time in comparison with asymmetric and symmetric system which uses key size about 256 bits. Message encrypted by 256 bits are more secure than 2048 bits keys and these are less computationally intensive. 

Public private key system also establishes an authenticated communication