In this article, we’ll discuss the Bipolar principles in cryptography now the goal here is for Alice to communicate securely with Bob

so what Alice wants to do is to send some plain text message m to Bob but if anna sends this message as is Bob what

can happen is Trudy might intercept this plain text message and she would be able to understand what Alice is sending to

Bob so Alice’s goal is to communicate securely with Bob in such a man and the Trudy cannot understand what she is sending to Bob

to do this but Alice does if she takes a plain text message and she would convert it to some **ciphertext **send it over the channel and once Bob

receives his ciphertext or Bob would do his Bob would regenerate the plaintext from this ciphertext even if Trudy is able to intercept this ciphertext truly

will not be able to get the plain text message that Alice sent to Bob so this is what cryptography would help Alice achieve so to do that what does Alice

## Bipolar principles in cryptography

need Alice needs an encryption algorithm at her end and an encryption key which is denoted by **K subscript** A, in this

slide what Alice does is Alice uses the encryption algorithm under key to generate a ciphertext which we denote as K subscript A with M within parenthesis

this ciphertext is sent over the channel and once Bob receives this ciphertext Bob uses the decryption key that is Kb and our decryption algorithm and is U

and by using both of these together bodies Bob is able to generate the plaintext so basically what the operations that happen on Alice firs

uses her encryption algorithm and her key K on the plaintext M this is what generates the ciphertext Ka(M) the ciphertext once is received by Bob

Bob applies the key Kb and the decryption algorithm to regenerate the plain text M the goal is is to make sure that even though Trudi

intercept the ciphertext Ka(M) she cannot apply any kind of key to decrypt the original message him as long as the key KB is safe with Bob

truly will not be able to understand what Alice sent Bob so let’s try to understand this with an example the

simplest cryptographic example this symmetric-key cryptography in symmetric cryptography what we assume is that both

Alice and Bob shared the same key do you know Becky s in this example of course a big question that arises is how Bob

and Alice agree upon the key value will not discuss this in this article and will defer this discussion to a later post

now both Alice and Bob have the same key KS so what Alice does is she uses the scheme KS and the encryption algorithm

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on the plaintext message m and what ciphertext she generates is K subscript test with M within parenthesis when that

the ciphertext is received by Bob but once again uses the same key KS to generate them plaintext time again so what’s an example of this kind of cryptography

an example is a key in the key is knowing substitution pattern in a monoalphabetic substitution cipher so let’s look at

this example in a substitution cipher what we do is we substitute one thing for another in a monoalphabetic science substitution cipher what is done is

each letter is substituted for another so let’s look at the plaintext here so here E is substituted by M B is substituted by n C is substituted by V and so on and

so forth so there is a one on one to one mapping between the I each alphabet in the plaintext and the ciphertext this

is the encryption key the mapping of 26 letters to another set of 26 letters is the encryption key and this is what a

shared between both Alice and Bob so let’s assume that Alice wants to send this plaintext message Bob I love you Alice the corresponding ciphertext

using this key would be as shown in the slide for example if you just consider you see that the mapping between plaintext in the ciphertext for B is n

for its scale and for beads and again so it is going to be MK n and by using the same logic you could construct the ciphertext for this plaintext and you

could verify that what we have in the slide is correct a more sophisticated encryption approach would be to use in substitution ciphers

m1 m2 all the way up to MN so what do I mean

so let’s assume that you have for such substitution ciphers that are n equal to 4 m1 m2 m3 and m4 and then you could use

acyclic code pattern in which you are going to use these ciphers for example the psychological pattern could be

M 1 M 3 M 4 M 2 sorry M 4 M 3 M 2 and repeat

this process again so how would you convert plaintext to ciphertext using this approach say you want to convert the plaintext dog to a ciphertext so

what you would do is you would convert D using M 1 o using M 3 and gu z m4 you see the pattern is M 1 M 3 M 4 M 3 M 2

so here we only have 3 alphabets so the first one is converted using the cipher M 1 the second is converted using M 3

and the third is converted using the cipher M 4 so the encryption key here is that the N substitution ciphers and the

psyche little pattern that is going to be used but this will conclude this lecture

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