Let's take a look at our essay first the algorithm is not a new development.
It was created back in 1977.
It's not the first asymmetric algorithm either.
The first application of the asymmetric cryptography scheme was Diffie and Hellmann secure key exchange
protocol the Diffie Hellman key exchange is still implemented today.
For example in public key infrastructure in sec this solution solve the problem with exchanging confidential
data through an untrusted channel.
What keeping the confidentiality of the data.
The point was not to send the key.
Which should not be done but to challenge a random message instead and receive a response both parties
make computations based on the challenge response messages a first user picks a key and generates a
challenge.
The second user picks a key receives the challenge.
Compute something based on it generates and sends a response.
Both users assume that they have provided the same key the result of the random cogeneration was the
same combination of digits.
Let's go back to rsa
the algorithm was granted a patent that expired in 2000.
To be able to use a before that time a license fee had to be paid the patent rights were given to RSA
data security on the expiry.
The RSA algorithm has been implemented in a number of solutions and software.
The basis for the operation here is key generation the encryption and decryption steps are relatively
uncomplicated.
Remember that the key the ciphertext and the plaintext will be you can represent any string as a number.
This is how computers operate.
Let's consider the key generating mechanism.
You have to pick two large primes the banks have to be large enough to be represented using 1024 2048
or preferably four thousand ninety six bits.
In this presentation we'll pick the standard prime numbers 7 and of computer product it's 77.
The next step is to find an exponent that satisfies an equation where the greatest common divisor of
the exponent and the product of the two primes minus one will be 1 as in the following formula.
This equation has many solutions.
In practice the smallest found is usually chosen.
The value has no bearing on the security of the ciphertext.
The smaller it is the faster the encryption will be for the two primes will picked.
You can choose.
E equals 37.
And this way you've found your public key.
The public key is made from the values and the 77 and 37.
Now a private key that corresponds to the public key has to be generated.
The private key will be generated based on the following equation.
You have to multiply B and D in such a way that you find a product of multiplying P minus one times
Q minus one as a Madieu operation parameter
for the values we calculated earlier D'Ken B 13 the value D will from this point be your private key.
It amounts to 13.
Why is this all working from what we officially know.
Finding the bodies and cube based on the value N is computationally complex as it turns out.
What we're able to calculate the Kedy by having the product.
If we don't know the values p and q we must resort to checking all possible solutions to the equation.
This is presumed infeasible because there are large prime numbers
encryption itself is easy.
It involves assuming that the plaintext has a value that is a bit smaller than n.
Next you perform a modular exponentiation.
The ciphertext you get is the plaintext raised the e power must do low n the values e n n are parts
of your public key.
If the plaintext was to the ciphertext will be 51
decryption as inverting this process to decode the ciphertext razy to the DB power model N.
In this way the result will recover to.