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Let's take a look at our essay first the algorithm is not a new development.

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It was created back in 1977.

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It's not the first asymmetric algorithm either.

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The first application of the asymmetric cryptography scheme was Diffie and Hellmann secure key exchange

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protocol the Diffie Hellman key exchange is still implemented today.

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For example in public key infrastructure in sec this solution solve the problem with exchanging confidential

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data through an untrusted channel.

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What keeping the confidentiality of the data.

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The point was not to send the key.

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Which should not be done but to challenge a random message instead and receive a response both parties

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make computations based on the challenge response messages a first user picks a key and generates a

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challenge.

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The second user picks a key receives the challenge.

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Compute something based on it generates and sends a response.

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Both users assume that they have provided the same key the result of the random cogeneration was the

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same combination of digits.

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Let's go back to rsa

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the algorithm was granted a patent that expired in 2000.

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To be able to use a before that time a license fee had to be paid the patent rights were given to RSA

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data security on the expiry.

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The RSA algorithm has been implemented in a number of solutions and software.

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The basis for the operation here is key generation the encryption and decryption steps are relatively

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uncomplicated.

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Remember that the key the ciphertext and the plaintext will be you can represent any string as a number.

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This is how computers operate.

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Let's consider the key generating mechanism.

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You have to pick two large primes the banks have to be large enough to be represented using 1024 2048

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or preferably four thousand ninety six bits.

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In this presentation we'll pick the standard prime numbers 7 and of computer product it's 77.

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The next step is to find an exponent that satisfies an equation where the greatest common divisor of

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the exponent and the product of the two primes minus one will be 1 as in the following formula.

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This equation has many solutions.

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In practice the smallest found is usually chosen.

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The value has no bearing on the security of the ciphertext.

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The smaller it is the faster the encryption will be for the two primes will picked.

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You can choose.

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E equals 37.

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And this way you've found your public key.

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The public key is made from the values and the 77 and 37.

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Now a private key that corresponds to the public key has to be generated.

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The private key will be generated based on the following equation.

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You have to multiply B and D in such a way that you find a product of multiplying P minus one times

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Q minus one as a Madieu operation parameter

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for the values we calculated earlier D'Ken B 13 the value D will from this point be your private key.

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It amounts to 13.

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Why is this all working from what we officially know.

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Finding the bodies and cube based on the value N is computationally complex as it turns out.

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What we're able to calculate the Kedy by having the product.

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If we don't know the values p and q we must resort to checking all possible solutions to the equation.

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This is presumed infeasible because there are large prime numbers

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encryption itself is easy.

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It involves assuming that the plaintext has a value that is a bit smaller than n.

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Next you perform a modular exponentiation.

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The ciphertext you get is the plaintext raised the e power must do low n the values e n n are parts

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of your public key.

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If the plaintext was to the ciphertext will be 51

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decryption as inverting this process to decode the ciphertext razy to the DB power model N.

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In this way the result will recover to.