• This is a program which uses RSA Cryptosystem to generate 1024 bit keys and encrypt texts.

• It requires Java 8 or higher.

1. Rsa Key Generation Tool Given Two Prime Numbers List
2. Rsa Key Generation Tool Given Two Prime Numbers Make 50

This, finally, is the heart of what makes RSA a trapdoor function: the gap between obtaining a number with two prime factors, and rediscovering the factors from the number itself. And the gap just keeps expanding as the numbers get larger. Dec 10, 2018 Generating the public key. Now that we have Carmichael’s totient of our prime numbers, it’s time to figure out our public key. Under RSA, public keys are made up of a prime number e, as well as n. The number e can be anything between 1 and the value for λ(n), which in our example is 349,716.

What is RSA Cryptosystem?

• RSA Algorithm is one of the first public-key cryptosystems and widely used for datatransmissions. In such a cryptosystem, the encryption key is public and it is different from the decryption key which is kept secret (private). In RSA, this asymmetry is based on the practical difficulty of the factorization of the product of two large prime numbers, the 'factoring problem'. The acronym RSA is made of the initial letters of the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who first publicly described the algorithm in 1978.

How To Use?

• To generate keys, open Key Generator from Tools menu. You can also see the prime numbers, p and q, which were used to generate keys.

• To Enter the text which will be encrypted/decrypted, open Text Pane from Tools menu. Write the text there and press ESC key to save and close the window. Press Process key to continue to encryption/decryption, then a window will be opened which has encrypted/decrypted text.

• Here is my e-mail address: burkaykirnik@gmail.com

• For further information or any questions, feel free to e-mail me.

RSA works using a public key and a private key and its strength relies on the hardness of prime factorization (a set of prime numbers that you multiply together to get another number). The first step in the RSA algorithm involves generating the keys.

Generating key

Choosing two primes

This is done in generate_keypair(private_key, public_key) function.Before we call this function we choose two different prime numbers (p and q), one for our private key and the other for our public key. Lets imagine I pick 2 and 7, and then we pass it to our function, so:

Calculating n

Now the first thing we do inside this function is to compute n and it's nothing more than p and q multiplied together. n is used as the modulus for the encrypting key and decryption key. So let't calculate our n:

Using Euler's totient function to calculate Phi (φ)

Next comes calculating Phi(n) (φ(n)) and it's used to calculate how many integers are less than or equal to n that do not share any common factor with n. What's interesting and important here, is that, calculating the phi function is hard, except in the case of prime numbers. Since prime numbers have no factors greater than one, the phi of any prime number, p is simply p - 1. Therefore:

In our code:

Choosing e

e is important for our encryption because e and n it will become our public_key. e must be picked randomly and have certain properties. Such as:

• 1 < e < φ(n) (in our case e must be between 1 and 288)
• Must be coprime with n and φ(n) (in our case, must be coprime with 323 and 288)We do so here:

/key-tasks-for-generativity-vs-stagnation-253.html. if g returns one then e is coprime with phi, so their greatest common divisor is 1, which means that 1 is the only positive integer (factor) that divides both of them, e and phi.

Calculating d

We use the Extended Euclid's Algorithm to generate d. This is a private exponent, it will be a part of our private key and this is used to undo the effect of e

Public key and Private key

With n, e and d, we can now get our public and private key pairs.

Public key

Rsa Key Generation Tool Given Two Prime Numbers List

The public key pair is (e, n). This is what the server sends us, its public and anyone can read it.

Private key

The private key pair is (d, n). This can not be shared with anyone. It will be used to decrypt messages encrypted with the public key.

For encrypting this is what we do: (m^e) % nThis function will use the public key to encrypt our plain text. We'll encrypt the string 'asd'.Let's first get our e and n from our public key pair. Then, we loop through each character in our string and get the Unicode value using ord() function. With this we then exponentiate that value by e and finally get the remainder with mod n.

Our encrypted message should look like this:

In the decrypting process we use our private key, and the process in almost the same, except that, we use d our private exponent instead of e. So:

Rsa Key Generation Tool Given Two Prime Numbers Make 50

Now we loop through each character performing our calculation. In the end we use chr() function to get our character back.