Encryption El Gamal

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The program shows the encryption algorithm El Gamal. You must enter P, Q, and X number and a word or sentence that you want zashirovat. Security El Gamal scheme due to the complexity of computing discrete logarithms in a finite field.
In order to generate a key pair (public key - private key), first choose a large prime number P and a large integer G, where G <R. The numbers P and G can be distributed among the group members. Then choose a random integer X, where X <P. The number of X is the secret key should be kept secret.
Next calculate Y = GX mod P. The number Y is the public key. To encrypt a message M, choosing a random integer K, 1 <K <P-1, such that the number of K and (P-1) are relatively prime. Then calculate the number a = GKmodP, b = YK M mod P. The pair of numbers (a, b) is the ciphertext. Note that the length of the ciphertext twice the length of the original plaintext M. In order to decrypt ciphertext (a, b), calculated M = b / aXmod R.