RSA Public-Key Algorithm

As cited in Kaufman, Perlman & Speciner the security features inherent to an RSA public-key algorithm depends on the difficulty that an attacker has in factoring very large, preferably prime numbers. One specific example of an RSA might be as follows: "Step 1: Choose two very large primes" usually by using random number generation, such as "simple e.g., P=47, Q=71 and set N = P*Q = 3337 and M = (P-1)*(Q-1) = 3220. Step 2:Choose E. relatively prime to M, e.g. E=79 Set D = E^-1 (mod M) = 79^-1 (mod 3220) = 1019. Step 3: Public key is (N, E) = (3337, 79). Step 4:Private key is (N, D) = (3337, 1019). Step 5:To encrypt n, C = cipher = n^E (mod N) = n^79 mode 3337." (Newman, 1997)

Finding the large primes p and q is usually done by testing random numbers of the right...
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