RSA Public-Key Algorithm as Cited in Kaufman,

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 size with probabilistic primary tests, which quickly eliminate most non-prime numbers. "If such a test finds a "probable prime," a deterministic test should then be used to verify that the number is indeed prime," and "p and q should not be "too close," else they are easily decrypted. (Wordiq Encyclopedia, 2004)

Another way of looking at the use of RSA in cryptography is provided by the Wordiq Encyclopedia. This reference posits the supposition that a user might wish to allow another user to send him or her a private message over an insecure transmission medium. The user would then take, to use RSA as a security device, "the following steps," as suggested above, and begin the factoring process by first generating a public key and a private key" using RSA formula.