Q:
# What Are the Benefits of Using a Program to Compute Number Combinations?

**A computer greatly reduces the time needed to encode information; it computes the multiplication number combinations and allows powerful algorithms to be implemented to generate codes that would be tedious to do by hand.** Computers are also necessary for decoding information transmitted.

For instance, in RSA encryption, there is what's known as a public key and a private key. The public key has two large integers, e and n, while the private key has two large integers, d and n. Note that both keys have the same number n, which is generated by multiplying two large prime numbers to form an even larger number. Due to the relationship between e, d, and n, the number d can be found if you know both e and n. The difficulty in finding what n is lies in factoring n into the two large prime numbers. There is no current method to find this combination in a reasonable time. As computer speed increases, to maintain security, n simply needs to be generated from larger prime numbers multiplied together. In 1990, 512-bit RSA keys were considered secure. As of 2016, n is a 4096-bit number, and there is no reason why it cannot be larger.

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