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### Prime Numbers in Cryptography

```
Date: 08/14/99 at 07:03:02
From: Peter Rebernik
Subject: Practical Use of Prime Numbers

What are the practical uses of prime numbers? Is there any real use
for them other than testing the knowledge of students?
```

```
Date: 08/14/99 at 18:45:03
From: Doctor Tom
Subject: Re: Practical Use of Prime Numbers

Hi Peter,

Almost all of the new methods for cryptography depend heavily on prime
numbers. Some of the best encoding schemes require the product of two
primes to do the encoding, but require the primes themselves to do the
decoding. In general, it is FAR more difficult to find the factors of
a number than to multiply the two numbers, so I can send secret
messages as follows:

I pick two primes, multiply them together, and give you the product.
You encode using the product, send me the encoded message, and I can
decode it because I know the two numbers. This is a "public" method,
since I can give the product to anyone, so anyone can send me a
message that only I can read.

The two numbers, by the way, usually are 100 digits long or so, so
factoring the product might require centuries on a large computer.

In addition, there are dozens of algorithms in computer science that
depend heavily on prime numbers - hashing schemes, sorting schemes,
and so on.

- Doctor Tom, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory
Middle School Prime Numbers

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