A Moment of Science

Internet Security and Prime Numbers

Ever wonder how websites like Amazon.com keep your personal information, like credit card numbers, safe from the internet bad guys? Well, here's the scoop.

Pile of credit cards

Photo: Andres Rueda (flickr)

When you enter private information online, your browser encodes your data and sends it off, including within the code a lock that can only be opened with the correct key.

Ever wonder how websites like Amazon.com keep your personal information, like credit card or check numbers, safe from the internet bad guys? Well, here’s the scoop.

At the Amazon website you enter in your private info, press “send”, and your internet browser quickly encodes your data and sends it off to Amazon. To make sure no one but Amazon can view your info, each code has a lock that can only be opened with the correct key, which Amazon has.

This is where prime numbers come into play. Prime numbers are those divisible only by themselves and 1, like the numbers two, three, five, seven, eleven etc. Of course these are very small prime numbers, but there are infinitely many of them and they can get big; the biggest found so far is thirteen million digits long!

The lock on the code protecting your private info is a very big number which is the unique product of two prime numbers, and the key to this lock are exactly these two primes. As a small example, take the number fifteen.

If this were our “lock” number, then the two primes three and five would be our “key”; since both are prime and three times five is fifteen. Unlike the small example however for a larger “lock” number it is nearly impossible to find the two “key” primes if you don’t already know them.

The best computers in the world might take years to find the “key” primes of a “lock” number only three-hundred digits long. Thankfully websites like Amazon typically use “lock” numbers at least this big, thus making it nearly impossible for a bad guy to sneak a peak at your private info online.

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