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== Modern Uses Of Cryptography ==
== Modern Uses Of Cryptography ==
Currently the most common form of cryptography is public key encryption. This relies on the fact that it takes significantly (order 10<sup>8</sup> times) longer to find two prime factors of 200 or more digit numbers than it does to multiply the numbers together to create the 1000 digit number in the first place.
Currently the most common form of cryptography is public key encryption. This relies on the fact that it takes significantly (order 10<sup>8</sup> times) longer to find two prime factors of 1000 or more digit numbers than it does to multiply the numbers together to create the 1000 digit number in the first place.
In this system there are two keys, the first is the "private key", which only the '''recipient''' knows. The second is the "public key" which can be sent freely to anyone, allowing them to encrypt messages with it such that only the owner of the private key can decrypt them. These public keys are calculated from the private keys, but as they are often over 1000 digits long and would take many decades to calculate the private key from them (RSA, the most commonly used encryption protocol uses 2048 digit numbers which would take over 4000 years to crack with a desktop computer)
In this system there are two keys, the first is the "private key", which only the '''recipient''' knows. The second is the "public key" which can be sent freely to anyone, allowing them to encrypt messages with it such that only the owner of the private key can decrypt them. These public keys are calculated from the private keys, but as they are often over 1000 digits long and would take many decades to calculate the private key from them (RSA, the most commonly used encryption protocol uses 2048 digit numbers which would take over 4000 years to crack with a desktop computer)