Why are prime numbers used in Encryption

[Name777]

Why are prime numbers used in Encryption and can people do encryption without prime numbers and is the encyption still strong

[jemidiah]

I know RSA uses primes heavily. I'm sure schemes can be thought up that don't use them....

[obi1kenobi]

Prime factorization of a number is a difficult and tedious process which cannot be automated at a satisfactorily high level, especially for huge prime numbers and their multiples. Thus it cannot be done by brute force quickly enough in order to crack the encryption in a reasonable amount of time. There are also other methods: discrete logarithm problem, elliptical curves and so on. Basically, all encryption methods are based on solving a difficult problem in number theory, in order to prevent a computer from solving it quickly enough. Here are some links you may find interesting:

http://en.wikipedia.org/wiki/Cipher
http://en.wikipedia.org/wiki/Cryptography
http://en.wikipedia.org/wiki/Digital_signature
http://en.wikipedia.org/wiki/Cryptog..._hash_function
http://en.wikipedia.org/wiki/One-way_function
http://en.wikipedia.org/wiki/One-way...ssion_function
http://www.keylength.com/en/4/
http://csrc.nist.gov/groups/ST/toolkit/index.html
http://www.cs.auckland.ac.nz/~pgut001/tutorial/
http://www.schneier.com/blowfish.html

These are all the useful links I have related to cryptography, I hope you find them educational as well as amusing, just as I have. Cheers!

[Matt_T_hat]

Prime factorization of a number is a difficult and tedious process which cannot be automated at a satisfactorily high level, especially for huge prime numbers and their multiples. Thus it cannot be done by brute force quickly enough in order to crack the encryption in a reasonable amount of time. There are also other methods: discrete logarithm problem, elliptical curves and so on. Basically, all encryption methods are based on solving a difficult problem in number theory, in order to prevent a computer from solving it quickly enough. Here are some links you may find interesting:

http://en.wikipedia.org/wiki/Cipher
http://en.wikipedia.org/wiki/Cryptography
http://en.wikipedia.org/wiki/Digital_signature
http://en.wikipedia.org/wiki/Cryptog..._hash_function
http://en.wikipedia.org/wiki/One-way_function
http://en.wikipedia.org/wiki/One-way...ssion_function
http://www.keylength.com/en/4/
http://csrc.nist.gov/groups/ST/toolkit/index.html
http://www.cs.auckland.ac.nz/~pgut001/tutorial/
http://www.schneier.com/blowfish.html

These are all the useful links I have related to cryptography, I hope you find them educational as well as amusing, just as I have. Cheers!

Your secrets are mine now...

(insert manical laughter)

[obi1kenobi]

Hardly, since I develop my own encryption algorithms, I don't copy-paste them from the links.

[Matt_T_hat]

Hardly, since I develop my own encryption algorithms, I don't copy-paste them from the links.

Darn.

[Shaggy Hiker]

Darn.

Hardly. Remember Shannon's Maxim noted in the second link: "The enemy knows the system."

The point is that knowing the algorithm is not sufficient in itself to assist in breaking good encryption, you STILL need to key to get anywhere.

[obi1kenobi]

Shaggy Hiker's got a point. If the algorithm is not well put together, knowing how it works may help you break it. But the better algorithms that are out there have all been published in articles and on the web, and they still resist invaders. Look at it this way: knowing the algorithm will only make the underlying mathematical problem visible, but will not provide any way to solve it. While solving the problem is not impossible by any means, it requires significant amounts of time and sheer computing power to solve it. That's the point of encryption, make the decryption difficult enough so nobody would dare attempt it, and not make it impossible - since only the one-time pad is impossible to break (if used properly).