One way encryption? How is possible?
My question is simple.
Is it true that I can encrypt something with a key and then be unable to decrypt it with that same key? This sounds impossible for a computer to not be able to back track its actions? How is this possible if it is?
Im thinking about when everyone has my public key, then they encrypt a message with my public key and send it to me. Why cant they and anyone else with my public key then decrypt it?
[453 byte] By [
dnoyeB] at [2007-9-26 4:21:31]
More accurately, it is mathematically extremely hard with today's technology and human knowledge to decryt that message. So you are right that it is not a "100% impossible" but rather a "practically almost 100% impossible today". For example, the following is the formula of RSA public key encryption. Looks simple, but if you can find a way to back-track it using today's computer, your famous name will be carved into the history of computer cryptography, I am serious! (In a typical public key, e is number like 350, and n is a 1024-bit integer, see following)
enjoy -
5.1.1RSAEP
RSAEP ((n, e), m)
Input:(n, e)RSA public key
mmessage representative, an integer between 0 and n-1
Output:cciphertext representative, an integer between 0 and n-1; or message representative out of range
Assumptions:public key (n, e) is valid
Steps:
1.If the message representative m is not between 0 and n-1, output message representative out of range and stop.
2.Let c = (POWER(m,e)) mod n.
3.Output c.
*** POWER(m,e) means m to the power of e
yilin at 2007-6-29 17:25:45 >
Example, your messag M has 1000 bytes, or 8000 bits, treat it as a 8000-bit integer, then with a 1024-bit public key such as (350, xxxxxxx....[1024-bit int]), the encrypted message is:
M to the power of 350, then mod that 1024-bit int.
Amazingly simple, but amazingly hard to back track (at least no human being has been able to do that in any means yet).
yilin at 2007-6-29 17:25:45 >
My point is that If I hold the key that I encrypted it with, how come that key does not decrypt. I guess Im struggling how one way encryption is even possible. Im not focusing on its decipherability. Im questioning hwo I can encrypt something with a key and not be able to decrypt it with that same key.
Maybe I need a book.
dnoyeB at 2007-6-29 17:25:45 >
> If I hold the key that I encrypted it with,
> how come that key does not decrypt
http://www.muppetlabs.com/~breadbox/txt/rsa.html
By the way: as public key encryption and decryption is slow, SSL only uses it to exchange symetric encryption keys. Such keys are used for both encrypting and decrypting. The keys are created on-the-fly, and only used for that specific SSL session.
a.
dnoyeB,
One can definitely decrypt using a key that was used to encrypt. You just need the key to be of that kind.
For example, using a cipher that is initialized with a DES based key, one can encrypt some data.
Then, you can use a cipher you can decrypt the encrypted data. But you would have to initialize this this cipher with the same key that you used to initialize the encrypting cipher.
Is that what you wanted to know ?
>
> > If I hold the key that I encrypted it with,
> > how come that key does not decrypt
>
> http://www.muppetlabs.com/~breadbox/txt/rsa.html
>
> By the way: as public key encryption and decryption is
> slow, SSL only uses it to exchange symetric encryption
> keys. Such keys are used for both encrypting and
> decrypting. The keys are created on-the-fly, and only
> used for that specific SSL session.
>
> a.
Cool, I read the paper. It basically says that one way encryption is essentially a lossy encryption. That is, lossy with respect to the public encrypting key. The private key happens to hold data such that it can fill in what was lost due to the public keys encryption.
Basically it uses modulus functions, and everyone knows modulus is not reversible.
the private key picks a number such that the public key can modulus with it, and the number the private key keeps for itself (which is the public keys pair number) will reverse the effects of that modulus.
dnoyeB at 2007-6-29 17:25:45 >
