Posted on :Friday, Dec. 17, 2004
Cryptography decrypted
{I found time and a working keybord to update my previous entry, so here goes...} Imagine this : Scenario 1 {There were also a similar discoveries made by Ellis, Cocks and Williamson prior to Diffie, Rivest, Samir and Alderman work. The similarity could be due to the fact that Diffie visited Ellis in 1982 after he heard the rumour of the classified work of Ellis, Cocks and Williamson from NSA.} BTW, see if you can figure this out. --- Forget Tangkak, Forget Nilai3 ... - Monday, Nov. 21, 2005
Two people want to share an intensely private message. The sender put his/her message in a very sturdy box and close it. He/she then put a secret padlock, keeps the key and then send it via a conventional courier. The recipient accept the box, add his/her own padlock (now there are two padlocks) and then resend the box to the original sender. The original sender receives the box, removes his/her padlock and then resend the box to the recient, again.the recipient can now open the box, because it is padlocked wit his/her own padlock. NO EXCANGE OF KEYS. Although this scenario is very ideal, a mathematical process to imitate the flow of the process has yet to be found.
Scenario 2
A need to send a secret container of paint to B. Only B can complete the paint mixture. A send a container of blue paint. Even if this container falls into the enemy hand midway, it is still an incomplete mixture. B receives it, and add red paint to the mixture, and the mixture become sort of purple (the final mixture). This is some sort of ONE WAY FUNCTION, since we can easily mix the paint colour, but it is quite impossible to un-mix them.
Scenario 3
A select 2 secret(say s1 and s2) prime numbers. She multiplies them both. Lets call this product of two secret prime numbers - P. She also select another prime number, e. Se then advertise P and e as her public keys. One approach which can be taken for somebody who wants to send A a private message is to use e and P to encrypt his/her message.
Let say the sender use some sort of one-way function stated by A:
EncryptedMessage = PlainMessage^e (mod P).
He/she then sends EncryptedMessage to A .
A has the two secret number (s1 and s2). She then calculate d, a special number which act a A’s private key:
e * d = 1 (mod (s1 -1) * (s2-1) )
Since e, s1 and and s2 is known, d can be calculated. Euclid Algorithm can also be used to deduce d .
To decrypt the EncryptedMessage, A use this one-way function:
DecryptedMessage = EncryptedMessage ^d (mod P)
This is the idea of RSA (Rivest, Samir Alderman Method).
Although a third party can break the encrypted message by guessing s1 and s2 (which make up P) via factoring, but if A picks a very large s1 and s2, it would take a lot of computing resource and time to guess s1 and s2. A short-cut to the factoring method has yet to be found.
Scenario 4
Miniaturization of communication components and reduction in production cost would enable continual communication between two parties. But how do we ensure that the communication is carried out securely. A recipient can add a pre-messured noise to the communication channel which connect this two parties. Even if the communication can be tapped, the interceptor would not be able to differentiate between the real message and the noise. James Ellis found this idea that KEY DISTRIBUTION (sharing of private key among sender/receiver) was not essential part of cryptography. He found this while rummaging through a war-time Bell Telephone report by an unknown author.
Reading List:
The Code Book by Simon Singh
BTW, a more comprehensive treatment on Cryptography can be referred to Bruce Schneider book: Applied Cryptography.
Recent:
James Blunt - Monday, Oct. 31, 2005
Believe Me - Monday, Oct. 24, 2005
Sunset - Friday, Sept. 23, 2005
Fuel Woes - Monday, Sept. 12, 2005
[::Links::]
[::Dialogue::]
|
| previously Powered by TagBoard Message Board |
|
[::Leave your thought::]
|
[::Hideouts::]
