Useful and clearly wriiten document on encryption

[mbravo]

I invite everyone to read an excellent, very clearly written document on public key encryption by Kristen Bayes, which is located at her site (http://www.bayes.org.uk/documents/secret_one.htm)

[DATA]

HI,



The digest is unique to a given document


While you cannot use the digest by itself to recreate the original document, what you can do is compare a document you have received with the digest: if the two match, the document has not been changed since the digest was created

as quoted frm the url mentioned

When we say that the digest is unique-it has to be thought about carefully.

lets take an example

lets Say we use Secure Hash Algorithm (SHA)

SHA-* produces a *60 bit message digest of the input text.

Now if we hash 2^*6* messages,then atleast two messages will hash to the same digest.
What we are doing is taking a larger domain and compressing it to a smaller domain,so certainly when we map a larger domain to a smaller domain,we will have more than 2 messaged that hash to the same digest,if the domain being mapped is greater than the smaller domain .
So we can't quite say the digest is unique for a document.This is none other than the pigeon hole principle which states that -"If there are m pigeons and n pigeon holes,where m>n,then atleast one pigeon will share a pigeon hole with another pigeon.

there is another popular attack called the birthday attack on hash functions.

What it does is to determine 2 randomly chosen that hash to the same digest.


A succeful birthday attack on SHA-* will take us to hash around 2^80 messages and we will get two random text messages that hash to the same digest with a *00 percent probability.




QUOTE]If a number is relatively prime to another number, it shares no common factors with it[/QUOTE]

It actually means that,if it is relatively prime-then there were be only one public key for the corresponding private key.
If it is not relatively prime,then we can have more than one public key for the corresponding private key or vice versa.

if there are n common factors,we can have n private keys for a corresponding public key or vice versa.

Its a nice and easy to read,article.good one.

Regards Data.

[johnny]

from the article:
Apparently the FBI came across encryption around one hundred times in the last year in the course of its investigations. In no instance did the presence of encryption seriously impede its inquiries.

The UK government back in **** in a submission to Parliament described a series of problems caused by encryption, but none of these difficulties were sufficient to lead to the failure of the prosecution.

In the cases described, everyone who went up against the authorities_ relying on encryption to avoid jail, everyone, was successfully prosecuted. If you're a bad person, and the Police come calling, encryption will not save you.