[Cryptography] PGP -- Can someone help me understand something?

[Derek Atkins]

Hi Matt,

On Thu, August 9, 2018 2:45 am, Matt Maxson wrote:
[snip]
> The question was, basically, if someone has access to both a PGP encrypted
> email and a plain text version of the same email, can an attacker
> determine the key.  The answer given was "no".
>
> I don't understand.  Why can't that happen?  For example, if I have 10 + x
> = 50  (this can be replaced with any formula that has exactly one
> unknown), I can solve for X.  In my thinking, isn't the unknown in the
> equation simply the key?  Sure, the maths are more complex, but it should
> be a trivial issue to work backwards and solve for the key.

Well, the no should have been added with a postscript saying that it COULD
if you had enough computation to perform the required operations to break
the cryptosystem.

Thinking about cryptography in terms of basic algebra doesn't work,
because the system isn't linear.  You cannot model a system like AES using
only a single variable.  Well, okay, you can say AES(Key, PlainText) =
Ciphertext and then ASSUME that this is the same as solving 10 + x = 50. 
But it's not.

Specifically, a system like AES is designed such that knowing the
plaintext and ciphertext does NOT provide a way to find the key.  It does
provide you a way to VERIFY that you've found the right key, but it
doesn't help you having to search through all 2^128 (or 2^256) possible
AES keys to find the one that matches.

If you had a cryptosystem that could be broken by a single
plaintext/ciphertext pair it would not be considered very strong.

Hope this helps.

-derek

-- 
       Derek Atkins                 617-623-3745
       derek at ihtfp.com             www.ihtfp.com
       Computer and Internet Security Consultant