You can be spied on even more easily than you thought.
ElectricAye
Posts: 4,561
It seems information theorists kinda made a wrong assumption years ago....
http://web.mit.edu/newsoffice/2013/encryption-is-less-secure-than-we-thought-0814.html
http://web.mit.edu/newsoffice/2013/encryption-is-less-secure-than-we-thought-0814.html
Comments
Excellent article, excellent research, cool tools. What's not to like - except increased vulnerability?
“It’s still exponentially hard, but it’s exponentially easier than we thought,”
And it's still exponentially easier to get at the data via a myriad of sloppy ways encryption is implemented and used, or via social engineering, or by having your government beat the keys out of you. Etc etc.
I thought this use of the word exponentially was a bit odd. I've always thought of exponentially as an adverb. You grow exponentially. Or you change exponentially. I would never think of hardness as being "exponentially," though I can imagine a hardness becoming exponentially greater. Could it be that he was sending somebody an encoded message with that? Hmmm... the key to Kryptos, maybe?
Often when computer scientists are discussing algorithms, they will casually say things like "It's a linear algorithm" or "It's a logarithmic algorithm" or "It's an exponential algorithm".
What do they mean? Well it's referring to the rate at which the execution time of the algorithm increases with the size of the data set it has to work on.
A thing can't just be "exponential" it can only be exponential with respect to something else. Often that something else is implied by the context and so these phrases taken alone don't make sense in the normal way.
So what is our man talking about? Exponential with respect to what?
Perhaps he meant with respect to key length "n".
He might mean for example that cracking a message took time "e to the power n cubed" but now we might be able to do it in time "e to the power n squared". Or some such.
Both exponential, with respect to key length, but one is exponentially easier.
And while I believe in being accurate in our wording, and that words mean things, mathematicians also at times appear to be their own distinct species. Perhaps we are trying to read too much in his choice of phrase. Since we have an entire article to glean context from, he is likely saying "It's still really, really hard, just not as hard as we had originally thought".
They are often analysing algorithms to see how their execution time goes up with the size of the data set.
For example, performing an array indexing operation is constant time, it does not matter how big the array is. That is O(1).
Where as visiting every element of an array to find a particular value will take linearly increasing time as the size of the array gets "n" gets bigger. That's O(n). "Order of n".
A binary search through a sorted array for a value might take log(n) time. O(log n). "Order of Log(n)."
The sloppy part of all this is that when you analyse all the steps in your algorithm, all the loops, inner loops etc you might find its run time us proportional to some complicated thing like log(n) + n + n**2. At that point you just think about what happens when you have lots of data i.e. "n" is very big. Then you see that the n**2 term above is vastly bigger than the other terms an so you ignore those and just say the algorithm is O(n**2) "Order of n squared".
This, I believe, is why we see our man casually talking about "exponential". It is actually technically correct in that context.
Sounds good and impressive anyway:)
If you want to geek out it's all here:
http://en.wikipedia.org/wiki/Time_complexity
By gosh you're right! I hadn't thought of it that way, but after checking it out, it appears that his use of "exponentially" is grammatically correct. For some reason it just rings exponentially weird in my ears.
AES 256 Hardware encrypt HDD ........ Go have fun .........
FPGAs make great crackers . I however see any form of encryption as more of a tamper indicator and a way to make it not worth it to crack .....
It keeps the Scrpt kiddies out of my stuff ..