What’s the shortest book in the world?
“The Even Prime Numbers”
which basically has one page which says the number “2”, followed by “The End”.
Well, researchers in the US have made the book a whole lot shorter by discovering certain weaknesses in using “2” as a prime number, and stumbled upon a major flaw in the implementation of public key on certain devices.
For this they have shaken the scientific world by discovering that “2” isn’t actually a prime number, as most people had thought. Leading cryptographers and security engineers are now looking rather embarrassed as they had just thought that the number “2” was prime.
The Inverse of two
Prime numbers are used extensively in public key encryption key. For example the RSA method takes two prime numbers and then multiplies them together to give a modulus (N). This modulus is often difficult to factorize as large numbers are used. It is also used extensively within key exchange methods, and where we use an exponential equation — such as G^x mod P- and where P is a prime number. The prime numbers used in the calculations are often large, as they should be difficult to find.
The usage of 2 as a prime number, though, has been useful in cryptography as it allows mobile devices to provide easier calculations. Many intruders, too, will not check for the number “2” in their calculations, as a flaw in their programs immediately dismisses all even numbers. In Python the code is:
if !(val% 2): search_for_prime(val)
Eve 1, a well-known crypto hacker, outlines that:
we just assumed that no-one would use “2”, so we wrote programs that just went for odd numbers. It saved so much time in testing if the value was even, so we just dismissed it.
Many think that law enforcement have been using “2” as one of their prime numbers as no-one checks for that as one of the prime numbers. As leading agency spoken person said, “It has allowed us to get under the radar for our crypto”. It is now reported that many law enforcement systems are now being searched for the usage of “2” within previously encrypted communications. Three airbases in the US are already on lock-down as the were found to be littered with number two’s. A leading air marshall defined that, “Our planes cannot cope with large prime numbers, so until we can upgrade all our hardware, our planes are grounded.”
The flaw, discovered by researchers at the MidTech Institute in Florida. They found that the commonly used Python library (PieCrypto) detected when a mobile device is being used, and, more often than not, used the value of “2” for one of the prime numbers. This meant that in 60% of the encryption tunnels that were created so that the cryptography within 1 pico second. With a quantum computer it would be expected that this could actually be cracked before the key was even generated, and that all the keys used in the future would actually be predicted in a single instance — and which has been defined as the “big bang crypto opening”.
Then the researchers, on investigating the number “2”, found that “2” is not actually a prime number. Prof Plant outlines, “It’s a bit silly. Everyone just assumed that two was a prime number, as we were told it was at school, and no-one realised it wasn’t. We found that it is paired with an re-imagined number — z2 — which is the inverse of 2, so when they were multiplied together they give the value of 2. We stumbled across it in some old school books and which outlined the method. Buried in the tutorial questions, the book basically asked what the inverse of “2” was … and when we looked at the answers in the back of the book we were shocked to find the as was “1 over 2, and which was defined as z2.”
He added that, “We define the devices that generate a prime number of “2” as suffering from the piger fabrica syndrome (trans: ‘lazy devices’) — as they really can’t be bothered to generate a big integer as a prime number. Basically they just gave up after generating the first number, which is often “2”. Also some mobile phone manufacturers detect the generation of prime numbers and disable the operation after the first one in order to save battery life. “
Device manufacturers are already rushing to find vulnerabilities in their products, and, in Scotland, it has been found that the bug has already shown some serious problems where an elevator in Glasgow refused to acknowledge the existence of prime numbers, including “11”:
The research community is scratching its head just now. As researchers were searching for extremely large prime numbers, they forgot to check the most basic one — 2. A massive series of patching exercises are underway today from network administrators and who are now searching for any place that the number 2 is used, and to delete it usage.
So the shortest book in the world, just got a little shorter, but has opened the Internet up to cyber criminals, identity thieves, and crackers.
Please help search for the number “2” on your computer systems, and delete it wherever you find it. This will give us a safer world to live in. If you are using a Mac computer, just open your Spotlight search and search for number two’s.
Also when you purchase your mobile phone, make sure that it does not disable the generation of large prime numbers — look for the sticker under the battery — it should have a graphic somewhere with a 2 and a cross on it. So for the sake of an extra day on your battery, wouldn’t you like to be just a little safer?