Problems With Public Key Crypto systems
that Publish Products of Large Prime Numbers as a Public Key
Problems with public key crypto systems that publish products of large prime numbers as a
public key to be used to encrypt information with is that an attacker can in his or her spare
time pre compute and store the products of all prime numbers reducing the 'factoring' of
products of prime numbers to a simple look up table search for the previously computed
products of prime numbers to find out which two prime numbers when multiplied together give
that product which is published as a public key. What was previously thought to be a
difficult to compute math problem and built into public key systems, the factoring of large
multiples of prime numbers, is now reduced to a pre computed look up table search... Here is a
simple program to create a pre computed look up table for calculating the products of prime
numbers (
http://Tibor_G_Balogh.IndITConsulting.com/home/school/csci/pprimes.cpp) and an example output
file looks like this (
http://Tibor_G_Balogh.IndITConsulting.com/home/school/csci/pprimes.txt)...
A 2048
bit public key where 2048 bits is represented by a 256 byte long hexadecimal number is derived
from multiplying two prime numbers. Previously thought to be difficult to factor this large
number derived from multiplying two smaller prime numbers to get to each prime number multiple
of this larger number can now be pre computed and stored on a look up table for all multiples
of prime numbers where the two prime numbers can be stored next to the result... (33 = 11 * 3)
While your kid sister may not be able to decode public key encoded messages, others
might very easily create large pre computed databases for products of prime numbers and store
the results in a look up table which can instantly tell the two prime numbers that when
multiplied together give that very large number used as a public key...
E-mail_1:tiborgbalogh@gmail.com
E-mail_2:Tibor_G_Balogh@HotMail.com
Last Update: 06.JAN.2006
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