128 bit encryption - Factorization

[neptune]

Hello,
I am back after long time

Everyone knows that factorizing 2^128 bit long number takes long time for computer, especially when it is a product of two equally long prime numbers.
My question is - why do they not maintain a list of prime numbers and their factors in a look up table, one wouldn't need to check what's the factor of the code is by normal division, number after number.
look up table could be like this-

11*11 = 121
11*13 = 143
11*17 = 187
...
...
13*13 = 169
13*17 = 221
...
...

 

[nsaspook]

"If someone created a database of all primes, won't he be able to use that database to break public-key algorithms? Yes, but he can't do it. If you could store one gigabyte of information on a drive weighing one gram, then a list of just the 512-bit primes would weigh so much that it would exceed the Chandrasekhar limit and collapse into a black hole... so you couldn't retrieve the data anyway"

Applied Cryptography by Bruce Schneier
((2^511) * 1) / (512 log(2)) = 4.35 × 10e151

I haven't worked out the math for size but the 128 bit database would also be pretty big.

 

[neptune]

Holy Sh.it !

 

[MrAl]

Hi,

Some enumerations of things dont seem that they could be that large, but then when we do the math we find out just how large some things can really be. Look at the number of possible legal chess positions in a normal chess game (the chess board only has 64 squares, and 16 pieces and 16 pawns at the start). That number is bigger than the number of atoms in the universe !