I propose to clarify with a little mathematics as best I can what I was, and am, asking... To those this material appears obvious too please feel free to delete. As I understand it MOD is a function which returns the remainder of a number (x) when divided by another number (n). As an example: 5mod3=2 ie 3 will go into 5 a single time and there will be a left over of 2. 11mod3=2 ie 3 will go into 11 a total of 3 times and there will be 2 left over. I propose there is a periodicity in the mod function: n 0 1 2 3 4 5 6 7 8 9 10 11 12 nmod5 0 1 2 3 4 0 1 2 3 4 0 1 2 this can be simplified into a generic formula for a sequence: rem = (kn)+i |big # |big # | | |i=0 |k=0 What this formual does is give you the sequence of any given remainder for xmodn. In a generic algorithm it appears as such: n = some number for k = 0 to "some really big number" for i = 0 to "some really big number" rem=(k*n)+i next i next k
From p.282 on Schneier the RSA encryption algorithm is given as: e c = m (mod n) i i
In my notation this reduces to: rem = (kn)+i | | | | | n=0 |i=0 What I am asking is that since the numbers we are looking at are very large there should (to the way I am thinking at the moment) some means of detecting a sequence of patterns of periodicity related to the difference between the actual key and the key we just select randomly. Specificaly what I am asking for is some reference to some work in this area. I don't know what it is called, it doesn't appear in any books that I have looked at. Thanks for any help you may be able to provide...