Diffie-hellman
Modulo
Given two numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder from the division of a by n. For instance, the expression “7 mod 5” would evaluate to 2 because 7 divided by 5 leaves a remainder of 2, while “10 mod 5” would evaluate to 0 because the division of 10 by 5 leaves a remainder of 0
1- Each Host A and B must agreed on a Prime Modulo and a Generator .
Lets say the Prime Modulo is 17 and the Generator is 3 :
then Host A and B select a Private number .
Lets say Host A choose 15 and Host B choose 13 ,
So host A calculate 3 to the power of 15 Mod 17 = 6
in detail :
3x3x3x3x3x3x3x3x3x3x3x3x3x3x3 = 14348907
So to do the modulo calculation : 14348907 / 17 = 844053.xxxxxxxxxxxxx
Then you multiply 844053*17 = 14348901
Then you subtract 14348907 from 14348901 = 6
So host B calculate 3 to the power of 13 Mod 17 = 12
in detail :
3x3x3x3x3x3x3x3x3x3x3x3x3x = 1594323
So to do the modulo calculation : 1594323 / 17 = 93783.xxxxxxxxxxxxx
Then you multiply 93783*17 = 1594311
Then you subtract 1594323 from 1594311 = 12
Then Host A send publicly his result to Host B and vice versa .
And now the TRICK !
Host A take Host B public result ( 12 ) and calculate it to the power of his private number ( 15 ) Mod 17 = 10
12x12x12x12x12x12x12x12x12x12x12x12x12x12x12x =15407021574586368
So to do the modulo calculation :
15407021574586368 / 17 =906295386740374.xxxxxxxxxxxxx
Then you multiply 844053*17 = 15407021574586358
Then you subtract 15407021574586368 from 15407021574586358 = 10
Host B take Host A public result ( 6 ) and calculate it to the power of his private number ( 13 ) Mod 17 = 10
6x6x6x6x6x6x6x6x6x6x6x6x6x =13060694016
So to do the modulo calculation :
15407021574586368 / 17 =768276118.xxxxxxxxxxxxx
Then you multiply 768276118*17 = 13060694006
Then you subtract 13060694016 from 13060694006 = 10
And we have obtain the Share Secret ( 10 )
TALAAAAAAAAAAA !
