Please don't tell me this is insecure and I shouldn't do it. I'm doing this purely for educational purposes and in no way will this be deployed in a non-experimental sense.
Since this is OTP, I need a keystream that is at least as long as the message being encrypted. From what I have read, it seems like DH needs a ridiculously large safe prime modulus. Or does it?
Every character needs a different random key, so for a string that is 10 characters long the DH key exchange needs to happen 10 times to create an array of common secret keys for that string.
However, I seem to be getting what may be integers that are way larger than necessary.
Let's say that the user makes an array of private keys:
var userPrivateKeys = [9,12,0,23,7,8,4,7,15,24]
And a 2048-bit safe prime modulus with 2 as the generator:
var prime = 32317006071311007300338913926423828248817941241140239112842009751400741706634354222619689417363569347117901737909704191754605873209195028853758986185622153212175412514901774520270235796078236248884246189477587641105928646099411723245426622522193230540919037680524235519125679715870117001058055877651038861847280257976054903569732561526167081339361799541336476559160368317896729073178384589680639671900977202194168647225871031411336429319536193471636533209717077448227988588565369208645296636077250268955505928362751121174096972998068410554359584866583291642136218231078990999448652468262416972035911852507045361090559 var generator = 2
The array of shared keys for the user ends up looking like this:
var userPublicKeys = [512,4096,1,8388608,128,256,16,128,32768,16777216]
After the user and the server exchange their public keys, we get this as the common key:
var commonKeys = [134217728,2.2300745198530623e+43,1,1.725436586697641e+69,72057594037927940,16777216,17592186044416,1.78405961588245e+44,6.216540455122333e+85,1]
Those integers are way way larger than the modulus of the alphabet, or even the modulus of ASCII.
I [think I] understand that the prime modulus must be huge in the context of creating keys to be used in ciphers like AES, but what about in the context of having different random keys for each character in OTP?
For example, let's say that my messages only feature letters a through z, and I have a smaller modulus:
p = 27 g = 3 userPrivateKeys = [9,12,0,23,7,8,4,7,15,24]
Our algorithm would be:
2^a mod 27
Math.pow(2, a) % 27
And we'll have generated a list of public keys:
userPublicKeys = [26,19,1,5,20,13,16,20,17,10]
That's way more manageable.
So in this context, is there a problem with the prime modulus being so small?
As far as I can tell, the only way to break this is through exhaustive search; since OTP cryptext contains no information about the original message, exhaustive search would be infeasible. I have read of other possible ways of breaking this and DH in general, but usually I don't understand them or they either depend on one of the secrets being known.
So is there something I'm missing?