By concatenating "words" and adding them Modulo 26, can we create a key that cannot be distinguished from one that was generated in a truly random manner?
For example, let's say we use three "words" to create a key (EATED, PIG, ELEPHANTINE), whose lengths are coprime, using Modulo 26 addition:
EATEDEATEDEATEDEATEDEATEDEATED... PIGPIGPIGPIGPIGPIGPIGPIGPIGPIG... _______________________________ TIZTLKPBKSMGIMJTIZTLKPBKSMGIMJ... ELEPHANTINEELEPHANTINEELEPHANT... _______________________________ XTDISKCUSFQKTQYAIMMTXTFVWBNIZC...
And sender and receiver have already agreed that they will only use certain values, say the 4th, 19th, and 21st letters of the final string, as the key. (I, M, X) The rest will be discarded. Then we use a different set of words and a different choice of values to keep, say the 6th, 11th, and 21st, determined ad hoc beforehand. The sender and receiver must have shared this information beforehand in a secure manner, of course.
The point is to get rid of the one-time pad and only have a list of words and numbers on you.
Repeat with different sets of three or more words whose lengths are coprime until we have our key, let's say thirty characters long.
Let's say we use a combined dictionary of Mandarin Chinese, Russian, and English words that has a total of 180,000 possible words (Mandarin and Russian are phoneticized). Let's say we choose each word in a random manner.
Only using a small number of letters from each result is going to create a short key and require effort, but the question is this: would such a key be indistinguishable from one generated in a truly random manner?
I think so--if the words are long enough and coprime to each other and the words were chosen in a manner that was random i.e., it did involve a TRNG.
Indistinguishable or not?