🚀 go-pugleaf

I was reading the article "Error Correcting Codes and Cryptography" in
_The Mathematical Gardner_ (A wonderful book, by the way) and noticed
something interesting in a discussion of the early Backpack codes.  (Yes,
I know the Backpack code has been broken, but bear with me)  This was
probably a simplified version of what was really going on, but the
article described the following method for creating the scrambled backpack
numbers for use in the encryption key:  Take the first n powers of 2
expressed in n-bit format, prefix and suffix them with a few random
digits (plus a column of zeros to protect the powers-of-2 from carries)
multiply the entire number by s, modulus r.  It seemed that the encrypters
first concern is that someone will solve the Backpack problem for the 
scrambled integers, not that someone will figure out r and s and thus
know how to decrypt.  In a later article by Martin Gardner himself, he
mentions that the Backpack problem had been solved in polynomial time
for most codes, so apparently this was the most fruitful way to attack
this code.  Now, it seems to me that the codebreaker knows a fair amount
of the "text" of those scrambled numbers (that they are the powers of
2 with a little noise on each end) and has n examples encrypted with
the same r,s key.  Is there no means of finding r and s?  Is y = (s*x) mod r
considered a good "conventional" cryptosystem, safe against plaintext
attack?  Or am I missing something?

--
Paul Ciszek, pciszek@nyx.cs.du.edu | Saddam Hussein still has a job; do you?