Diffusion in Stream Cipher The diffusion property of a cipher defined by Shannon refers to the ability of a cipher to cause a lot off bits in the cipher text to be modified, when even a single bit in the plaintext is flips. 

However, in stream ciphers – when the cipher text is the xor of the plaintext with the key pattern – a flip in the plaintext will always cause exactly one bit modification in the cipher text. 

Does this mean that stream ciphers have a low level of diffusion?
Stream ciphers in general are more efficient but less secure than a block cipher, provided all else being equal in terms of each construction following both necessary and preferred principles (Katz &amp; Lindell, 2009; Boneh, 2013).

Shannon's “confusion and diffusion” refers to good confusion and diffusion of message block bits and secrecy bits based upon linear and non-linear functions as you mostly point out. 

There are different kinds of stream ciphers as there are different block ciphers. Some stream ciphers did not pass two or more critical statistical tests to show powerful diffusion. 

In general you are correct: stream ciphers either have low or even slow diffusion rates. However, linear masking and improve initialization processes helps reduce vulnerability to linear and side attacks. Stream cipher Hc-256 is a good candidate to test further.

Stream ciphers are faster than block ciphers, but block ciphers with proper construction have higher diffusion – still, pseudo-randomness can be generated from a block cipher to stream ciphers to reduce attack vulnerabilities. 

Additional reading:


http://publications.drdo.gov.in/ojs/index.php/dsj/article/view/1435/4669
http://www3.ntu.edu.sg/home/wuhj/research/publications/wuhongjun_thesis.pdf


Same author as thesis but shorter and more straightforward:


http://www3.ntu.edu.sg/home/wuhj/research/hc/hc256_fse.pdf