ure paper, we will present information-theoretic analysis of the effect of a keyed connection polynomial. Such ciphers can clearly be implemented in software, and to a considerable extent in hardware with field programmable logic, thus retaining much of the convenience of LFSR in practical applications. We do not believe information-theoretic security can be obtained this way, but it may greatly increase the complexity of at least FCA type attacks, thus providing useful practical security in some situations.

Thirdly, we now give an ENC design for Y-00 that leads to exponential complexity for CTA according to current knowledge, and more security that AES for KPA generally. Consider the ENC of Fig. 2 where a bank of $m$ parallel AES in a stream cipher mode is used to provide the $m=\log_2 M$ bits running key segment $K'(m)$ which determines, through the mapper, the basis of a qumode. Typically in our previous experimental demonstrations, $m \sim 10$ and $|K|$ is in the thousands. Thus each $K_i$ may be readily chosen to be of 256 bits. Under heterodyne or any other quantum measurement by Eve, the result is a noisy version of $K'(m)$ with independent coherent-state induced randomization for each qumode. According to the present state of knowledge, no KPA on AES is better than exhaustive (exponential) search [@stinson]. Even in a divide-and-conquer type attack as in FCA, so that a single AES is to be considered, one needs to deal with the KPA problem of artifical noise from such strategy with the addition of *real* coherent-state noise, in a CTA on the Y-00 seed key. Let $N_1$ be the length of the qumode sequence used for the attack, so that Eve may parallelize $N/{N_1}$ attacks simultaneously from the total length $N$. It is clear that even without noise, the attack complexity remains exponential for any realistic $N \leq 2^{80}$ and any $N_1$. In a KPA, the comparison is to be made with the same $N_1$ for no parallelization. Thus, Y-00 is equivalent to AES in a stream cipher mode with output observed in noise, th