On the security of \alpha\eta: response to 'some attacks on
quantum-based cryptographic protocols'
(pp561-582)
Horace P. Yuen, Ranjith Nair,
Eric Corndorf, Gregory S. Kanter, and Prem Kumar
doi:
https://doi.org/10.26421/QIC6.7-1
Abstracts:
Lo and Ko have developed some attacks on the cryptosystem called $\alpha
\eta$}, claiming that these attacks undermine the security of $\alpha\eta$
for both direct encryption and key generation. In this paper, we show
that their arguments fail in many different ways. In particular, the
first attack in [1] requires channel loss or length of known-plaintext
that is exponential in the key length and is unrealistic even for
moderate key lengths. The second attack is a Grover search attack based
on `asymptotic orthogonality' and was not analyzed quantitatively in
[1]. We explain why it is not logically possible to "pull back'' an
argument valid only at $n=\infty$ into a limit statement, let alone one
valid for a finite number of transmissions n.
We illustrate this by a `proof' using a similar asymptotic orthogonality
argument that coherent-state BB84 is insecure for any value
of loss. Even if a limit statement is true, this attack is a
priori irrelevant
as it requires an indefinitely large amount of known-plaintext,
resources and processing. We also explain why the attacks in [1] on
$\alpha\eta$ as a key-generation system are based on misinterpretations
of [2]. Some misunderstandings in [1] regarding certain issues in
cryptography and optical communications are also pointed out. Short of
providing a security proof for $\alpha\eta$, we provide a description of
relevant results in standard cryptography and in the design of $\alpha\eta$
to put the above issues in the proper framework and to elucidate some
security features of this new approach to quantum cryptography.
Key words: quantum
cryptography |