## Quantum Cryptography Based on the Deutsch-Jozsa Algorithm

**Authors:** Koji Nagata, Tadao Nakamura, Ahmed Farouk

Recently, secure quantum key distribution based on
Deutsch's algorithm
using the Bell state is reported \cite{NN2}.
Our aim is of extending the result to a multipartite system.
In this paper, we propose a highly speedy key distribution protocol.
We present secure quantum key distribution based on a special
Deutsch-Jozsa algorithm
using Greenberger-Horne-Zeilinger states.
Originally,
Bob has promised to use a function $f$
which is of one of the two kinds; either the value of $f(x)$ is constant
for all $x$, or the value of $f(x)$ is balanced,
that is, it is equal to $1$
for exactly half of all the possible $x$, and $0$ for the other half.
Here, Bob uses a special function when it is not constant.
We may say the value of $f(x)$ is special.
Our quantum key distribution overcomes a classical counterpart by a factor
$O(2^N)$.

**Comments:** 10 Pages. International Journal of Theoretical Physics, (2017), DOI: 10.1007/s10773-017-3456-x

**Download:** **PDF**

### Submission history

[v1] 2017-07-02 06:30:15

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