Abstract—Length and mismatch rate of secret bit strings
derived from channel characteristics by legitimate users for key
generation are affected by quantization algorithm significantly.
Existing schemes cannot achieve both a string and a low
mismatch rate at the same time because of the static
quantization method. In this paper we first propose an adaptive
quantization algorithm formed of an quantizer offset with the
quantization noise at one side and a quantization-level
optimizing method, which maximize the length of secret bit
string under the constraint of mismatch rate. Based on this
algorithm, a key agreement scheme selection approach is
presented to harvest longer bit strings. As a result, an adaptive
key generation scheme based on quantization of channel
characteristics is proposed using the above methods. With this
scheme, bit strings with length close to theoretical limit can be
generated, and the mismatch rate is lower than 5%.
I. INTRODUCTION
OMPARED with traditional communication, wireless
communication is less restricted by environment and
location. As a result, wireless communication is more
and more popular in people’s life. But due to its broadcast
nature, security remains a crucial problem. As secret key
distribution is difficult to implement in wireless environment,
physical- layer security method is required.
Ahlswede, Csiszar [1], and Maurer [2] first proposed
legitimate users generating keys with common randomness.
After that, Hershey [3] suggested to make use of the
characteristics of radio channel between legitimate users to
get common information, and convert this information to
binary vectors as keys using quantization algorithm. This
method relies on the reciprocity of channel to distribute keys,
and independence to prevent eavesdropping. Then, many
practical schemes were put forward. The process contains at
least two stages [4]: quantization phase and key distillation
phase, to enable legitimate users to share information and
agree on identical cryptographic keys respectively. These
studies investigated the performance of different channel
features in key generation, and showed that the quantization
Manuscript received December 30, 2012. This work was supported by a
grant from the National Natural Science Foundation of China(No.
61176108), National Science and Technology Major Project(No.
2011ZX03006-003), and the National High Technology Research and
Development Program of China(863 program)(No. 2011AA010604).
Q Dai, corresponding author, is with the China National Digital Switching
System Engineering & Technological R&D Center. Zhengzhou, PRC
(phone: 0371-81632917; e-mail: daiqiaoyy@gmail.com).
J Liang is with the China National Digital Switching System Engineering
& Technological R&D Center. Zhengzhou, PRC (e-mail: 130076023
60@wo.com.cn).
K Huang is with the China National Digital Switching System
Engineering & Technological R&D Center. Zhengzhou, PRC (e-mail:
huangkaizhi@gmail.com).
algorithm has a great influence on performance of key
generation [5]-[8]. Lower quantization level can lead to lower
key disagreement ratio, but shorter secret bit strings at the
same time with less randomness. On the other hand,
multiple-bit quantization will increase the mismatch rate of
bit strings extracted by different communication parties, thus
more efforts are needed in key distillation phase. So there is a
tradeoff between the length of bit strings and correlation of
different bit strings. However, little consideration is taken to
solve this problem.
In this paper we first analyze the variation of bit error rate
(BER) with quantization level of secret strings. Based on this,
we propose an adaptive algorithm of quantization made up of
a quantizer with offset and a quantization-level optimization
method. The quantizer with offset can minimize the error rate
by eliminating the effect of Alice’s quantization noise. With
the level optimization method, the upper bound of level
which can satisfy the requirement of no bit error is selected to
maximize the entropy and guarantee a low BER at the same
time. Then we propose a selecting algorithm of two different
key agreement schemes (error correction and error detection)
according to their performance in security with the above
algorithm. By summing up the above two algorithms, an
adaptive key generation scheme based on quantization of
channel characteristics is proposed. Simulation result shows
that with this scheme, the key entropy rate is very close to the
upper bound and the BER is lower than 5%. Thus the entropy
and correlation of secret bit strings are both guaranteed. In
section II, we introduce the system model and problems
statement. In section III the adaptive key generation scheme
is presented in details. And in section Ⅳ performance of this
scheme is evaluated.
II. SYSTEM MODEL AND PROBLEM STATEMENT
A. Secure Communication Model Based On Channel
Characteristics
Key extraction model based on the channel characteristics
is illustrated in Figure 1. Alice is the transmitter, Bob is the
legal receiver, and Eve is the eavesdropper, all with single
antenna. Main channel is the channel between Alice and Bob,
and wiretap channel is the one between Alice and Eve. One of
the channel features (RSS, impulse response, etc.)
0
u of main
channel is selected as the base to generated keys,
E
u of
wiretap channel correspondingly. The channel is assumed to
be a narrow band block fading channel,
0
u and
E
u stay still
in a time slot, and vary independently in different slots.
0
u is
modeled as a random signal source. Alice and Bob
Adaptive Key Generation Based on Quantization of Channel
Characteristics
Qiao Dai, Jin Liang and Kaizhi Huang
C
Third International Conference on Information Science and Technology
March 23-25, 2013; Yangzhou, Jiangsu, China
978-1-4673-2764-0/13/$31.00 ©2013 IEEE