Spread spectrum signal generation method, spread spectrum...

Details Spread spectrum signal generation method, spread spectrum... Spread spectrum signal generation method, spread spectrum...

2000-02-24

2002-10-29

Pham, Chi (Department: 2766)

Pulse or digital communications

Spread spectrum

C380S270000

Reexamination Certificate

active

06473448

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a spread spectrum signal generation method of and a spread spectrum signal generator for generating a chaos sequence as a spread spectrum signal.
The invention also relates to a stream encryption method where stream encryption is performed by using a binary code sequence according to the method and the generator.
The invention relates further to a stream enciphered codes communication method where communication is performed by using a cipher code obtained by the stream encryption method.
2. Description of the Related Art
As the digital high-speed communication spreads, it is desirable to implement a code division multiple access (CDMA) communication system using a spread spectrum communication system. In this field of endeavor, a binary number sequence generated by tossing a coin, is considered ideal as a spread spectrum signal (hereinafter called ‘SS signal’).
In conventional application to the spread spectrum communication system, a sequence obtained by cutting, in suitable length, a maximum length sequence, a Kasami sequence, Gold sequence or the like, is used as the SS signal. A maximum length sequence generated from multi-staged shift registers is also used.
However, conventional spread spectrum code sequences to be used conventionally as SS signal are limited in kinds, and may be insufficient to cope with expectable future demands for communications.
For example, for a sufficient secrecy to be secured for communications, it is necessary to avoid a so-called see-through state of an original text. To be so, an SS signal having a periodical temporal sequence suppressed of auto-correlation as well as of cross-correlation is desirable. It however is difficult for the conventional concept of generation to provide a periodical temporal sequence suppressed in auto-correlation and cross-correlation, with a good repeatability.
To this point, the present inventors paid attention to a chaos containing whole frequency components and capable of generating a sequence of integers complicated of combination (with a binary code sequence inclusive, and hereinafter called ‘chaos sequence’), and have carried forward a concentrated research to make use of a chaos sequence for SS signal generation, reaching a new object as mentioned below.
That is, because a desirable binary code sequence for use as an SS signal should be free of inclination between numbers of ‘0’s and ‘1’s, it has come up as an object to be solved how to generate an SS signal in the form of a chaos sequence meeting such a requirement.
SUMMARY OF THE INVENTION
The present invention has been made to give solution to the object described and it is an object of the invention to provide a spread spectrum signal generation method and a spread spectrum signal generator which can generate, from a binary code sequence of a chaos sequence, an SS signal free of inclination between numbers of ‘0’s and ‘1’s
Another object of the invention is to provide a stream encryption method which employs a binary code sequence determined by a novel spread spectrum signal generation method disclosed herein, for a stream encryption to be executed to thereby generate a cipher code to be optimum in use, for example, for communications and very high secrecy.
A still another object of the invention is to provide a stream cipher communication method which employs a cipher code, determined by a novel stream encryption method disclosed herein, for stream cipher communications to be performed to thereby implement a stream cipher communication with very high secrecy.
To achieve the object described above, there is provided a spread spectrum signal generation method comprising the steps of: starting an operation by substituting an initial value x(0) to an expression (1), having a resultant value based on an expression (2) again as an input to the expression (1), determining a time series x(t)−t by repeating such operations; and, substituting a quantization resolution n=1 to an expression (3), determining an isomorphic transform and quantization based on the expression (3) in correspondence to the time series x(t)−t, determining a time series y(t)−t from the determined isomorphic transform and quantization, generating a spread spectrum signal having, as a period thereof, a binary code sequence y (t) arbitrary cut out of the time series y(t)−t, where
Logistic mapping:
x
(
t
+1)=4
x
(
t
){1−
x
(
t
)}  (1),
Feedback:
x
(
t
)=
x
(
t
+1)  (2), and
Isomorphic transform and quantization:
y
(
t
)=[{2/&pgr;·arc sin {square root over (
0
)}
x
(
t
)}·2
n
]  (3),
where, t is a discrete time, x(t) is an internal state of a chaos given as a real number with double-precision normalized between ‘0’ and ‘1’, and [ ] is an operator representing a round-off operation of a decimal fraction of a value in the [ ].
According to the invention, there can be provided a concrete method of obtaining, from a logistic mapping as a symmetrical nonlinear mapping and a basic mode (n=1) of a nonlinear quantization observation, multiplicity of binary code sequences free of bias, to generate SS signal which is most suitable in use for CDMA multiple communications.
To achieve the object described above, there is provided a spread spectrum signal generator comprising: a program storage unit for storing a program for execution of operations depending on expressions (1) to (3),
Logistic mapping:
x
(
t
+1)=4
x
(
t
){1
−x
(
t
)}  (1),
Feedback:
x
(
t
)=
x
(
t
+1)  (2), and
Isomorphic transform and quantization:
y
(
t
)=[{2/&pgr;·arc sin {square root over ( )}
x
(
t
)}·2
n
]  (3)
where, t is a discrete time, x(t) is an internal state of a chaos given as a real number with double-precision normalized between ‘0’ and ‘1’, and [ ] is an arithmetic operator representing a round-off operation of a decimal fraction of a value in the [ ],
a database for storing a quantization resolution n=1 and an initial value x(0); and
an arithmetic processing unit for starting an operation by substituting to the expression (1) the initial value x(0) stored in the database, having a resultant value based on the expression (2) again as an input to the expression (1), determining a time series x(t)−t by repeating such operations, substituting to the expression (3) the quantization resolution n=1 stored in the database, determining an isomorphic transform and quantization based on the expression (3) in correspondence to the time series x(t)−t, determining a time series y(t)−t from the determined isomorphic transform and quantization, generating a spread spectrum signal having, as a period thereof, a binary code sequence y(t) arbitrarily cut out of the time series y(t)−t.
According to the invention, a spread spectrum signal generator to be implemented in particular as a hardware chip such as a general purpose industrial CPU outputs binary code sequence y(t) determined when the quantization resolution n=1 as spread spectrum signal as necessary.
When the internal state x(t) of chaos ideally including waves having all frequencies is quantized as integer sequence and then observed, 2
n
combinations of integer sequence is generated in time series where n is a quantizing resolution. At this time, if the observation is performed while a non-liner mapping is linearly quantized, the distribution of integers to be taken out has bias.
On the other hand, logistic mapping: x(t+1)=4
x
(
t
){1
−x
(
t
)} is an ideal and representative mathematical model of low-division chaos. Isomorphic transform and quantization: y(t)=[{2/&pgr;·arc sin {square root over ( )}x (t)}·2
n
] for the logistic mapping generates almost flat distribution of integers from 0 to 2
n
when long observation is performed

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