Cryptography – Communication system using cryptography – Symmetric key cryptography
Reexamination Certificate
1999-06-01
2004-03-09
Barrón, Gilberto (Department: 2132)
Cryptography
Communication system using cryptography
Symmetric key cryptography
C380S256000
Reexamination Certificate
active
06704420
ABSTRACT:
The present invention concerns transmissions using encryption by deterministic chaos.
The invention finds one advantageous application in the confidential transmission of information in optical networks.
It also finds an application in the microwave field for encrypting radio communications.
In encryption using chaos, the message is concealed in a chaotic signal, that is to say a signal that fluctuates in a random but deterministic manner. The sender of the message has a chaos generator that is used to conceal the message in clear in a chaotic signal. The receiver has another chaos generator which must be synchronized to the first one to be able to decrypt the message correctly.
The chaos generators of most interest for use in encryption are devices known as “non-linear systems with delay”. They comprise a light source which has a feedback loop formed of a non-linear element and a delay line.
They have the advantage of being simple whilst producing chaos with very large dimensions, that is to say very complex chaos, which enables a very high level of confidentiality to be obtained.
The problem that arises with this type of chaos generator is that the sender and the receiver must be synchronized so that the message can be decrypted in real time. Very few implementations in the optical domain have been described before now.
Patent FR 2 743 459 describes an encryption system using as the sender a chaos generator formed of a wavelength tuneable source and a non-linear wavelength component. The device encrypts a message in the form of chaotic modulation of the wavelength emitted by the light source. The document reports that encryption and decryption are effected by the sender and the receiver using non-linear wavelength elements which must be identical in the sender and in the receiver.
This process has the advantage of being simple to implement but it is difficult to use over long distances (i.e. in systems employing optical fibres) because the same wavelength non-linearities must be conserved between the sender and the receiver over the whole distance.
This condition is not satisfied when the transmission channel is a standard optical fibre. The fibre introduces chromatic dispersion effects which affect the wavelengths transmitted between the sender and the receiver, which makes it difficult to obtain conditions enabling the receiver to decrypt the message.
The solution to the problem of producing chaos that is usable over long distances and of avoiding dispersion problems is to use a chaos generator producing chaotic modulation of the luminous intensity from a monochromatic source. Existing devices, referred to hereinafter as “intensity chaos generators”, cannot be used in the encryption and decryption process described in the previously mentioned patent FR 2 743 459, however, for reasons that will now be explained.
FIG. 1
shows an intensity chaos generator the effect of which is to produce chaotic modulation of the luminous intensity from the monochromatic source
1
, as described by P. Celka in an article entitled “Chaotic synchronization and modulation of nonlinear time-delayed feedback optical systems”, IEEE Transactions on Circuits and Systems, 42, 8, pp 455-463, 1995. The source
1
is optically connected to an integrated Mach-Zehnder interferometer
2
whose output intensity P(t)
3
is converted by the photodetector
4
into an electrical signal looped to the control electrodes of the interferometer after passing through a delay line T
5
. The reader is also referred to the following documents in which the non-linear energy element is an electro-optical crystal, an acousto-optic crystal or a Michelson or Fabry-Pérot interferometer:
F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker “Bifurcation to chaos in optical bistability”, Phys. Rev. A, 25, 4 pp 2172-2182, 1982;
R. Vallée, C. Delisle “Route to chaos in an acousto-optic bistable device”, Phys. Rev. A, 31, 4 pp 2390-2396, 1985;
Y. Liu, J. Ohtsubo “Chaos in an active interferometer”, J. Opt. Soc. Am. B, 9, 2, pp 261-265, 1992;
T. Takizawa, T. Liu, J. Ohtsubo, “Chaos in a feedback Fabry-Pérot interferometer”, IEEE J. of Quantum Electronics, 30, 2, pp 334-338, 1994.
In all the above systems the non-linear element induces energy non-linearity directly in the light issuing from the source and the chaotic luminous signal obtained in this way is looped, after optical-electrical conversion, via a feedback loop with delay to the source or to the electrodes of the non-linear element. The law of evolution of the intensity produced by all the above systems is different from that of the chaos on which the encryption process described in the previously mentioned patent is based, however, which means that it cannot be transposed to the above systems.
Thus in
FIG. 1
, the luminous intensity P(t) emitted by the emitter is governed by the following equations:
P
(
t
)
=
P
0
[
1
+
cos
2
π
λ
V
(
t
-
T
)
]
and
V
(
t
)
+
τ
ⅆ
ⅆ
t
V
(
t
)
=
η
P
(
t
)
where V(t) is the electrical signal produced by the photodetector, &eegr; is its electrical gain, &tgr; is the time constant of the feedback loop and &lgr; is the wavelength of the source.
The above two equations can be combined in the form of a non-linear differential equation with delay which governs the law of evolution of the chaos intensity P(t) produced at the output
3
of the interferometer:
λ
2
π
cos
-
1
[
P
(
t
)
P
0
-
1
]
+
τ
ⅆ
ⅆ
t
cos
-
1
[
P
(
t
)
P
0
-
1
]
=
η
P
(
t
-
T
)
(
1
)
The chaos obtained and the equation (1) that governs it are different from the model described in the previously cited patent FR 2 477 459, in which the chaos must obey an equation of the type:
P
(
t
)
+
τ
ⅆ
ⅆ
t
P
(
t
)
=
π
[
A
-
μ
sin
2
{
MP
(
t
-
T
)
}
]
(
2
)
This makes it impossible to use the simple encryption method described therein.
A much more complex method that is already known per se can be used.
FIG. 2
shows this solution to the problem of decrypting the chaos governed by equation (1). It is based on the method of synchronizing chaos described by Pecora and Caroll in the document “Synchronization in chaotic systems” published in Physical Review Letters, vol. 64, pp 821-824 in 1990. The sender
6
is a chaos generator formed of two coupled sub-systems, a master chaos generator
7
and a slave chaos generator
8
. The master generator generates chaos as shown to control the chaos from the slave generator. The message s(t) to be encrypted is encoded (generally in the form of a simple addition) on the slave chaos which behaves like interference noise. The combination is transmitted to the receiver
9
. This includes a slave generator
10
(identical to the slave generator of the sender), controlled by the synchronization signal from the master generator of the sender. When the chaos from each generator has been synchronized, the message s(t) can be recovered by subtraction. Note that this method generally necessitates two transmission channels
11
and
12
, one for the encrypted signal and the other for the synchronization signal.
One embodiment in the optical domain is described by P. Celka in the previously cited article “Chaotic synchronization and modulation of nonlinear time-delayed systems” published in IEEE Transactions on Circuits and Systems, vol. 42, number 8, pp 455-463 (August 1995). The device uses a monochromatic light source and a plurality of Mach-Zehnder interferometers controlled by feedback loops with delay to obtain synchronization between chaos generated by the sender and by the receiver.
FIG. 3
shows the encryption and decryption system proposed in the above article and provides a basis for some explanation of its operating principle. The sender
13
compr
Goedgebuer Jean-Pierre
Langer Laurent
Merolla Jean-Marc
Barrón Gilberto
Blakely & Sokoloff, Taylor & Zafman
France Telecom
Zand Kambiz
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