Expe imen al Ve i ica ion o Chao ic Enc yp ion o Audio using Monoli hic Chao ic Modula o s
M. Delgado-Res i u o, A. Rod Iguez-Vázquez and M. Li lán
Dep . o Analog Design, CNM
Edi icio CICA, C/ Ta ia sn, 41012-Se illa, SPAIN
Phone #34 5 462381 1, FAX #34 5 4624506
ABSTRACT
This pape epo s he i s expe imen al e i ica ion o chao ic enc yp ion o audio signals using in eg a ed ci cui s. I is based
on a g—Cmodula o /demodula o analog CMOS IC ha implemen s a 3 d-o de nonlinea di e en ial equa ion. This has been
ab ica ed in 2.4J1m double-poly echnology and includes on-chip uning ci cui y based on ampli ude de ec ion. I is capable o
gene a ing con ollable con inuous- ime chao ic signals. Also, measu emen s demons a e how o exploi he synch oniza ion
be ween wo o hem o enc yp ed ansmission. In hese expe imen s, he wo s -case signal o noise a io o he eco e ed signal
is g ea e han +40dB (a he low co ne o he audio spec um) wi h less han -0.2dB loss o he inpu signal powe . A highe
equencies, he signal- o-noise a io ises up o +60dB, while e aining simila losses a he ecei e .
KEYWORDS: Chao ic Ci cui s, Chao ic Enc yp ion, Nonlinea Mic oelec onics, Analog In eg a ed Ci cui s
I . INTRODUCTION
In he las yea s, many expe imen al esul s ha e con i med ha he cells in a ne wo k o chao ic oscilla o s may e ol e in
phase, in spi e o hei in insically i egula beha io and sensi i i y o ini ial condi ions .Thisnon i ial ac has d awn consid-
e able in e es , no only a a heo e ical le el (gi ing ise o an inc easing numbe o pape s abou he phenomenon), bu also due
o he po en ial enginee ing applica ions based on so-called chao ic synch oniza ion.
One o he mos p omising applica ions e e s o he enc yp ion o da a. The basic idea is o exploi he noise-like appea ance
o a chao ic ca ie o hide an in o ma ion-bea ing signal, and make use o he synch oniza ion p ope y o eco e he da a. Fig. 1
shows a block diag am o he ealiza ion o his idea based on chao ic modula ion2'3 A he emi e side he in o ma ion bea ing
signal, ep esen ed by he cu en 5( ), iS injec ed in o a chao ic oscilla o (modula o uni ), he eby modi ying i s dynamics. I he
powe o he chao ic signal is la ge as compa ed o ha o he in o ma ion signal, he ansmi ed signal ( ) emains chao ic and,
hus, undeciphe able. Howe e , his ansmi ed signal s ill con ain he in o ma ion ela ed o 5( ), which can be eco e ed a he
ecei e side by using a demodula o uni which synch onizes o he modula ion used in he ansmi e .
5( )
Fig. 1 : Chao ic Modula ion Scheme.
This concep ually simple enc yp ion mechanism open new is as o inno a i e applica ion o analog in eg a ed ci cui s, based
on nonlinea signal p ocessing concep s. Howe e , p ope design o his kind o ci cui s in ol e a s ic comp omise be ween he
obus ness agains pa ame e a ia ions o he chao ic synch oniza ion, needed o decode he enc yp ed signal, and he secu i y o
he communica ion, so ha an in ude canno in e cep he in o ma ion con en . Al hough some g oups ha e ealized chao ic
enc yp ion using disc e e ci cui s, he abo e di icul ies ha e p ecluded hei ealiza ion using monoli hic modula o /demodula o
uni s. This pape epo s he i s expe imen al e i ica ion o chao ic enc yp ion o audio signals using in eg a ed ci cui s.
2. MATHEMATICAL MODEL AND CIRCUIT DESIGN
I is ep esen ed by a hi d o de con inuous- ime nonlinea s a e equa ion,
98 /SPIE Vol. 2612 O819419761/95/$6.OO
emi e ecei e
Downloaded F om: h ps://www.spiedigi allib a y.o g/con e ence-p oceedings-o -spie on 27 Ap 2020
Te ms o Use: h ps://www.spiedigi allib a y.o g/ e ms-o -use
-x( ) = Ax( ) + B [DTx( )] (1)
whe e x( ) = {x( ),y( ), z( )] Tis he s a e ec o ; A=[ a is a eal ma ix which de ines he linea pa o he sys em; B[ b,}
and D=[ d1J a e eal ec o s; and (.) is a eal- alued odd symme ic piecewise-linea (PWL) unc ion,
so — Si
(i)=s1i÷ 2
Smoo he app oxima ions o his PWL unc ion also quali y o da a enc yp ion pu poses.
(2)
S a e equa ions (1) can be mapped on o a gm—Cci cui whe e s a e a iables a e ep esen ed by he capaci o ol ages. Fig.2
shows a block diag am whe e a equals gj/Cj,b1 equals and he componen s o D a e implemen ed ia ini e gain ol age
ampli ie s.
--
—=AA/ ciA
/gmi3
'IL
—
—
-
=
=
AA L cLA
/gm23
IL
4x,cL:x / C3I/
/gm33
IL
2d3
,.J
Fig. 2: Chao ic Uni Block Diag am.
The in ended applica ion o da a enc yp ion can be ealized using many di e en se o pa ame e alues. The poin is o iden-
i y hose which a e he bes sui ed o monoli hic implemen a ion. I in ol es sea ching in he pa ame e space o ind he op i-
mum solu ion owing o conside a ions on misma ching, loading, e c. In pa icula , loading conside a ions ecommend o equalize
he capaci o s, i.e. C C1 C2 C3, and o keep each capaci o loaded by he same numbe o ansconduc o s. On he o he
hand, ma ching o he ansconduc o s is imp o ed by en o cing he ollowing ules:
. T ansconduc ances mus be in ege mul iples o a gi en uni elemen gmu• Thus, non-in ege n/ n a ios can be ealized by
sepa a ely g ouping n and n uni ansconduc o s. Applica ion o his c i e ium signi ican ly simpli ies he design o he
ci cui , since only one ansconduc o need be designed o ep oduce all he es .
. Sp ead o ansconduc ances should be minimized.
This, oge he wi h he use o on-chip uning, p o ide accu acies o abou 1 -2% in he pole equency --enough o gua an ee syn-
ch oniza ion o he emi e (modula o ) and he ecei e (demodula o ) uni s. Wi h hese ules in mind we ha e done an exhaus i e
sea ch in he pa ame e space o (1), o de e mine he op imum con igu a ion. The esul ing model is desc ibed by he ollowing
se o equa ions:
whe e .) is gi en by (2), and he pa ame e alues a e:
SPIE Vol. 2612 / 99
(x)+ay dy dz
—= —=cx(x—z)—y
d (3)
Downloaded F om: h ps://www.spiedigi allib a y.o g/con e ence-p oceedings-o -spie on 27 Ap 2020
Te ms o Use: h ps://www.spiedigi allib a y.o g/ e ms-o -use
(a, 3, s0, s1) = (3,4,—2, 2) (4)
Mon e Ca lo analysis wi h unco ela ed ela i e a ia ions o up o 7% om he nominal alues in (4), show ha 100% o he
ob ained ajec o ies e ol e owa ds a chao ic a ac o .
The p elimina y conside a ions o he design a e comple ed by he choice o he ime cons an , ' =2icCIg. Ou pu pose in
his expe imen al p o o ype is he signal ansmission in he oice-band, which, a e se e al beha io al ials, has led o he ol-
lowing nominal alues, C= 3OpF and mu .0 A/ .
Fig.3 shows he schema ics used o he ansconduc o , which includes a sou ce-degene a ion scheme o linea iza ion .Fig.4
shows he ci cui used o he PWL unc ion consis ing o a on -end ansconduc o and a nonlinea ci cui ha ope a es in cu -
en domain based on he high-accu a e ec i ica ion mechanism p oposed by he au ho s in .All pa ame e s in his nonlinea
cha ac e is ics ha e been made ex e nally con ollable o se e as c yp og aphic key in he audio ansmission scheme.
Fig. 4: PWL Func ion Ci cui .
Fig.5 shows he block diag am o he ci cui used o on-chip uning, based on ampli ude de ec ion. He e, a e e ence sinusoidal
signal passes h ough an in eg a o and he changes in he ou pu ampli ude, i he signal equency changes, a e de ec ed and used
o une he sys em.
Fig. 5: On-chip Au oma ic Tuning.
3. EXPERIMENTAL RESULTS
Fig.6 shows a mic opho og aph o he chao ic modula o /demodula o uni , which includes he on-chip uning scheme, and
o he auxilia y ci cui y o biasing and measu emen pu poses. The dimensions o he ci cui (de eloped in a 2.4 jm double-poly
double-me al CMOS echnology) has been also indica ed in Fig.6. Powe dissipa ion is less han 1 .8mW o a symme ical biasing
o
Fo he p e iously ci ed design pa ame e s he oscilla o gene a es ully ape iodic, e godic wa e o ms a x( ), y( ), and z( ).
Despi e hei ape iodici y, hese ajec o ies emain con ined o egions o egula , cha ac e is ic shape wi hin he s a e space, c e-
100/SPIE Vol. 2612
Fig. 3: Linea ized ansconduc o .
Downloaded F om: h ps://www.spiedigi allib a y.o g/con e ence-p oceedings-o -spie on 27 Ap 2020
Te ms o Use: h ps://www.spiedigi allib a y.o g/ e ms-o -use
a ing a ac o s. Fig.7 shows he double-sc oll Chua's a ac o ,measu ed om he ab ica ed p o o ype. The pic u e ep esen s
he Lissajous p ojec ion on o he (x, z) plane o he s a e space (ho izon al axis 25OmV/di , e ical axis 35OmV/di ). Resul s a e
in ull acco dance wi h he heo y and simula ions.
Fig.8 illus a es he pe o mance o he whole secu e communica ion scheme. Inpu signal (Fig.8(a)) consis s o a segmen o
speech. The wo s -case signal o noise a io o he eco e ed signal (Fig.8(b)) is g ea e han +40dB ( his occu s a e y low e-
quencies) wi h less han -0.2dB loss o he inpu signal powe . A highe equencies, he signal- o-noise a io ises up o +60dB,
while e aining simila losses a he ecei e . As can be seen om Fig.8, he ansmi ed signal (Fig.8(c)) keeps no esemblance o
he in o ma ion con en .
4. ACKNOWLEDGMENTS
This esea ch has been suppo ed pa ially by ESPRIT IV P ojec 8795 AMFIS.
2620j. m
5. REFERENCES
0
1. M. J. Ogo zalek: "Taming Chaos--Pa I: Synch oniza ion". IEEE T ansac ions on Ci cui s and Sys ems -I: Fundamen al
SPIE Vol. 2612 / 101
Fig. 6: Chip Mic opho og aph.
Chao ic Enc yp ion
5.0
0.0
-5.0
0.Oms
(a)
(b)
(c)
200.Oms
Fig. 7: Measu ed Chao ic A ac o .
100.Oms
Time (2Oms/di )
Fig. 8: Audio Da a T ansmission.
Downloaded F om: h ps://www.spiedigi allib a y.o g/con e ence-p oceedings-o -spie on 27 Ap 2020
Te ms o Use: h ps://www.spiedigi allib a y.o g/ e ms-o -use
Theo y and Applica ions, Vol.40, No.10, pp. 693-699, Oc . 1993.
2. M. Hasle : "Synch oniza ion P inciples and Applica ions". P oc. o he m . Symp. on Ci cui and Sys ems, Tu o ial 6.2,
pp. 314-327, 1994.
3. K.S. Halle, C.W. Wu, M. I oh, L.O. Chua: "Sp ead Spec um Communica ion h ough Modula ion o Chaos". m . J. Bi u -
ca ion and Chaos, Vol.3, No.2, pp. 469-477, 1993.
4. F. K ummenache and N. Joehi: "A 4MHz CMOS Con inuous-Time Fil e wi h On-Chip Au oma ic Tuning". IEEE J.
Solid-S a e Ci cui s SC-23, pp. 750-758, Jun. 1988.
5. M. Delgado-Res i u o and A. Rod Iguez-Vázquez: "Swi ched-Cu en Chao ic Neu ons". Elec onics Le e s, Vol.30,
No.5, pp. 429-430, Ma . 1994.
102 ISPJE Vol. 2612
Downloaded F om: h ps://www.spiedigi allib a y.o g/con e ence-p oceedings-o -spie on 27 Ap 2020
Te ms o Use: h ps://www.spiedigi allib a y.o g/ e ms-o -use