Experimental verification of chaotic encryption of audio using monolithic chaotic modulators

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