On the Effectivity of Different Pseudo-Noise nd Orthogonl Sequences for Speech Encryption from Correltion Properties V. Anil Kumr, Ahijit Mitr nd S. R. Mhdev Prsnn Astrct We nlyze the effectivity of different pseudo noise (PN) nd orthogonl sequences for encrypting speech signls in terms of perceptul intelligence. Speech signl cn e viewed s sequence of correlted smples nd ech smple s sequence of its. The residul intelligiility of the speech signl cn e reduced y removing the correltion mong the speech smples. PN sequences hve rndom like properties tht help in reducing the correltion mong speech smples. The men squre periodic uto-correltion (MSAAC) nd the men squre periodic cross-correltion (MSACC) mesures re used to test the rndomness of the PN sequences. Results of the investigtion show the effectivity of lrge Ksmi sequences for this purpose mong mny PN sequences. Keywords Speech encryption, pseudo-noise codes, mximl length, Gold, Brker, Ksmi, Wlsh-Hdmrd, utocorreltion, crosscorreltion, figure of merit. I. INTRODUCTION WHILE trnsmitting informtion (speech, imge or other dt) through insecure chnnels, there might e unwnted disclosure s well s unuthorized modifiction of dt if tht is not properly secured. Therefore, certin mechnisms re needed to protect the informtion within insecure chnnel. One wy to provide such protection is to convert the intelligile dt into unintelligile form prior to trnsmission nd such process of conversion with key is clled encryption []- [3]. At the receiver side, the encrypted messge is converted ck to the originl intelligile form y the reverse process of the encryption clled decryption. Cryptogrphic techniques re minly clssified s privte key cryptogrphy nd pulic key cryptogrphy [2],[3]. In privte key cryptogrphy, lso clled symmetric key cryptogrphy, sme key is used for oth encryption nd decryption. In pulic key cryptogrphy, on the other hnd, different keys re used for encryption nd decryption nd it is thus clled n symmetric key cryptogrphy. The min disdvntge of privte key encryption technique is the distriution of key to uthorized users ut it is fster when compred with pulic key cryptogrphy. Security is needed ginst two types of ttckers, nmely csul listeners nd professionl ttckers termed s cryptnlysts. The strength of cryptogrphic system [4],[5] is mesured in terms of time nd the resources required to rek the system for getting ck the messge in intelligile form. Removing the intelligiility of messge tht is to e Mnuscript received My 3, 27; revised Septemer 7, 27. The uthors re with the Deprtment of Electronics nd Communiction Engineering, Indin Institute of Technology (IIT) Guwhti, Indi. E-Mil: (v.nil,.mitr, prsnn)@iitg.ernet.in. trnsmitted is sufficient to provide security ginst csul listener, ut cryptnlysts would need strong cryptogrms. In this pper, symmetric key encryption technique for speech smples sed on the simple XOR opertion with different PN sequences is used to test the performnce of the sequences for speech encryption, nd the residul intelligiility present in the encrypted speech using different sequences is oserved y informl listening tests nd y signl inspection methods. This encryption scheme is esy to implement, less complex nd it provides etter security ginst csul listeners. Usully, speech encryption techniques using PN sequences mke the speech signl unintelligile y removing the correltion etween the smples of the speech signl. The sequences used for the encryption, in ny cse, should not portry the sttisticl properties of the trnsmitted signl so tht the ttcker cnnot use sttisticl nlysis to ttck the system. PN sequences [6]-[8] hve noise like properties; these sequences re sttisticlly independent nd uniformly distriuted. XOR opertion of these sequences with the speech smples mkes the speech signl noise-like signl, nd the encrypted speech signl sounds like rndom noise signl. The PN sequences which hve good uto-correltion nd cross-correltion properties remove the correltion mong the speech smples nd results in n encrypted signl of less residul intelligence. The rndomness of inry sequences is mesured y men squre periodic uto-correltion (MSAAC) nd men squre periodic cross-correltion (MSACC) mesures [9],[]. The sequences which hve etter rndom noise properties will hve less MSAAC nd MSACC vlues. This pper is orgnized s follows: in Sections 2 nd 3, we riefly del with different types of PN nd orthogonl sequences. Section 4 descries the techniques to mesure the correltion or rndomness of the PN sequences. Section 5 nrrtes the speech encryption using PN sequences nd the min otined results long with the comprison of the different PN sequences re given in Section 6. The pper is concluded y summrizing the present work in Section 7. II. DIFFERENT PN SEQUENCES FOR SPEECH ENCRYPTION PN sequences re strems of s nd s. Here, the wveform is tken s rndom-like, mening tht it cn e generted y mthemticlly precise rules, ut sttisticlly it stisfies the requirements of truly rndom sequence in the limiting sense. These pseudo-rndom or pseudo-noise (PN) properties include, mong other properties, () lnce, () run nd (c) 45
uto-correltion properties [8]. These three properties mke PN sequences efficient for speech encryption. However, due to the third property, djcent its correltion ecomes considerly less, therey mking the PN sequences more effective for speech encryption when compred with dt encryption due to high djcent correltion present in the speech signls. Therefore, PN sequences tht re useful for speech encryption must hve very good uto-correltion nd cross-correltion properties s well s mintining some rndomness properties. Below, we riefly descrie different PN sequences useful for speech encryption. Note tht in some cses we shll represent inry sequences using zeros nd ones nd in other cses + s nd s. The pproprite mpping is tht the zeros re mpped to + s nd ones re mpped to s. A. Mximl Length Sequences The Mximl length sequence (m-sequence) genertor is usully constructed with liner feedck shift registers (LFSR) [],[2]. The m-sequences re, y definition, the lrgest codes tht cn e generted y given shift register of given length with feedck. The feedck function, lso clled s chrcteristic polynomil, determines the length nd type of the sequence generted. B. Gold Sequences Gold sequences re generted y the modulo-2 opertion of two different m-sequences of sme length. Any two m- sequences re le to generte fmily of mny non-mximl product codes, ut preferred mximl sequences cn only produce Gold codes [7], [8]. C. Gold-Like Sequences There exists clss of sequences which hs prmeters similr to those of Gold sequences except tht it is otined from decimted sequence. Let u e n m-sequence of length N = 2 n generted y primitive polynomil of degree n nd let q e n integer such tht gcd(q, N) = 3. Also, let v (k), k =,, 2, denote the sequences otined y decimting T k u y q. In tht cse, the new sequences formed y different comintions of u nd v re clled Gold-like sequences [3]. D. Brker Sequences Brker sequences re short length codes tht offer good correltion properties. A Brker code is sequence of some finite length N such tht the solute vlue of discrete utocorreltion function r(τ) for τ [4], [5]. Brker sequences hve mny dvntges over other PN sequences. These sequences hve uniformly low uto-correltion sideloes ( ), ut the size of these fmilies is smll. E. Brker-Like Sequences Brker sequences hve good correltion properties with the pek correltion vlue eing ounded y. The numer of existing Brker sequences, however, re very less. We cn generte more numer of sequences y mking certin relxtion on the pek vlue of the correltion function long with mximum llowed shift etween the sequences. This newly generted sequences re clled Brker-like sequences [6]. F. Ksmi Sequences Ksmi sequences re lso PN sequences of length N = 2 n, which re defined for even vlues of n [3],[7]. There re two clsses of Ksmi sequences: (i) smll set of Ksmi sequences, (ii) lrge set of Ksmi sequences. Smll set of Ksmi sequences re optiml in the sense of mtching Welch s lower ound for correltion functions. A smll set of Ksmi sequences [3] is set of 2 n/2 inry sequences. Fig. shows the lock digrm representtion for the genertion of smll set of Ksmi sequences, ech of length 63 it. Smll set of Ksmi sequences re optiml sequences nd hve etter correltion properties compred to Gold sequences. But the set contins less numer of sequences. For the shift register of length n the numer of possile sequences for the smll Ksmi sequence set is only 2 n/2 sequences, wheres Gold code set contins 2 n + 2 sequences. The numer of sequences cn e incresed y mking some relxtion on the correltion vlues of the sequences. The resulting set of sequences is clled lrge set of Ksmi sequences [3],[7]. III. DIFFERENT ORTHOGONAL CODES FOR SPEECH ENCRYPTION Two sequences re sid to e orthogonl when the inner product etween them is zero, i.e., c i (kτ), c j (kτ) = where c i (kτ) nd c j (kτ) re the i th nd j th orthogonl memers of n orthogonl set, respectively, M is the length of the set nd τ is the symol durtion. There re two kinds of orthogonl codes: fixed- nd vrile-length. Fixed length orthogonl codes include Wlsh Hdmrd (WH) nd modified WH (MWH) codes. Among vrile length codes, orthogonl Gold codes nd orthogonl vrile spreding fctor (OVSF) codes re mentionle. WH codes re orthogonl codes possessing low utocorreltion properties. The WH sequences [8],[9] of length N re defined with clss of orthogonl mtrices H N, clled Hdmrd mtrices, s H N H T N = NI N where H T N is the trnsposed Hdmrd mtrix of order N, nd I N is the N N unity mtrix. MWH codes re generted y multiplying the Hdmrd mtrix H N y digonl mtrix D N of sme order [9],[2] such tht W N = H N D N. WH codes nd MWH codes re fixed length orthogonl codes; the dot product of ny two sequences is zero. Vrile length orthogonl codes c k (i), i =, 2,..., 2 k, re those with different lengths stisfying the orthogonl property [7]. The codes re tken from code tree nd this orthogonl vrile spreding fctor (OVSF) tree genertion lgorithm is similr to the recursive genertion of the Wlsh codes y mens of the Hdmrd mtrices. New levels in the code tree re generted y conctenting root codeword with replic of itself. 46
5 4 3 2 9 8 7 6 5 4 3 2 Ksmi sequences 7 6 5 4 3 2 Fig.. An exmple of 63 it smll set of Ksmi sequence genertor. One cn find tht mny cross-correltion vlues of Gold codes re. By pdding one zero to the originl Gold codes, it is possile to mke cross-correltion vlues to t no shift mong the two sequences. In fct, 2 n + orthogonl codes cn e otined y this simple zero pdding. These codes re clled orthogonl Gold codes. A detiled discussion on ll these PN nd orthogonl codes cn e found in [2]. IV. MEAN SQUARE CORRELATION MEASURES The performnce of the different PN sequences re evluted y men squre periodic uto-correltion R AC (MSAAC) nd men squre periodic cross-correltion R CC (MSACC) mesures [2]. These correltion mesures hve een introduced y Oppermnn nd Vucetic []. If c i (n) represents non-delyed version of c k (i), c j (n + τ) represents the delyed version of c k (j) y τ units nd N is the length of the sequence c i, then the discrete periodic correltion function is defined s r i,j (τ) = N N τ= N c i (n)c j (n + τ). () The men squre periodic uto-correltion vlue for code set contining M sequences is given y R AC = M M N i= τ= N,τ r i,i (τ) 2 (2) nd similr mesure for the men squre periodic crosscorreltion vlue is given y R CC = M(M ) M M N i= j=,j i τ= N r i,j (τ) 2. (3) Auto-correltion refers to the degree of correspondence etween sequence nd phse shifted replic of itself, wheres cross-correltion is the mesure of greement etween two different codes. These two mesures hve een used s the sis for compring the sequence sets in this pper. The sequences which hve good uto-correltion properties will hve poor cross-correltion properties, nd vice-vers, nd they hve wide nd flt frequency spectrum. The sequences which hve less MSAAC vlues removes the correltion mong the its with in smple, nd the sequences which hve less MSACC vlues removes the smple to smple correltion, nd mke the speech signl less intelligile. A. Figure of Merit As hs een mentioned, the price for eing le to select good cross-correltion properties will e degrdtion in the uto-correltion properties of the set of sequences. A degrdtion of the uto-correltion properties hs direct reltion on the frequency spectrum of the sequences in the set. If the R AC vlues re poor, the spectrum of the sequence will not e wide-nd nd flt. In order to determine quntittively how significnt this degrdtion is for given set of sequences, Figure of Merit (FoM) is required to judge the suitility of the frequency chrcteristics of the sequences. Sequences with low FoM hs nrrow flt spectrum nd they re neither suitle for CDMA nor for speech encryption. The FoM for sequence, c i (n), of length N hving the uto-correltion function r i (τ) is given s: F x = r 2 i,i () r i,i (τ) 2 = N 2. (4) 2. N r i,i (τ) 2 τ τ= This is nothing more thn the inverse of the MSAAC vlue for given sequence. In our cse, this FoM my e extended to the whole sequence set s ech sequence in the set hs the sme solute vlue of uto-correltion vlue. Thus we my use the inverse of the vlue clculted for the R AC s the FoM. V. SPEECH ENCRYPTION USING PN SEQUENCES Speech signl cn e viewed s sequence of smples nd ech smple cn e viewed s sequence of its. Speech signl cn e encrypted, y removing the correltion etween speech smples, y the XOR opertion of speech smple with PN sequence selected t rndom from tle of PN sequences. Pseudo rndom index genertors (PRIG) [] re used to select specific PN sequence from given list of sequences. The lock digrm of PRIG is similr to tht of m-sequence genertor. The deciml index vlue is generted y converting the inry output of ech shift register in to deciml vlue y using inry to deciml converter. The PN sequence corresponding to this deciml index vlue is tken from the tle nd XOR operted with the its of the ech speech smple to get the encrypted speech smple. At the receiver side sme opertion is performed to get the decrypted speech signl. The performnce of the different PN sequences is compred y nlyzing the encrypted speech signl in time domin nd the spectrum of the encrypted speech signl. 47
VI. RESULTS AND DISCUSSIONS The ove proposed techniques, MSAAC, MSACC mesures nd speech encryption using different PN sequences, re implemented in MATLAB. TABLE I APERIODIC CORRELATION MEASURES FOR PN SEQUENCES OF LENGTH 63 BITS Sequence MSAAC MSACC FoM Mx-CC A. Correltion Mesures PN sequences nd orthogonl codes of desired length re generted s descried in Sections 2 nd 3, nd the MSAAC nd MSACC mesures re computed for the code sets. Tle I shows the correltion mesures for PN sequences of length 63 its. From the results, mong ll PN sequences, m-sequences nd Brker sequences hve low MSAAC vlues since these sequences hve single pek uto-correltion function nd ll sideloes mplitudes re very less. The FoM of these sequences is lso high for which these sequences hve flt power spectrum. These sequences, however, re not suitle for speech encryption since there is only one possile sequence for given LFSR length nd given primitive polynomil, nd the security provided y these sequences is therey less. Note here tht the circulr shifted sequences of originl sequences re not tken s different sequences. The Gold nd Gold-like sequences hve four vlued uto-correltion nd three vlued cross-correltion functions with the mximum cross-correltion of t(n)/n [e.g., for n = 6, the mximum correltion vlue is.2698]. However, the FoM of Goldlike sequences is more thn tht of Gold sequences nd the numer of codes tht cn e generted is lso similr, therefore these sequences re more preferle thn Gold sequences. The correltion vlues of Brker-like sequences depend on the vlue of m, i.e., the upper ound on the pek correltion function. For Brker sequences of length N = 63 nd for m = 5, the otined MSAAC nd MSACC vlues re shown in Tle I. These sequences hve less uto-correltion vlues nd therefore high FoM vlue. As hs een mentioned, the uto-correltion vlue decreses with the increment of crosscorreltion vlues. Brker-like sequences lso hve less utocorreltion vlues. Although smll Ksmi sequences hve less uto-correltion vlues too nd hence more cross-correltion vlues ut the numer of sequences tht cn e generted re less. Thus the security provided y these sequences is less compred to Brker-like sequences. The smll set of Ksmi sequences hve less MSAAC vlue mking the FoM of these sequences high. On the other hnd, the lrge set of Ksmi sequences hve mny unique fetures. The FoM of these sequences is similr to tht of Brker-like sequences. The mximum cross-correltion vlue of lrge set of Ksmi sequences is sme s tht of Gold sequences. The possile numer of lrge Ksmi sequences for given structure re more when compred with ll other PN sequences. All these fetures mke lrge Ksmi sequences effective for speech encryption. Tle II shows the correltion mesures for 64-it length orthogonl codes. Orthogonl codes hve zero cross-correltion when there is no time shift etween the two sequences ut the correltion vlues re high when there is shift etween the sequences. The correltion vlues of orthogonl codes re high compred to tht of PN sequences. The uto-correltion vlues Mximl.4429 2.2577 Gold.975.9849.256.3333 Gold-Like.9227.9859.838.2857 Brker (3 it).7 4.833 Brker-Like.6547.546.5274.984 Smll Ksmi.764.998.35.2222 Lrge Ksmi.948.9979.932.9524 TABLE II APERIODIC CORRELATION MEASURES FOR ORTHOGONAL CODES OF LENGTH 64 BITS Sequence MSAAC MSACC FoM Mx-CC Wlsh Hdmrd.396.853.962.9844 MWH 5.328.954.877.953 OVSF 5.328.954.877.9844 Orthogonl Gold.9739.9848.268.3438 of WH codes re very high nd the FoM vlue is less so the spectrum of these sequences is not so wide nd flt. However, the MWH codes hve less correltion vlues compred to WH codes mking the cross-correltion vlues of these codes high. The correltion functions nd the MSAAC nd MSACC vlues of OVSF codes re lmost sme s tht of MWH codes. The correltion vlues of OVSF codes depends on the repetitive sequence. In Tle II the correltion vlues of OVSF codes re for the repetitive sequence {,,, } nd it is seen tht with this repetitive sequence the otined OVSF codes hve less correltion vlues. The orthogonl Gold codes hve the correltion vlues similr to tht of originl Gold codes. Correltion mesurements of encryption with different 3/32 it sequences re provided in Tle III which cn e compred with Tles I nd II. Also, correltion mesures for different repetitive sequences of OVSF code set of length 6 nd 32 re provided in Tle IV from which one cn choose the optimum sequence ccording to the requirement. B. Speech Encryption with PN Sequences Speech signl smpled t 8 khz is quntized with 2 6 levels, nd it is encrypted with the ove PN sequences s descried in Section 5 nd the residul intelligiility within the encrypted speech signl is oserved. Fig. 2() shows the time domin representtion of 3 ms voiced speech segment tken from the speech utternce /vnde mtrm/ nd Fig. 2() is its spectrogrm representtion computed y 52 point fst Fourier trnsform (FFT). The encrypted speech signl nd its spectrum y using ll the sequences re compred with 48
TABLE III CORRELATION MEASURES OF A FEW PN/ORTHOGONAL SEQUENCES OF LENGTH 3/32 BITS Sequence MSAAC MSACC m-sequences (3 its).487 - Gold Codes (3 its).6866.745 Brker Sequence.827.55 WH Codes 6.5938.7873 MWH Codes 3.288.8962 TABLE IV CORRELATION MEASURES FOR OVSF CODE SET OF LENGTH 6 AND 32 BITS Repetitive N = 6 N = 32 Sequence MSAAC MSACC MSAAC MSACC (,,, ) 4.625.7292 6.5937.7873 (,,, ).825.8792 3.288.8962 (,,, ).825.8792 3.288.8962 (,,, ) 4.625.7292 6.5938.7873 (,,, ).825.8792 3.288.8962 (,,, ) 4.625.7292 6.5937.7873 (,,, ) 4.625.7292 6.5938.7873 (,,, ).825.8792 3.288.8962 (,,, ).825.8792 3.288.8962 (,,, ) 4.625.7292 6.5938.7873 (,,, ) 4.625.7292 6.5937.7873 (,,, ).825.8792 3.288.8962 (,,, ) 4.625.7292 6.5938.7873 (,,, ).825.8792 3.288.8962 (,,, ).825.8792 3.288.8962 (,,, ) 4.625.7292 6.5937.7873 the informtion is present in the encrypted speech signl using Brker sequences. 4) Brker-like Sequences: Brker sequences gives etter performnce compred to other sequences. The residul intelligiility of the encrypted speech signl using Brker sequences is very less, it sounds like noise signl. Fig. 2(k)-(l) shows the encrypted speech signl nd its spectrum using Brker sequences. From the figure, we cn oserve tht there is no periodicity preserved in the encrypted signl, the signl looks like rndom noise signl nd the spectrum of the encrypted signl is flt, the formnt peks re suppressed in the spectrum. 5) Ksmi Sequences: The correltion vlues of smll set of Ksmi sequences is less ut the numer of sequences in the set is less, so the residul intelligiility of the encrypted speech is somewht high s compred with the Brker sequences. Lrge set of Ksmi sequences hve etter performnce compred with the ll other sequences since the numer of lrge Ksmi sequences re more, so the residul intelligiility is less. If the numer of sequences re more, y encrypting ech smple with different sequences the smple to smple correltion in speech signl is etter removed, so the residul intelligiility of the encrypted signl is less. Fig. 2(m)-(n) re the time domin nd spectrogrm representtions for encrypted speech signl using smll set of ksmi sequences nd Fig. 2(o)-(p) shows the encrypted speech signl nd its spectrum using lrge set of Ksmi sequences. this voiced speech segment. If we encrypt ech smple of the speech signl with different inry sequence, the residul intelligiility is less s compred with the encrypted speech signl with single sequence. The code set which hve more numer of sequences with good correltion properties hve etter performnce nd the encrypted speech signl sounds like noise signl. ) m-sequences: Speech encryption using m-sequences reduces the residul intelligiility of the encrypted speech ut they re not suitle for rel time pplictions since, there is only one possile sequence of given length. Fig. 2(c)-(d) shows the encrypted speech wveform nd its spectrogrm representtion using m-sequence of length 63 its. From the Fig. 2(c) we cn oserve tht the periodicity of the speech signl is retined in the encrypted signl. 2) Gold Sequences nd Gold-like Sequences: The performnce of Gold sequences is similr to tht of the Goldlike sequences The performnce of the gold sequences is good compred to m-sequences since, y using different Gold sequences the smple to smple correltion is lso reduced. The size of these fmilies is lrge, ut prcticlly gold codes re more suited for speech encryption. Fig. 2(e)-(f) shows the encrypted speech signl nd its spectrum using Gold sequences nd Fig. 2(g)-(h) re the encrypted speech nd its spectrogrm representtions for Gold-like sequences. 3) Brker Sequences: Brker sequences of some length only re existing nd the numer of known Brker sequences re lso less, so these sequences re not suitle for speech encryption. Fig. 2(i)-(j) shows the encrypted speech signl nd its spectrum using Brker sequence of length 3 its. Most of C. Speech Encryption with Orthogonl Codes Orthogonl codes of length 64 its re generted nd ech smple of the coded speech smple is XOR operted with the orthogonl codes to get encrypted speech smple. Ech smple of the speech signl is represented with 6 its, nd four smples of the originl speech signl re XOR operted with the 64 it sequence to get four smples of the encrypted speech signl. ) Wlsh Hdmrd Codes: WH codes stisfies the orthogonl property ut they hve poor correltion properties nd the residul intelligiility present in the encrypted speech signl is lso more. Fig. 3()-() re the wveform of encrypted speech signl nd its spectrogrm representtion using WH codes. 2) Modified Wlsh Hdmrd Codes: Fig. 3(c)-(d) shows the encrypted speech signl nd its spectrogrm representtion using MWH codes. The performnce of MWH codes is good compred with the WH codes ecuse these codes hve etter correltion properties compred to WH codes. The residul intelligiility of the encrypted speech signl is lso less compred to WH codes. 3) Vrile Length Orthogonl Codes: Fig. 3(e)-(f) shows the encrypted speech signl nd its spectrum using OVSF codes with repetitive sequence {,,, }. The MSAAC nd MSACC vlues for this repetitive sequence re less nd the residul intelligiility of the encrypted speech signl is lso less. 4) Orthogonl Gold Codes: The performnce of Orthogonl Gold codes is sme s tht of originl Gold codes since oth hve similr correltion vlues nd the numer of sequences re lso nerly equl. Fig. 3(g)-(h) re the time 49
domin nd spectrogrm representtions for encrypted speech signl using orthogonl Gold codes. VII. CONCLUSION In this pper, we hve investigted different PN nd orthogonl sequences tht re pproprite for speech encryption y the correltion mesures to test the rndomness of these inry sequences. The sequences which hve less correltion vlues hve more noise like properties nd mke the speech signl less intelligile y reducing the correltion mong successive speech smples y encrypting the speech signl with those sequences. The security offered y the system depends on the numer of PN sequences present in the code set. Also, the residul intelligiility is very less if ech smple of the speech signl is encrypted with different sequence insted of using sme sequence for ech smple therefore, the signl is etter encrypted if the code set contins more numer of sequences. Among ll the sequences, m-sequence nd Brker sequences hve very less uto-correltion vlues nd high FoM vlues ut these sequences re not suitle for encryption since there is only one possile sequence for given shift register length. The security offered y these sequences is thus less. Brker-like sequences hve etter uto-correltion properties nd the residul intelligiility within the encrypted speech signl is less ut genertion of these sequences is complex when compred with other sequences. The lrge set of Ksmi sequences hve good correltion vlues, high FoM vlue nd these sequences hve wide flt spectrum which mkes these etter suited for speech encryption. The encrypted speech signl using lrge Ksmi sequences sounds s noise like signl. For given shift register length the numer of possile lrge Ksmi sequences re lso lrge so the security offered y these sequences is lso lrge. The genertion of these sequences is lso esy when compred with Brker like sequences. These sequences re therefore effective for speech encryption. The WH, MWH nd orthogonl Gold codes hve zero cross-correltion when there is no shift in the sequences. They hve, however, very high correltion vlues if there is ny shift in the sequences. These sequences thus my not serve s good option for speech encryption. [9] J. H. Lindholm, An nlysis of the pseudo rndomness properties of the susequences of long m-sequences, IEEE Trns. Inform. Theory, vol. IT-4, pp. 569-576, July 968. [] I. Oppermnn nd B. S. Vucetic, Complex spreding sequences with wide rnge of correltion properties, IEEE Trns. Commun., vol. COM- 45, pp. 365-375, Mrch 997. [] L. T. Wng nd E. J. McCluskey, Liner feedck shift register design using cyclic codes, IEEE Trns. Comput., vol. 37, pp. 32-36, Oct. 988. [2] A. Fuster nd L. J. Grci, An efficient lgorithm to generte inry sequences for cryptogrphic purposes, Theoreticl Computer Science, vol. 259, pp. 679-688, My 2. [3] D. V. Srwte nd M. B. Pursley, Correltion properties of pseudo rndom nd relted sequences, Proc. IEEE, vol. 68, no. 5, pp. 593-69, My 98. [4] S. W. Golom nd R. A. Scholtz, Generlized Brker sequences, IEEE Trns. Inform. Theory, vol. IT-, no. 4, pp. 533-537, Oct. 965. [5] D. G. Luenerger, On Brker codes of even length, Proc. IEEE, vol. 5, pp. 23-23, Jn. 963. [6] C. K. Chn nd W. H. Lm, Generlised Brker-like PN sequences for qusisynchronous spred spectrum multiple ccess communiction systems, IEE Proc. Commun., vol. 42, no. 2, pp. 9-98, April 995. [7] X. Wng, Y. Wu nd B. Cron, Trnsmitter identifiction using emedded pseudo rndom sequences, IEEE Trns. Brodcsting, vol. 5, no. 3, pp. 244-252, Sep. 24. [8] V. Milosevic, V. Delic nd V. Senk, Hdmrd trnsform ppliction in speech scrmling, Proc. IEEE, vol., pp. 36-364, July 997. [9] Ti-Kuo Woo, Orthogonl vrile spreding codes for widend CDMA, IEEE Trns. Vehiculr Tech., vol. 5, no. 4, pp. 7-79, July 22. [2] B. Wysocki nd T. A. Wysocki, Modified Wlsh Hdmrd sequences for DS-CDMA wireless systems, School of Electricl, Computer nd Telecommunictions Engineering, University of Wollongong, Austrli. [Online] Aville: www.elec.uow.edu.u/stff/wysocki/pulictions/j.pdf. [2] A. Mitr, On Pseudo-Rndom nd Orthogonl Binry Spreding Sequences, to pper in Int. J. Info. Tech., 27. REFERENCES [] H. J. Beker nd F. C. Piper, Secure Speech Communictions, London: Acdemic Press, 985. [2] W. Stllings, Cryptogrphy nd Network Security, Englewoods Cliffs, NJ: Prentice Hll, 23. [3] W. Diffe nd M. E. Hellmn, New directions in cryptogrphy, IEEE Trns. Inform. Theory, vol. 22, pp. 644-654, Nov. 976. [4] N. S. Jynt, B. J. McDermott, S. W. Christensen nd A. M. Quinn, A comprison of four methods for nlog speech privcy, IEEE Trns. Commun., vol. COM-29, pp. 8-23, Jn. 98. [5] B. Goldurg, S. Sridhrn nd E. Dwson, Design nd cryptnlysis of trnsform sed speech scrmlers, IEEE J. Selected Ares Commun., vol., no. 5, pp. 735-744, June 993. [6] R. L. Pickholtz, D. L. Schilling nd L. B. Milstein, Theory of spred spectrum communictions A tutoril, IEEE Trns. Commun., vol. COM-3, no. 5, My 982. [7] E. H. Dinn nd B. Jri, Spreding codes for direct sequence CDMA nd widend CDMA cellulr networks, IEEE Commun. Mgzine, vol. 36, no. 4, pp. 48-54, Sep. 998. [8] B. Sklr, Digitl Communictions: Fundmentls nd Applictions, 2nd Ed., NJ: Prentice Hll, 2. 5
.5.5.5.5 5 5 2 25 3.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5 () () (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) Fig. 2. Time domin nd its spectrogrm representtion for 3 ms speech segment of the utternce /vnde mtrm/ re shown in ()-(). The encrypted time domin speech segment nd its spectrogrm re shown using: (c)-(d) m-sequences, (e)-(f) Gold sequences, (g)-(h) Gold-like sequences, (i)-(j) Brker sequences, (k)-(l) Brker-like sequences, (m)-(n) smll set of Ksmi sequences, nd (o)-(p) lrge set of Ksmi sequences. 5
.5.5.5.5 5 5 2 25 3.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5.5.5.5 5 5 2 25 3.5 () () (c) (d) (e) (f) (g) (h) (i) (j) Fig. 3. Time domin nd its spectrogrm representtion for the sme 3 ms speech segment when encrypted with: ()-() orthogonl codes, (c)-(d) Wlsh Hdmrd codes, (e)-(f) modified Wlsh Hdmrd codes, (g)-(h) OVSF codes, nd (i)-(j) orthogonl Gold codes. 52