Integrity Control in Nested Certificates

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1 Ingriy onrol in Nsd s $OEHUW/HYLDQG08IXNdD OD\DQ %R D]LoL8QLYHUVLW\'HSDUWPHQWRI&RPSXWHU(QJLQHHULQJ Bbk, Isanbul 80815, Turky lvi@boun.du.r caglayan@boun.du.r Absrac Nsd crificas [3,4] ar proposd as crificas for ohr, subjc, crificas. Howvr, any malicious modificaion ovr h subjc crifica canno b locad by h vrificaion of i via a nsd crifica. This ingriy conrol problm can b solvd by mploying on way hash funcions. In his papr, wo ingriy conrol mhods for h subjc crifica vrificaion ar dscribd. Thir rlaiv advanags and disadvanags ar also discussd. 1. Inroducion A classical crifica [1,2] is usd o vrify h binding bwn h public ky and h idniy of h ownr of ha crifica. This vrificaion is don by h vrificaion of h digial signaur ovr h crifica conn. Th digial signaur issuanc and vrificaion ar carrid ou by mploying public ky cryposysm opraions. Anohr advanag of his digial signaur vrificaion is o chck h ingriy of h crifica conn. Th digial signaurs ar snsiiv o h informaion signd, which is h crifica conn. A h vrificaion phas, if h crifica conn changs, hn h signaur will no b vrifid and h alraion in h crifica conn will b dcd by h vrifir. Nsd crificas [3,4] ar usd o crify anohr crificas. Th crificas, which ar crifid by nsd crificas, ar calld as subjc crificas. Subjc crificas can b classical or ohr nsd crificas. In h original proposal for nsd crificas in [3], h acual signaur ovr h subjc crifica is conaind wihin h nsd crifica conn and his conn is signd by a Nsd Auhoriy (NA). A nsd crifica can b vrifid by h vrificaion of h signaur ovr is conn via crypographic opraions as in h classical crifica vrificaion. By his way, any alraion wihin h nsd crifica conn can b dcd in h vrificaion phas. On h ohr hand, nsd crificas ar usd o vrify hir subjc crificas also. Vrificaion of a crifica as h subjc crifica of a nsd crifica is calld as subjc crifica vrificaion. I is possibl o vrify boh classical and nsd crificas by using subjc crifica vrificaion mhod. In [3], subjc crifica vrificaion mhod is givn as h comparison of h subjc crifica signaur in h nsd crifica wih h acual signaur ovr h subjc crifica. If ha comparison yilds qualiy, hn h subjc crifica bcoms vrifid. By his comparison, h alraion in h signaur par of h subjc crifica can b asily dcd by h vrifir. Howvr, any modificaion in h subjc crifica conn canno b snsd by his comparison, sinc h signaurs ar sill h sam afr h alraion of h conn. This problm is calld as h ingriy problm in h subjc crifica vrificaion mhod Th sourc of his problm is h fac ha, in a nsd crifica, hr is no binding bwn h subjc crifica signaur and h acual conn of h subjc crifica.

2 Such an ingriy problm is valid for boh nsd crificas, for which h subjc crificas ar classical crificas, as wll as for h nsd crificas, for which h subjc crificas ar ohr nsd crificas. Morovr, h oucoms of h subjc crifica alraions dpnd on h subjc crifica yp. If h subjc crifica is a classical crifica, hn h alraion of i causs o vrify a wrong public ky idniy binding. On h ohr hand, if h subjc crifica is anohr nsd crifica, hn h alraion of i rsuls in vrificaion of a malicious crifica. Th ingriy problm can b solvd by using on way hash funcions [5,6,7], as will b xplaind in h Scion 2. Th gnralizaion of his soluion o h crifica pahs will b givn in h Scion 3. A brif discussion on h im and spac rquirmns of h ingriy conrol mhod can b found in h Scion 4. Morovr, a nw ingriy conrol mhod, in which boh ingriy conrol and vrificaion ar combind, will b dscribd in h Scion 4. A comparaiv advanag and disadvanag analysis of hos wo soluions will b givn also in h sam scion. Scion 5 summarizs h conclusions. 2. Soluion o h Ingriy Problm Th ingriy problm of h subjc crifica vrificaion mhod can b solvd by adding a binding bwn h subjc crifica signaur, which is sord in h nsd crifica, and h acual subjc crifica conn. Tha binding mus b includd in h crifir nsd crifica and mus saisfy h following wo rquirmns. 1. By using ha binding, h public ky of h A/NA of h subjc crifica and h subjc crifica signaur sord in h crifir nsd crifica, h NA for h nsd crifica mus b abl o prov ha h subjc crifica had bn issud by h corrsponding A/NA. 2. By knowing only ha binding and h acual subjc crifica conn, i mus b possibl for anyon o dc if h acual subjc crifica conn had bn maliciously modifid or no. Th firs rquirmn is usful whn h NA of h nsd crifica wans o prov o a hird pary ha i has signd h corrc binding bwn h subjc crifica conn and h signaur ovr h subjc crifica. Th scond rquirmn is for h vrifir, who dos no know h public ky of h A/NA of h subjc crifica, o chck h ingriy of h subjc crifica conn. Th rquird binding bwn h subjc crifica signaur, which is sord in h nsd crifica, and h acual subjc crifica conn can b h hash of h subjc crifica conn. This hash can b calculad by using on-way hash funcions [5]. Th on-way hash funcions ak an arbirary lngh mssag as paramrs and rurn fixd lngh uniqu fingrprins of hm. Th mos widly usd on-way hash funcions ar h MD5 [6] and h SHA-1 [7] sysms. Th hash of h subjc crifica conn mus b sord in h crifir nsd crifica conn oghr wih h subjc crifica signaur. Th rlaionships bwn a nsd crifica and is subjc crifica ar givn in Figur 1.

3 Nsd (rifir) Exising Subjc (o b rifid) r i f i c a o n n Ohr Filds Hash of Subjc onn Subjc Signaur on way hash funcion copy onn Signaur (issud by A/NA of h Subjc ) Signaur (issud by NA) Issuanc NA of h Nsd Figur 1 Th rlaionships bwn a nsd crifica and is subjc crifica Th hash soluion saisfis h rquirmn 1. Th acual signaur of h subjc crifica is, acually, h signaur ovr h hash of h subjc crifica conn and h sam hash is sord in h nsd crifica. Morovr, h signaur of h subjc crifica is conaind in h nsd crifica. Thrfor, anyon, who knows h public ky of h A/NA of h subjc crifica, can vrify h subjc crifica signaur by using h subjc crifica signaur and h hash of h subjc crifica conn filds of h nsd crifica. By his way, h NA of h nsd crifica provs ha i has signd a corrc binding. Th hash soluion also saisfis h rquirmn 2. Afr h vrificaion of a nsd crifica, h vrifir compus h hash of h subjc crifica conn. Thn, h vrifir compars i wih h xising hash in h nsd crifica. If boh hashs mach, hn h vrifir concluds ha h subjc crifica has no bn modifid. Th mismach of hm mans ha h subjc crifica conn has bn modifid afr h issuanc of h nsd crifica. In his soluion, h NA also signs h hash of h subjc crifica, bu his mus no b hough as h corrcnss guaran of h NA ovr subjc crifica conn. Th NA signs h hash of h subjc crifica conn only for ingriy conrol purposs, i dos no giv any guaran abou h corrcnss of h subjc crifica. Th NA only guarans h corrc binding bwn h subjc crifica and is signaur. Hr, our aim is only o dc any malicious modificaion ovr h subjc crificas of nsd crificas. Howvr, sinc h classical and h nsd crificas ar public daa and ar no assumd o b sord in saf placs, hr is no way of procing hm from malicious manipulaion. 3. Ingriy onrol in Pahs Th applicabiliy and h corrcnss of h prviously dscribd hash mhod as h soluion of h ingriy problm mus b discussd in rms of crifica pahs. In h crifica pahs, h nsd crificas ar usd o vrify a classical crifica as a chain. Such a chain is calld as a nsd crifica pah and conains a squnc of nsd crificas a h bginning and a classical crifica a h nd. Thr xampls of nsd crifica pahs ar givn in Figur 2. Thr may b on, as in h Figur 2c, or mor, as in h Figurs 2a and 2b, nsd crificas in h nsd crifica pahs.

4 Vrificaion of a classical crifica via a nsd crifica pah is a squnc of crifica vrificaions saring wih h firs crifica of h pah. Th firs nsd crifica of a nsd crifica pah mus b vrifid crypographically, using public ky cryposysm basd signaur vrificaion mhods. Ohr crificas, including h final classical crifica, ar vrifid as h subjc crificas of hir prdcssor nsd crificas. For xampl, h crificas 1 in Figur 2a, 2b, and 2c ar vrifid crypographically, bu h crificas 2, 3, 4, 5 and 6 in Figur 2a, h crificas 2, 3 and 4 in Figur 2b and h crifica 2 in Figur 2c ar vrifid as subjc crificas. In [3], h subjc crifica vrificaion mhod has bn xplaind by a simpl comparison of acual subjc crifica signaur wih h subjc crifica signaur fild of h prdcssor nsd crifica. As discussd a h bginning of his papr, his mhod canno assur ingriy of h subjc crifica. In h subsqun pars of his scion, h ingriy conrol issus for a nsd crifica pah will b discussd in dail. Th hash mchanism will b analysd as h soluion o h ingriy problm. This analysis will b givn in wo pars dpnding on h way of crifica vrificaion. a) ingriy conrol for h firs nsd crifica in a nsd crifica pah, b) ingriy conrol for h rmaining crificas of a nsd crifica pah. 3 D 4 F 3 D A B 2 E 5 6 G A B 2 4 E A B 2 (a) (b) (c) lassical Nsd Figur 2 Thr xampl nsd crificas pahs 3.1. Ingriy onrol for h Firs Nsd of a Nsd Pah Th vrifir firs ris o vrify h firs crifica of a nsd crifica pah (crifica 1 of Figur 2a, 2b or 2c using h public ky of h NA for crifica 1 (A in Figur 2). Any modificaion in h conn of crifica 1 can asily b dcd by h vrifir. Bcaus, h vrifir will ry o vrify h digial signaur ovr crifica 1 using public ky cryposysm basd opraions and ha signaur canno b vrifid if h crifica conn changs. Tha mans, i is no possibl o maliciously modify h conn of h firs nsd crifica of a nsd crifica sris wihou vrifir dcion Ingriy onrol for h Rmaining s of a Nsd Pah Th firs crifica of a nsd crifica pah is vrifid by public ky cryposysm basd signaur vrificaion. Th ingriy problm and h soluion for his cas hav bn discussd in h prvious subscion. Ohr crificas in h pah ar vrifid as subjc crificas. According o h original subjc crifica vrificaion schm dscribd in [3], a subjc crifica, say crifica n, is vrifid by comparing h acual signaur in crifica n wih h subjc crifica signaur in is prdcssor nsd crifica,

5 crifica n-1, in h pah. By his way, any malicious modificaion ovr h signaur par of a subjc crifica can b dcd. Howvr, h malicious modifir may modify only h conn, no h signaur, of h crifica n. Th vrifir will no b abl o dc his modificaion by only signaur comparison bwn h modifid crifica n and crifica n-1, bcaus h signaur of h modifid crifica n is sill h sam as h subjc crifica signaur fild of crifica n-1. For xampl, suppos ha h malicious modifir modifis h conn of h crifica 4 in Figur 2a. Th vrifir will no b abl o dc his modificaion by comparing h subjc crifica signaur fild of crifica 3 and h acual signaur ovr crifica 4. Bcaus, alhough h conn of h crifica 4 has bn modifid, is signaur is sill h sam as h original on. Th hash basd soluion o h ingriy problm, which is xplaind in h Scion 2 for a singl subjc crifica vrificaion, can b auomaically xndd o nsd crifica pahs. In his soluion, h hash of ach subjc crifica conn is sord in is prdcssor nsd crifica in h pah. Th ingriy conrol par of h nsd crifica pah vrificaion algorihm is oulind blow. {rypographic vrificaion rouins for h firs nsd crifica of h nsd crifica pah com hr} succss := TRUE; FOR i:=h firs subjc crifica TO h las subjc crifica of h nsd crifica pah DO {subjc crifica vrificaion rouin for crifica i coms hr} {Ingriy conrol for h crifica i follows} compu h hash of h acual crifica i conn; compar i wih h xising subjc crifica hash wihin is prdcssor nsd crifica (crifica i-1 ); if hy mach hn rmark h conn of h crifica i has no bn modifid ls {if hy do no mach} rmark h conn of crifica i has bn maliciously modifid ; succss := FALSE; {nd of ingriy conrol} if succss hn rurn h nsd crifica pah has bn vrifid succssfully ls rurn h nsd crifica pah is invalid Now, w will analys h corrcnss of h ingriy conrol mchanism. Suppos h malicious inrudr has modifid a crifica, crifica n, of h nsd crifica pah. In ordr o mask his modificaion ovr h conn of h crifica n, h malicious modifir rplacs h hash of h crifica n conn wih h hash of h modifid crifica n conn in h crifica n-1. This is, acually, a modificaion ovr h crifica n-1 conn. Th vrifir is no b abl o dc his modificaion by comparing h compud hash wih h xising hash, sinc hy ar maliciously qual. Forunaly, ha modificaion was b abl o b dcd whn h crifica n-1 was bing conrolld for ingriy as h subjc crifica of is prdcssor, crifica n-2. Bcaus, h hash of h original crifica n-1 conn is conaind in crifica n-2. Morovr, sinc h compud hash of h modifid crifica n-1 conn will no mach h corrc hash of h crifica n-1 conn, which is in h crifica n-

6 2, h vrifir will b abl o dc h modificaion ovr h conn of h crifica n-1. Thrfor, in ordr o cha h vrifir, h malicious modifir mus rplac h hash valu in ach nsd crifica wih h hash valu of h conn of is modifid subjc crifica up o and including h firs nsd crifica of h pah backwards. Sinc any modificaion in h firs crifica of a nsd crifica pah can b dcd, as dscribd in h prvious subscion, h vrifir can asily dc h malicious modificaion in h pah. Tha mans, by adding h hashs of h subjc crifica conns ino hir prdcssors, h vrifir bcoms capabl of dcing any malicious modificaion in a nsd crifica pah. For xampl, suppos h malicious modifir has changd h conn of crifica 4 in Figur 2b. Th vrifir will b abl o dc his modificaion, sinc h hash of h crifica 4 conn, which is sord wihin h crifica 3, dos no mach h compud hash of modifid crifica 4 conn. In ordr o mask his modificaion, h modifir rplacs h hash of crifica 4 conn, which is sord wihin crifica 3, wih h hash of h modifid crifica 4 conn. Howvr, h vrifir was b abl o dc his modificaion ovr h crifica 3 conn whil sh was chcking h ingriy of i by comparing h hash of h crifica 3 conn, which is in h crifica 2, wih h compud hash of h modifid crifica 3 conn. Thrfor, in ordr o cha h vrifir furhr, h malicious modifir rplacs h hash of crifica 3 conn, which is sord wihin crifica 2, by h hash of h modifid crifica 3 conn. Again, h vrifir was b abl o dc his modificaion ovr h crifica 2 conn whil sh was chcking h ingriy of i by comparing h hash of crifica 2 conn, which is in h crifica 1, wih h compud hash of h modifid crifica 2 conn. Th las hing ha h malicious modifir can do is o rplac h hash of h crifica 2 conn, which is sord in crifica 1, wih h hash of h modifid crifica 2 conn. Howvr, sinc h crifica 1 is h firs crifica of h pah, h vrifir was b abl o dc any modificaion in h crifica 1 by crypographic signaur vrificaion. As can b sn from his xampl, h vrifir is abl dc any malicious modificaion in a nsd crifica pah. 4. Discussion In his scion, h im and spac rquirmns and implmnaion issus of ingriy conrol via hash addiion mchanism will b discussd. Morovr, a nw schm, which combins h ingriy conrol wih h subjc crifica vrificaion, will b givn hr also Tim and Spac Rquirmns for Ingriy onrol Th discussion on h im and spac rquirmns for ingriy conrol will b daild for nsd crifica issuanc and subjc crifica vrificaion sparaly Issuanc In ordr o chck h ingriy of a subjc crifica in a nsd crifica pah, is hash mus b nclosd in is prdcssor crifica in h pah a h issuanc im of h prdcssor. This opraion rquirs only a hash compuaion for h subjc crifica conn. Indd, his hash compuaion dos no caus an xra prformanc ovrhad. Bcaus, h NA mus vrify h signaur ovr h subjc crifica bfor issuing a nsd crifica for i and for his signaur vrificaion, h NA mus compu h hash of h subjc crifica. Thrfor, h NA dos no nd o rcompu h sam hash again for h nsd crifica issuanc. Whavr h siz of inpu daa is, h on way hash funcions produc fixd siz hashs. Th MD5 [6] hash mhod producs 128 bis hashs. Th SHA-1 [7] hash mhod producs 160

7 bis hashs. Thrfor, h spac rquirmn o sor h hash of h subjc crifica conn in a nsd crifica is 128 bis for MD5 hash mhod, 160 bis for h SHA-1 hash mhod Vrificaion In ordr o chck h ingriy of a subjc crifica, h vrifir compus h hash of ha subjc crifica conn and compars i wih h hash, which is sord wihin h prdcssor nsd crifica. Thrfor, h im rquirmn o chck h ingriy of a subjc crifica in a nsd crifica pah is jus a hash compuaion and a comparison. A hash mhod is a squnc of prmuaion and subsiuion basd block opraions ovr an inpu sram. Thrfor, h im rquird for a hash compuaion is significanly lss hn public ky ncrypion and dcrypion. Thrfor, h subjc crifica vrificaion mhod, including ingriy conrol, is mor fficin han h crypographic crifica vrificaion as discussd in [11] and [12]. Th prformanc valuaion in [11] is analyic, whras h discussion in [12] is basd on simulaion rsuls. Morovr, h fficincy of h hash mhods is xamind in [8, 9, 10] A Nw Schm Hash and Signaur ombinaion Insad of h subjc crifica signaur and h hash of h subjc crifica conn, h hash of h whol subjc crifica (conn + signaur) can b pu in h crifir, i.. prdcssor, nsd crifica. By signing ha hash, h NA signs h hash of boh h subjc crifica conn, which is o b usd for ingriy conrol, and h subjc crifica signaur, which is o b usd for vrificaion. Th vrifir vrifis h subjc crifica and chcks for h ingriy by only comparing h compud hash of h whol subjc crifica wih h hash xising in h crifir nsd crifica. Bcaus, any malicious modificaion ovr h subjc crifica conn or is signaur dircly changs h hash ovr h whol crifica and ha modificaion can b dcd by h vrifir. Th rlaionship bwn h nsd crifica and is subjc crifica in his nw schm is shown in Figur 3. In his nw schm his signaur comparison can b combind wih h ingriy conrol by h following algorihm. {rypographic vrificaion rouins for h firs nsd crifica of h nsd crifica pah com hr} succss := TRUE; FOR i:=h firs subjc crifica TO h las subjc crifica of h nsd crifica pah DO {vrificaion and ingriy conrol for crifica i } compu h hash of h whol acual crifica i (signaur + conn); compar i wih h xising hash wihin is prdcssor nsd crifica (crifica i-1 ); if hy mach hn rmark crifica i has bn vrifid and h conn of crifica i has no bn modifid ls {if hy do no mach} rmark h conn or h signaur of crifica i has bn maliciously modifid succss := FALSE; {nd of vrificaion and ingriy conrol} if succss hn rurn h nsd crifica pah has bn vrifid succssfully ls rurn h nsd crifica pah is invalid

8 Nsd (rifir) Exising Subjc (o b rifid) r i f i c a o n n Ohr Filds Hash of Subjc onn Signaur (issud by NA) on way hash funcion onn Signaur (issud by A/NA of h Subjc ) Issuanc NA of h Nsd Figur 3 Th rlaionship bwn a nsd crifica and is subjc crifica in h nw schm whr h hash and signaur combind Alhough his nw schm savs crifica spac, i dgrads h prformanc of nsd crifica issuanc and dgrads h prformanc of h vrificaion and h ingriy conrol of subjc crifica vrificaion. Morovr, i has som disconformiis o h rquirmns. Thos advanag and disadvanags will b daild blow Improvmn in spac rquirmns Sinc h siz of a hash is indpndn of is inpu, h nw hash in his schm has h sam siz wih h on in h original schm. Morovr, sinc h subjc crifica signaur is mbddd in his nw hash, h spac rquird o sav h subjc crifica signaur bcoms a spac saving in his nw schm Dgradaion in im rquirmns for vrificaion and ingriy conrol As can b sn from h abov algorihm, using a singl hash compuaion and comparison, boh h subjc crifica vrificaion and ingriy conrol can b prformd. As compard o h original schm, in h nw schm h duraion o compar h signaurs for vrificaion bcoms a im saving. Howvr, his improvmn is minimal, sinc his comparison dos no ak oo much im as compard o hash compuaion. Morovr, in h nw schm, h inpu of h hash compuaion is longr han h original schm. Bcaus, h hash of h whol subjc crifica (conn + signaur) will b compud. Th diffrnc is h signaur par of h subjc crifica. This xra cos of hash compuaion is grar han h gain from h signaur comparison. Thrfor, i can b said ha, h nw schm dgrads h prformanc of h vrificaion and ingriy conrol, as compard o h original schm Prformanc dgradaion in nsd crifica issuanc As dscribd in h Scion 4.1.1, h hash compuaion for h subjc crifica conn is no an xra ovrhad for h original schm. Howvr, in his nw schm, h compuaion of h hash of h whol subjc crifica is an xra ovrhad. Bcaus, h issur for h nsd crifica has no compud h hash of h whol subjc crifica bforhand and sh has o compu i a h issuanc im.

9 Disconformiis o rquirmns In h original schm, in cas of a malicious modificaion ovr h subjc crifica, i is possibl o dc whhr h modifid par is h conn or h signaur, bcaus h informaion usd and h procdurs for vrificaion and ingriy conrol ar diffrn. Howvr in h nw schm, sinc h subjc crifica conn and h signaur ar mrgd ino a singl hash, i is no possibl o dc h modifid par. Alhough h oucom of boh modificaions rsuls in rjcion of h subjc crifica for h im bing, i is rasonabl o diffrnia bwn hm for fuur rquirmns. Mor imporanly, in h nw schm, hr is no binding in h nsd crifica bwn h subjc crifica conn and is signaur. On can argu ha h hash ovr h whol subjc crifica (conn + signaur) is a binding. Howvr, sinc ha hash canno b vrifid using h public ky of A/ NA of h subjc crifica, i canno b considrd as h rquird binding bwn h conn and h signaur as xplaind in h rquirmn 1 of h Scion 2. Thrfor, h nw schm causs a disconformiy o h iniial rquirmns Th rasons o insis on h original schm A h firs glanc, h nw schm, in which h hash and h signaur combind, sms o b accpabl and mor fficin han h original schm. Howvr, h daild xaminaion on is advanag and disadvanags has shown ha i is no mor im fficin. Th only advanag of h nw schm is h lss spac rquirmn, bu an xra hash calculaion is ncssary a h issuanc im. Morovr, h prformanc of vrificaion procss is wors in h nw schm. Furhrmor, h binding in h nw schm is no h rquird on. Thrfor, h original hash soluion schm is mor rasonabl o us X.509 Rcommndaion and Hashs On way hash funcion is no a nw concp for h ITU X.509 Rcommndaion [1]. On way hash funcions ar usd in h issuanc and vrificaion of digial signaurs for X.509 crificas, bu hy ar no sord in h crificas. In a nsd crifica, h hash of is subjc crifica conn mus b sord oghr wih h subjc crifica signaur. Th adapaion issus of nsd crificas ino X.509 hav bn discussd in [4]. Th subjc crifica signaur can b sord as a bi sring in a nsd crifica. Th hash of h subjc crifica conn can b appndd o h subjc crifica signaur as a bi sring also. By his way, h nsd crificas wih ingriy conrol can b adapd o X onclusions If h conn of h subjc crifica of a nsd crifica is modifid maliciously, hr was no mchanism o dc i. This is calld h ingriy conrol problm in nsd and subjc crificas. In his papr, a soluion, which is basd on on way hash funcions, o h ingriy problm has bn proposd. Morovr, his soluion has bn daild wih algorihms for nsd crifica pah vrificaion. This soluion rquirs h hash o b sord in h nsd crificas, which is 128 or 160 bis dpnding on h hash algorihm usd. Thrfor, i can b said ha his soluion is no spac complx. Morovr, hr is no xra ovrhad for h im rquird for h nsd crifica issuanc for ingriy conrol. In h vrificaion im, h hash of h subjc crifica mus b rcalculad for h ingriy conrol. Howvr, h im rquird for his hash calculaion is qui small as compard o public ky cryposysm basd signaur vrificaion opraions.

10 Furhrmor, anohr soluion o h ingriy problm, which is also basd on on way hash funcions, has bn givn in his papr also. This soluion combins h subjc crifica signaur and h hash of h subjc crifica conn ino a singl hash. Alhough his ida sms promising, a closr look ino his nw schm has shown ha h im rquirmns for boh issuanc and vrificaion ar wors han h original hash schm. Th only advanag of his nw schm is h saving h spac rquird for h subjc crifica signaur in h nsd crificas. Morovr, his nw schm dos no m h rquirmns from h soluion of h ingriy conrol problm. Thrfor, i has bn concludd h original soluion is prfrabl. Acknowldgmns This work has bn suppord by TUBITAK undr gran EEEAG-237 and by Turkish Sa Planning Organizaion (DPT) undr gran 96K Rfrncs [1] ITU-T Rcommndaion X.509, ISO/IE , Informaion Tchnology - Opn Sysms Inrconncion - Th Dircory: Auhnicaion Framwork, 1997 Ediion. [2] P. Zimmrmann, PGP Usr's Guid Volum I: Essnial Topics, availabl wih fr PGP sofwar from hp:// [3] $/HYL08dD OD\DQ$0XOWLSOH6LJQDWXUH%DVHG&HUWLILFDWH9HULILFDWLRQ6FKHPHLQ h procdings of BAS 98, Th Third Symposium on ompur Nworks, Jun ø]plu7 UNL\HSS± [4] $/HYLDQG08dD OD\DQ1HVWHG&HUWLILFDWHVDQG7KHLU$SSOLFDWLRQVLQ3XEOLF.H\,QIUDVWUXFWXUHV7HFKQLFDO5HSRUW)%(&PS(%R D]LoL8QLYHUVLW\ [5] harli Kaufman, Radia Prlman, Mik Spcinr, Nwork Scuriy PRIVATE ommunicaion in a PUBLI World, hapr 4, pp , Prnic Hall, Nw Jrsy, 1995 [6] R. Rivs, Th MD5 Mssag Digs Algorihm, RF 1321, April 1992 [7] Naional Insiu of Sandards and Tchnology (NIST), Fdral Informaion Procssing Sandard (FIPS) PUB 180 1, Scur Hash Sandard, U.S. Dparmn of ommrc, Washingon, 17 April 1995, availabl a hp:// or hp://csrc.nis.gov/fips/fip180-1.pdf [8] A. Bosslars, R. Govars and J. Vandwall, Fas Hashing on h Pnium, Advancs in rypology, Procdings of rypo 96, LNS 1109, N. Kobliz Ed., pp , Springr-Vrlag, 1996 [9] A. Bosslars, Evn Fasr Hashing on h Pnium, Prsnd in h rump sssion of Eurocryp 97, Kosanz, Grmany, May 11 15, 1997, availabl from fp://fp.sa.kuluvn.ac.b/osi/bossla/pniumplus.ps.gz [10] J. D. Touch, Prformanc Analysis of MD5, Procding of h AM SIGOMM 95, ompur ommunicaion Prviw, vol. 25, no. 4, Ocobr 1995 [11] $/HYLDQG08dD OD\DQ$QDO\WLFDO3HUIRUPDQFH(YDOXDWLRQRI1HVWHG&HUWLILFDWHV Submid o IFIP WG 7.3 Prformanc 99 onfrnc, [12] $/HYL08dD OD\DQ9HULILFDWLRQRID&ODVVLFDO&HUWLILFDWHVYLD1HVWHG&HUWLILFDWHV and Nsd Pahs, Submid o AM SIGOMM 99 onfrnc, 1999

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