International Journal of Advanced Research in Computer Science and Software Engineering

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1 Volu, Iu 0, Ocobr 0 ISSN: 77 8X Inrnaional Journal of Avanc Rarch in Copur Scinc an Sofwar Enginring Rarch Papr Availabl onlin a: wwwijarcco A Nw Varian of RSA Digial Signaur Ahih Vijay * Priyanka Trikha Kapil Mahur MTch un Ain Profor MTch un Copur Enginring Copur Enginring Copur Enginring SBCET, Jaipur SBCET, Jaipur SBCET, Jaipur ABSTRACT-Gnrally, igial ignaur algorih ar ba on a ingl har probl lik pri facorizaion probl or icr logarih probl or llipic curv probl If on fin oluion of hi ingl har probl hn h igial ignaur algorih will no longr b cur an u o larg copuaional powr, hi ay b poibl in fuur Th RSA igial ignaur algorih (RSADSA i an ayric crypographic chniqu, who curiy i rla o h ifficuly of facorizaion Bu if on woul olv h facorizaion probl hn h woul g h priva ky oo RSADSA i no only vulnrabl o h pri facorizaion aack bu alo o h all priva ponn an all public ponn aack So o iprov curiy, hi papr prn a nw varian of igial ignaur algorih which i ba on wo har probl, pri facorizaion an h roo probl Th propo algorih i a oificaion of h RSA igial ignaur algorih KEYWORDS: h roo; RSA; Facorizaion; Digial Signaur; Crypanalyi I INTRODUCTION A igial ignaur algorih i ahaical ch which provi auhniciy of a igial ag an aur h rcipin ha h ag wa cra by an auhoriz nr an wa no oifi in rani RSA Digial Signaur Algorih (RSADSA [6] propo by Riv, Shair an Alan, i a popular an wll known igial ignaur algorih Th RSA ignaur algorih i unforgivabl in h rano oracl ol auing h ingr facorizaion probl i unolvabl Thi ch i ba o h RSA public ky crypoy [6] Howvr if, in nar fuur, on can olv h ingr facorizaion probl, hn h can alo forg h ignaur cra by hi ch In hi papr, a nw varian of igial ignaur algorih i propo, call Enhanc RSA Digial Signaur Algorih (ERSADSA, which i ba on h cobin ifficuli of ingr facorizaion probl an h roo probl Th propo algorih i acually a oificaion of RSADSA algorih In pa, any ffor hav bn on for vloping ulipl har probl ba igial ignaur algorih In orn crypography [7], h curiy of igial ignaur algorih i ba on h ifficuly of olving o har nubr horical probl Th algorih ay cur a long a h probl, on which h algorih i ba, ay unolvabl Th o u har probl for igning a ignaur algorih ar pri facorizaion (FAC [6] an Dicr Logarih (DL [8] probl For iproving h curiy, h algorih ay b ign ba on ulipl har probl Unoubly, h curiy of uch algorih i longr han algorih ba on a ingl probl Thi i u o h n of olving boh h probl iulanouly Many igial ignaur algorih hav bn ign ba on boh FAC an DL [9,,,, 7, 9, 5, 7, 9, 0] bu o ign uch algorih i no an ay ak inc any of h hav bn hown o b incur [0, 8, 9, 0,, 8, 9, 0] R of h papr i organiz a follow Scion crib brif ovrviw of RSA igial ignaur algorih Scion conain h propo algorih In Scion, analyi i carri ou for h propo algorih Finally, in Scion 5, papr i conclu II BRIEF OVERVIEW OF RSA DIGITAL SIGNATURE ALGORITHM RSADSA i an ayric igial ignaur algorih a i u a pair of ky, on of which i u o ign h aa in uch a way ha i can only b vrifi wih h ohr ky RSADSA i ba on on way rap-oor funcion In ca of RSADSA, h ia i ha i i rlaivly ay o uliply pri nubr bu uch or ifficul o facor Muliplicaion can b copu in polynoial i whr a facoring i can grow ponnially proporional o h iz of h nubr Th algorih i a follow: A Ky Gnraion: Following ar h ky gnraion p: - Gnra wo larg rano pri, p an q - Copu n p q an ( p ( q - Choo an ingr, aifying, uch ha gc (, 0, IJARCSSE All Righ Rrv Pag 66

2 Ahih al, Inrnaional Journal of Avanc Rarch in Copur Scinc an Sofwar Enginring (0, Ocobr- 0, pp Copu h cr ponn, aifying < <, uch ha o = - Th public ky i an h priva ky i By uing h ky, ignaur gnraion an ignaur vrificaion ar prfor B Signaur Gnraion: Following ar h ignaur gnraion p: - Cra a ag ig H ( a an ingr of h inforaion o b n bwn 0 an n - Copu h ignaur by uing h priva ky a H( - i h ignaur of h ag Sn wih h ag o rcipin C Signaur Vrificaion: Signaur vrificaion p ar a follow: - By uing nr public ky, copu ingr v v b h ag ig calcula by nr -Inpnnly copu h ag ig of h ag ha ha bn ign - If boh ag ig ar inical, h ignaur i vali Scuriy of RSADSA algorih i ba on ifficuly of olving h pri facorizaion probl Thr ar any ffor hav bn on in pa o olv h pri facorizaion probl [,,, ] In 00, Wgr [6] crib a nw aack for olving pri facorizaion probl a if hr i all iffrnc bwn h pri facor of oulu hn a polynoial i crypanalyi for facoring oulu i poibl In 00, Bonh an Bruly [] onra a or pracical aack capabl of rcovring RSA facorizaion ovr a nwork conncion Thi aack ak avanag of inforaion lak by h Chin rainr hor opiizaion u by any RSA iplnaion RSADSA i no only vulnrabl o h pri facorizaion aack bu alo o h priva ky Paul Kochr[6] crib ha if an Avrary Ev know Alic harwar in ufficin ail an i abl o aur h crypion i for vral known ciphr, h can uc h crypion ky quickly N, hr ar any hra if h RSA priva ponn i chon all Th fir ignifican aack on all priva ponn RSA wa Winr coninu fracion aack [] Givn only h public ky (, n, h aack facor h oulu uing inforaion obain fro on of h convrgn in h coninu fracion panion of /n I wa hown by Copprih [], ha an RSA oulu wih balanc pri coul b facor givn only / of h o ignifican bi of on of h pri I wa lar hown by Bonh, Durf an Frankl [] ha / of h la ignifican bi of on of h pri wa alo ufficin A horical harwar vic na TWIRL ign by Shair an Tror in 00 [5], quion h curiy of 0 bi ky Now ay u o h availabiliy of high n rourc of copuaion h chanc of h variou yp of aack hav incra I i qui poibl ha an organizaion wih ufficinly p pock can buil a larg cal vrion of hi circui an ffcivly crack an RSA 0 bi ag in a rlaivly hor prio of i In arch of h igial ignaur algorih ha ar vulnrabl o abov nion aack, ubqun cion conain a nw varian of igial ignaur algorih III THE PROPOSED SIGNATURE ALGORITHM Thi cion propo a nw varian of igial ignaur algorih ba on h wo NP-Copl probl na pri facorizaion an h roo Th algorih i a follow: A Ky Gnraion: Following ar h ky gnraion p: - Choo wo larg pri nubr p an q an calcula - Calcula ( n ( p ( q - Calcula uch ha o ( n n p q an Choo uch ha gc - Choo rano nubr b an Hr houl no rlaiv pri o b c(o n - Calcula c uch ha - public ky i (n,, c, an priva ky i (, b B Signaur Gnraion: Following ar h ignaur gnraion p: H( - Calcula - if (i i a ivior of hn gnra again ( H( b (, ( n (n - Calcula- H ( i a on way hah funcion (, i h ignaur of ag Snr n ignaur wih h ag o rcivr 0, IJARCSSE All Righ Rrv Pag 67

3 Ahih al, Inrnaional Journal of Avanc Rarch in Copur Scinc an Sofwar Enginring (0, Ocobr- 0, pp 66-7 C Signaur Vrificaion: Rcivr fir calcula H ( uing h rciv ag an chck h following wo coniion for ignaur vrificaion: Vrify, if an H( H( c ( hn h ignaur i vali l rjc h ignaur D Proof of corrcn Thi cion conain h corrcn proof of h propo igial ignaur algorih Fir coniion (quaion No i a vrificaion of RSA algorih an proof of con coniion (quaion No i a follow RHS ( c ( H ( b H ( H ( L H S b c c IV ANALYSIS OF THE PROPOSED ALGORITHM Thi cion conain analyi of h propo algorih in r of curiy an prforanc A Scuriy Analyi Thr ar o poibl ara whr an avrary (Av can ry o aack on hi nwly vlop ignaur algorih Following ar h poibl aack (no hauiv: Ky-Only Aack: Av wih o obain priva ky (b, uing all inforaion ha i availabl fro h y For, Av n o olv h pri facorizaion probl o fin p an q fro oulu n which will provi Av h valu of / n for fining b, Av ha o olv b c which i NP-Copl for larg b bcau Av ha o fin h roo of c L u call hi probl h roo probl h roo probl iffr fro h facorizaion probl of RSA A in RSA, if pri facor of n ar known hn wih h hlp of public ky, h roo of ag (whr i a priva ky coul b rin Bu in h h roo probl, i no rlaiv pri o o ( n (n (, o i uliplicaiv invr wih rpc o o no i Thrfor an Av ha o olv h roo probl an a FAC probl iulanouly for fining h copl priva ky Thi fac ak h propo algorih cur nough for hi yp of aack Known Parial Ky Aack: L u au ha Av can olv h FAC In hi ca, o forg h ignaur, Av ha o olv h roo probl which will provi hi h valu of b Now if Av can olv h roo bu no FAC probl hn o forg h ignaur, Av rquir valu of an for ha h ha o olv facorizaion probl Hnc, h Av canno ign i own ag uing nr ignaur vn if h know h par of h cr ky by braking h FAC or h roo probl H ha o olv boh h probl iulanouly Blining: In hi aack, in ca of RSADSA uppo Av wan nr ignaur on hi ag For hi Av ry h following: h pick a rano * r Z n an calcula r o n H hn ak nr o ign h ag ( Snr ay provi hi ignaur on h ag Bu w know ha Av now copu / r an obain nr ignaur on h original Thi chniqu, call blining, nabl Av o obain a vali ignaur on a ag of hi choic by aking Snr o ign a rano blin ag Snr ha no inforaion a o wha ag h i acually igning So, RSA i vulnrabl o hi aack Unlik RSA, ERSADSA i no vulnrabl o Blining an i i plain a follow: By uing a rano nubr r, Av g Snr ignaur (, ( r r r b for hi ag, whr an Av / r now g h ignaur (, for ag by copuing / an r Bu i rla o, o ignaur will no b quivaln o h original ignaur of ag For fining, Av ha o calcula valu of b h ( an for ha h ha o olv roo probl a follow: 0, IJARCSSE All Righ Rrv Pag 68

4 b Ahih al, Inrnaional Journal of Avanc Rarch in Copur Scinc an Sofwar Enginring (0, Ocobr- 0, pp 66-7 r b ( r r b Hnc ERSADSA i cur again hi aack Chon-Mag Aack: In hi aack, Av rquir o g ign o ag of hi choic by h auhoriz ignaory Wih h hlp of chon ag an corrponing ignaur, Av gnra anohr ag an can forg nr ignaur on i Th RSADSA algorih i forgabl for hi aack For aack on RSADSA, uppo, Av ak ignr o ign wo lgiia ag an for hi L u au an ar ignaur of an rpcivly Av lar cra a nw ag = wih ignaur Av can hn clai ha ignr ha ign ERSADSA i alo vulnrabl o hi yp of aack Suppo (, an (, ar igial ignaur of ag an rpcivly Thn Av can gnra ignaur for hi ag = For hi Av gnra ignaur (, of ag a follow ( Th ignaur (, for o obain i acually a vali ignaur of Snr, bcau: ( ( ( b b ( b b b ( b b Hnc, ERSADSA i no cur again chon ag aack B Prforanc Analyi Uing h cririon prn in [], h copliy of ach ho i ia a a funcion of nubr of bi opraion rquir Th baic ponnial opraion hr i O(log b M( n M (n a b an i copliy of hi opraion i, whr h copliy of uliplying wo n bi ingr In h propo algorih ignaur gnraion rquir oular ponniaion an ignaur vrificaion rquir oular ponniaion which la o h copliy of h algorih o b vrificaion rpcivly a hr b O(n O( log 0, IJARCSSE All Righ Rrv Pag 69 n an O( log n for ignaur gnraion an an i copliy of uliplying wo n bi ingr i O(log n O(log n Thrfor h ovrall copliy for ignaur gnraion an vrificaion i if h copliy of propo DSA i copar wih ohr DSA algorih of a cagory (i DSA algorih ha ar ba on ulipl har probl hn w ha h Diirio Poulaki ignaur algorih [5] rquir 6oular ponniaion in ignaur gnraion an oular ponniaion in ignaur vrificaion Iail E S ignaur algorih [] rquir 5oular ponniaion in ignaur gnraion an 5oular ponniaion in ignaur vrificaion ShiinWi ignaur algorih [0] rquir 5 oular ponniaion in ignaur gnraion an oular ponniaion in ignaur vrificaion So i i clar ha h copliy of h propo algorih i quivaln o o of h igial ignaur algorih which ar ba on pri facorizaion an icr logarih an ha i O(log n

5 Ahih al, Inrnaional Journal of Avanc Rarch in Copur Scinc an Sofwar Enginring (0, Ocobr- 0, pp 66-7 A a fuur rarch prpciv, h propo algorih can b iprov for following raon: Thr ar any organizaion whr ignaur gnraion ari frqunly han ignaur vrificaion a a ingl aion lik bank c For apl, a Bank can gnra any igial ignaur in a ay (in cah vouchr, rcip, whil h bank cuor ha rciv hi ignaur, ha uually a uch allr loa So, h prforanc of ignaur gnraion proc of hi algorih can b iprov by uing M-Pri RSA [, 5], in plac of RSA, wih h roo probl V CONCLUSION In hi papr, a nw varian of igial ignaur algorih i propo which i ba on h wo har probl call pri facorizaion an h roo I i hown ha h nw algorih i cur nough again variou aack an on hav o olv boh h probl for crypanalyi of h propo algorih Howvr, h propo algorih i no cur again Chon-ag aack lik RSADSA Th prforanc of h propo algorih i coparaivly quivaln o h o of h igial ignaur algorih which ar ba on ulipl har probl REFERENCES [] C Alion an CAM Paiao An fficin varian of h RSA crypoy 00 [] D Bonh an D Bruly Ro iing aack ar pracicalprocing ofh USENIX Scuriy Sypoiu, 00 [] D Bonh, G Durf, an Y Frankl Epoing an RSA priva ky givn a allfracion of i bi Full vrion of h work fro Aiacryp, 98, 998 [] D Bonh an H Shacha Fa varian of RSA CrypoBy (RSA Laboraori, 5:-9, 00 [5] T Collin, D Hopkin, S Langfor, an M Sabin Public ky crypographic apparau an ho Ocobr US Pan RE0,50 [6] B D Wgr Crypanalyi of RSA wih all pri iffrnc Applicabl Algbra in Enginring, Counicaion an Copuing, (:7-8, 00 [7] W Diffi an M Hllan Nw ircion in crypography Inforaion Thory, IEEE Tranacion on, (6:6-65, 00 [8] T ElGaal A public ky crypoy an a ignaur ch ba on icr logarih Inforaion Thory, IEEE Tranacion on, (:69-7, 00 [9] L Harn Public-ky crypoy ign ba on facoring an icr logarih In IEE Proc-Copul Digi Tch, volu, pag 9-95 IET, 99 [0] L Harn Con: Enhancing h curiy of El Gaal ignaur ch IEE Procing- Copur an Digial Tchniqu, :76, 995 [] J H an T Kilr Enhancing h curiy of El Gaal ignaur ch In Copur an Digial Tchniqu, IEE Procing-, volu, pag 9-5 IET, 99 [] W H H Digial ignaur ch ba on facoring an icr logarihelcronic Lr, 7(:0-, 00 [] MJ Hink Crypanalyi of RSA an i varian Chapan & Hall/CRC, 009 [] ES Iail, NMF Taha, an RR Aha A Nw Digial Signaur Sch Ba on Facoring an Dicr Logarih Journal of Mahaic an Saiic, (:-5, 008 [5] BKalikiTWIRL an RSA Ky Sizhp://wwwraco/ralab/noap?i=00, 00, Acc on Nov 00 [6] P Kochr Tiing aack on iplnaion of Diffi-Hllan, RSA, DSS, an ohr yin Avanc in CrypologyCRYPTO96, pag0- Springr, 996 [7] CS Laih an WC Kuo Nw ignaur ch ba on facoring an icr logarih IEICE TRANSACTIONS on Funanal of Elcronic, Counicaion an Copur Scinc, 80(:6-5, 997 [8] NY L Scuriy of Shao ignaur ch ba on facoring an icr logarih In Copur an Digial Tchniqu, IEE Procing-, volu 6, pag 9- IET, 00 [9] NY L an T Hwang Moifi Harn ignaur ch ba on facorizing an icr logarih In Copur an Digial Tchniqu, IEEE Procing, volu, pag96-98iet, 00 [0] NY L an T Hwang Th curiy of H an Kilr ignaur ch In Copur an Digial Tchniqu, IEE Procing-, volu, pag 70-7 IET, 00 [] J Li an G Xiao Rark on nw ignaur ch ba on wo har problelcronic Lr, (5:0, 00 [] PL Mongory A urvy of orn ingr facorizaion algorih CWIquarrly, 7(:7-65, 99 [] MA Morrion an J Brillhar A Mho of Facoring an h Facorizaion off 7 Mahaic of Copuaion, 9(9:8-05, 975 [] C Poranc A al of wo iv Bicui of Nubr Thory, pag 85, 008 [5] D Poulaki A varian of Digial Signaur Algorih Dign, Co an Crypography, 5(:99-0, 009 [6] RL Riv, A Shair, an L Alan A ho for obaining igial ignauran public-ky crypoy Counicaion of h ACM, (:0-6, 978 0, IJARCSSE All Righ Rrv Pag 70

6 Ahih al, Inrnaional Journal of Avanc Rarch in Copur Scinc an Sofwar Enginring (0, Ocobr- 0, pp 66-7 [7] Z Shao Signaur ch ba on facoring an icr logarih In Copur an Digial Tchniqu, IEE Procing-, volu 5, pag - 6 IET, 00 [8] Z Shao Scuriy of a nw igial ignaur ch ba on facoring an icrlogarih Inrnaional Journal of Copur Mahaic, 8(0:5-9,005 [9] SF Tzng, CY Yang, an MS Hwang A nw igial ignaur ch ba on facoring an icr logarih Inrnaional Journal of Copur Mahaic, 8(:9-, 00 [0] S Wi A Nw Digial Signaur Sch Ba on Facoring an Dicr Logarih Progr on Crypography, pag 07-, 00 [] MJ Winr Crypanalyi of hor RSA cr ponn Inforaion Thory,IEEE Tranacion on, 6(:55-558, 00 Auhor Biography Ahih Vijay wa born on Spbr 985H i h MTch un in SBCET, Jaipur (RajahanH ha copl BE (CSE in 007 fro Univriy of Rajahan, Jaipur Priyanka Trikha ha copl hr BTch an MTch gr in Copur Scinc an Enginring fro Faculy of Enginring an Tchnology, MITS, Lakhangarh, Sikar, RajahanNow Sh i aian profor in cop c Dp of SBCET,Jaipur Kapil Mahur wa born on 9 Spbr 98H i h MTch un in SBCET, Jaipur (Rajahan H ha copl BE (IT in 007 fro Univriy of Rajahan, Jaipur 0, IJARCSSE All Righ Rrv Pag 7