Data-Depend Hash Algorithm
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1 Dt-Dp s Algortm ZJ Xu K Xu uzwz@gml.com ukzp@gml.com Astrct: W stuy som tcologys tt popl vlop lys ttck s lgortm. W wy tt us t-p uc rsst rtl ttck. T w sg s lgortm tt cll Dt-Dp s Algort(DDA. A DDA s smpl strog ur rtl ttck. Ky Wor: s lgortm t-p uc. Itrouc s lgortm s t lgortm tt computs sz mssg gst rom rtrry sz mssgs. Atr SA- ws puls som tcologys tt lys ttck s lgortm r vlop. T mor tcologys s rtl ttck. Pprs[Wy Du] s pl t ttck. Drtl ttck s t st tcqu ttck s uc. To ttck s uc t o t work s ollow:. osttut sl rc pt tt s goo posslty.. osttut t qut cos t rc pt.. F som tcqu rs t posslty o t rc pt. From m ov scrp o rtl ttck t s sy kow tt costtutg sl rc pt s t g. I t c mk t r costtut sl rc pt t wll r ttck t s uc. I pp w kow tt t t-p crculr st s goo c tur. A w mssg pso uc tt mk y rc pt wll s t lst gt t-p crculr st rc [pp ]. Ts mk t r costtut sl rc pt. At t sm tm w stuy som tcologys[] tt us ttck s lgortm DDA us som wys rsst ts ttck tcologys. T ollowg oprs r ppl -t or -t wors
2 DDA:. vrl ssgmt. Btws logcl wor oprs: AND! OR XOR Ng.. A + moulo or moulo.. T st rgt opr SR ( wr s -t or -t wor s tgr wt < (rsp. <..T st lt opr SL ( wr s -t or -t wor s tgr wt < (rsp. <.. T rott rgt (crculr rgt st opr ROTR ( wr s -t or -t wor s tgr wt < (rsp. <.. T rott lt (crculr lt st opr ROTL ( wr s -t or -t wor s tgr wt < (rsp. <.. Dt-Dp s Algortm (DDA DDA s two s ucs: DDA-(-tvrso DDA- ( tvrso. DDA- s us mssg o ggr t DDA- s us mssg o ggr t T proprts s ollow: wor Mssg sz Block sz s vlu sz DDA- < DDA- < Proprts o DDA s ucs(sz ts I DDA t mssg wll prprocss. Atr mssg s prprocss t mssg wll prs N mssg locks ts locks wll procss wt comprsso uc orr.. Prprocssg Prprocssg DDA clu stps:. pg t mssg M prsg t p mssg mssg locks. sttg t tl s vlu.. Pg prsg
3 Suppos tt t lgt o t mssg M s L ts. App t t t o t mssg ollow y k zro ts wr k s t smllst o-gtv solu t qu L++k! mo (rsp. L++k! 9 mo. T pp t -t lock tt s qul t umr L prss usg ry rprst. Atr mssg s p t mssg wll prs N -ts(rsp. -ts mssg locks... Itl s Vlu costts DDA us t sm tl s vlu s tt o SA- (gv s ollow: DDA- DDA- 9 c 9c 9 c9 9 cc9 c c 9 9cc 9 c99 T tl s vlu DDA DDA us costt wors ts wors r sprt two prts s ollow: DDA- c cc c c 9 99 DDA- 9 c 99 cc c c cc9 9c 999c
4 c c c c c ostts o DDA s ollow: DDA- DDA c c c c c c c c c c c c c ccc c c c c ostts o DDA. procssg. I tr r N mssg locks... M N M. T DDA s comprsso uc. T put o comprsso uc clu cg vrl( wors... mssg lock( wors m m... costts( wors otr prmtrs. T t procssg s oollow:
5 t oc oc N tm N + tp occ t oc tm t rtur comprsso( rpttm m tm oc c c tm oc tm tm tm tp N ( tm + m + occ comprsso( rpttm m < m tp ls ( tm m t occ oc t t + tp + tp t > m oc oc + occ tm t tm N + tp N oc tm c c Procssg o DDA. comprso uc T uc comprsso(rpttm m tmocctct tks s put sv vlus: * tgr vlu rpttm. Usr c st rpttm gt gr tsty. T ult vlu o rpttm s. * mssg lock m m m... * c vlu... * vlu tm tm...tm.
6 * vlu oc oc oc. * ostt ct ct... ct * ostt ct ct... ct T comprsso uc us two ucs: SR(m ctct ME(m. I DDA t wor s crv up st prts vry prt s us s prmtr o t-p crculr st oc. A uc ME(m t crculr st opr s s o prt ot t... SR(mctct T uc SR(mctct tks s put our vlus: * c vlu... * mssg lock m m...m * ostt ct ct... ct * ostt ct ct... ct A SR(mctct s ollow: m >> + ( mo t t + t t t t t ( m ( >> + ROTR ROTR ROTR + ROTR + m + + m ( m m ( m + ( m + ( m m mo + ( mo >> (( rv >> ( rv m m ( >> (( + rv >> (( + rv ( + + m ( t + ct ( t + ct m
7 t t SR uc o DDA I DDA- t wor lgt s s rv s. I DDA- t wor lgt s s rv s... mssg pso uc ME(m T mssg pso uc ME(m tks s put o vlu: * mssg lock m m...m A ME(m s ollow: t ( m t m ROTR m ( t m t t ( m t rtur m m ( m t ( m uc ME o DDA I DDA- t wor lgt s s. I DDA- t wor lgt s s. Wt uc SR(mctct ME(m t comprsso uc s ollows: c ct c ct m m c m ME( m c tm
8 t c c c c t c c c c SR( m c c SR( m c c + rtur tm tm rpttm > t oc oc c c rpttm t ROTR ( c ROTR ( c comprsso uc o DDA I DDA- t wor t-lgt s. I DDA- t wor t-lgt s. Scurty o DDA I ts sc w scuss t rsstc o DDA Drtl ttck Lgt tso Multcollsos.. Drtl ttck From pp w wll kow tt tr s y rc t mssg t rc pt DDA wll s t lst gt t-p crculr st rc tt r r s t prmtr o t-p crculr st. By propos A. t s kow tt t-p crculr st rc tt ( r r t posslty o t-p crculr st gc rc s gc s t grtst commo vsor o ( r r. I DDA t prmtr o t-p crculr st lss t (rsp.. t tr s:
9 r r < < ( r r < gc GD( r r DDA r r < < ( r r < gc GD( r r DDA So t posslty o rc pt DDA wll : p (gc ( rsp. At t sm tm rc pt DDA c vlu tt r s cs som ts t prmtr r wll ts p o t cs tt t c vlu s. r w suppos ttckr c t cs.. Lgt tso Lgt tso s t ttc gst ky s o m k (m or ( k m. T ttck s: gv k (m t pg t s p t m ' tt mk ( k m p m'. T ( m p m' s t rct mssg. Lt tm s sum o t mssg locks lst lock. I DDA (... m N m N s p mssg t N m s t lst mssg lock t l c vlus s N N comprsso( rpttm m N tm oc c c. I lock N m s t t t c vlu N N tw m m N N N comprsso( rpttm m tm oc c c rom N N N comprsso( rpttm m tm oc c c. T kowlg o N N DDA (... m m c ot us comput t s o (... m N N N m m.. Multcollsos My tcqu s vlop Multcollsos o s uc Jou s tcqu[] Klsy/Scr s tcqu[] s rprsttv tcqu... Jou s tcqu Jou [] s propos tcqu ucs wt -t s vlus k / s ollow: k -collso s
10 m m m m m m k k k + To pr ( I rplc m + wt m + wll ot cg y prmtr ollow clcul t c pply Jou s tcqu. Lt tm s sum o t rst mssg locks oco s t mur o o lock -t cg s vlu. I DDA rplc m + wt m + wll cg t prmtr tm ollow clcul. + A t c ltr Jou s tcqu pply t o DDA. To pr ( t mssg locks ( m... m m... m tt stsy (.. lt ocou s t mur o o lock ( m... m ocou s t mur o o lock ( m... m A ocou ocou. + So Multcollsos o DDA vry pr c vlu ( t k mssg locks tt stsy (.. T -collso DDA t mssg locks must sty k systs tt lk (.. tm m tm m m m ocou ocou comprsso( rpttm m tm + m oco c c + comprsso( rpttm m tm + m oco + ocou c c...( + comprsso( rpttm m tm + m oco + ocou c c (. comprsso( rpttm m tm + m oco c c + comprsso( rpttm m tm + m oco + ocou c c...( + comprsso( rpttm m tm + + m oco ocou c c.. Klsy/Scr s tcqu Klsy/Scr s tcqu ss o -pots o s uc. W costtut Multcollsos s uc Klsy/Scr s tcqu[] wll cg t orr o t locks.
11 I DDA cg t orr o t locks my cg t prmtr tm or oc som ollow clcul. It s r pply Klsy/Scr s tcqu o DDA. Tr s smpl wy rsst ts ttck t us som prmtr tt s rlt t orr o t lock locks.. Improvt I comprsso uc tr r t-p crculr st oprs ts wll crs t clcul. I DDA us mssg pso uc tt s gr mmum mmg wgt lss p mssg wors t wll mk DDA s sm tsty wt lss clcul. Tr s mssg pso uc s ollow: t t t t t t m 9 m ROTR ( m ROTR ROTR ROTR ROTR ROTR ROTR m ( (+ (+ ( m ( m ROTR ( m ( m ( m ( m ( m ROTR ( m ROTR 9 ( m ( m
12 t 9 9 ROTR ROTR ROTR ROTR ROTR ( ( ( ( 9 ( ROTR ROTR ROTR ROTR ROTR ( ( ( ( 9 ( ROTR ROTR ROTR ROTR ROTR uc ME o DDA I DDA- t wor lgt s s. I DDA- t wor lgt s s. Fuc ME s crctr st clu rt pso mssg wors t s rt mmum mmg wgt. W gv t mmum mmg wgt r: pso mssg wors mmum mmg wgt Fuc ME wll prouc pso mssg wors wc mmum mmg wgt s. t wll ruc t clcul.. oclusos Atr stuy t tcologys[wy Du] t c tur o t-p uc w mssg pso uc tt wll mk vry c pt DDA wll s t lst gt t-p crculr st cs ts mk t r costtut sl rc pt tt s goo posslty. Bs o t-p uc t mssg pso uc w sg t s uc DDA. At t sm tm w stuy otr ttck tcologys[] lgt tso w us som msurs vw o ts tcologys ts msurs wrck t co tt pplyg t tcologys ts mk t rr pply ts tcologys o DDA. DDA uss vlu rpttm tt usr c st t vlu cg rous cg t strgt. It mk t sy rs t tsty o syst. So DDA opts vrous msurs vw o t tcqus tt us ttck s uc ts wll mk DDA wll rsst ts ttcks. ( ( ( ( 9 (
13 Rrcs: [WY] Xoyu Wg ogo Yu. ow rk MD otr s ucs. I rmr [r] pgs 9. [Du] Mgus Dum. ryptlyss o s Fucs o t MD-Fmly. PD tss Rur-Uvrst t Bocum. [] A Jou. Multcollsos trt s ucs. pplc csc costruc-s. I RYPTO. t [] Jo Klsy Bruc Scr. Sco prgs o -t s ucs muc ss work. I EURORYPT.
14 App : Drc o t-p crculr st r w ust scuss crculr rgt st. A w ust scuss XOR rcs[du]. I F s -ts s: (... r < ( rsp. I y s -ts wor s (rsp. s tgr tt s (rsp. ts t t crculr rgt st s: gc r y ROTR ( (( << ( r ( >> r I tr s (yr (yr mt: y ROTR At srt tr s:( log r wl ( y ROTR r ( wl ± r r ( ( r r y: ( r r y : ( r r ( : ( (... ( ( y y : ( ( r r... ( r r Lt t grtst commo vsor o ( r r s GD( r r. T tr sts:. rr tr s: ( y y ( ( ROTR r r ( r... ( ( (... So rr t rc o y y wll ust p o t rc o. o cours t lso p o r. To gv ( y y tr r. To gv ( ( y y tr s r tt mt ( LOTR (. So tr r pr ( s sm ( y y.. r r. Dv ( y y ( gc prts s ollow: ( r r
15 p : ( ( ( + gc mo...( / gc py : ( ( ( + r+ gc...( / gc To gv c o ptr p py : mo ( + gc...gc mo ( r + + gc mo...gc ( A. : ( ( ( + gc mo ( + gc mo...( / gc / gc Tr r c s ollow: y : ( ( ( + r+ gc mo ( r + + gc mo...( / gc To gv pr ( y tr sts: ( /gc /gc ( ( ( ( + + r gc ( + gc ( + r+ gc mo mo Propos A.: r r ( ( y y ( mo ( + gc ( + r+ gc mo mo ( r + + gc mo ( A. t posslty o rc pr gc s. Proo: At rst Dv ( y y ( gc prts s (A. vry prt stsy (A.. To gv pr ( y t wll s t syst: y ( + gc mo...( / gc ( + r+ gc mo ( + gc...( / gc mo ( r + + gc mo ( A. T syst s ( / gc vrls / gc qus.
16 Apply lm mto o syst (A. t wll gt (A.. T syst s two roots o GF(. T rc pr ( ( y y ( clu gc prts tt stsy gc (A. (A.. So tr r pr ( sty ts systs. gc So tr r pr ( v t gv rc ( ( y y (. O cours ts prs ( stsy (. To gv rc ( ( tr r A gv pr ( ( tr s tt stsy ( so tr r pr ( v t gv rc ( (. gc So t posslty o rc pr ( ( y y ( s.
17 App : Mssg_pso(m I DDA t mssg m s p rom wors wors. It c us ( rsp. grr mtr scr t. It lttl r out t mmum cs p mssg wors wt t g mtr. W wll out t mmum cs p mssg wors wt otr wy. At rst t ollow cts s us smply t scusso:. Bcus t gr o t Algrc Norml Form (ANF tt scr uc ME(m s. Fg out t mmum cs p mssg wors s qul g out t mmum mmg wgt o t p mssg wors w t mmg wgt o mssg ggr t.. T wors DDA s crv up st prts. So t c scr wor s ollow: W ( w... w : Wr w : ( J... < vry prt w s J ts. T t mssg wors m p mssg wors s ollow: m : ( m m... m m : (... m.. m... T uc ME(m c scr wt stps s ollow lt m m clu wors. T tr sts: m ( m m m ROTR ( m + ( m m m m ( + mo Lt W(w s mmg wgt o w. T tr sts: Propos B.: I : (... y : ( y... y (
18 Tr sts:. I t W(yW(.. I t W(y-W(.. I W ( > t ( y. I W ( > t W ( y. proo: Tr sts: W (. I T T. I T T W. ( B.. y ( ( B.. W(yW( y ( W ( y y ( ( W ( ( B... I ( W W ( tr s. So: W ( By (B.. tr sts: W ( y W (. I ( W so tr sts: W ( tr s W ( By (B.. tr sts: ( y W ( W Propos B.: I mssg wors o DDA tr sts mk m T tr st W (. Proo: Tr s: m m Suppos I } W... { m ((
19 Tr s: m ( By propos B. tus W (( m m... m I Lt J {( + mo I... } tr r - mrs J. Bcus m m ( + mo T m m m m ( + ( + + mo mo I J Tr sst: ( m m By propos B. tr ts: T + W (( W ((... m... m ( J J J + J W ( W ((... + W ((... + ( Propos B.: I mssg wors o DDA W ( m tr st W (. Proo: Tr sts: m W ((... W (( m... m. tr sts mk y propos B. tr s
20 sts:. tr sts W ( > ( B... T tr sts: m m ( m ( + mo Lt I { } t: I { m } I { m { I } W ( m W ((... } Lt JB {...} { ( I > } cus T y propos B.: ( I T tr s: So tr st: m ( (.. JB B I m m ( + mo W (( m... m W (( m... m W ((... ( B... I tr sts c mk ( m c y propos B. (B.. tr sts: W (( W (( W (( W (( m W (( W (( m... m W (( m c c c... m. I ( m. T tr st:... m c + W ((... + W (( m c + W (( m... m > ( B.. c c c c... m c
21 W (( m ( m m... W ( m ( B.. Bcus W ( m tr r t lst o mr JB. Lt y propos B. tr r t lst two mrs Suppos I t: T tr s: m m m m m m ( + ( + mo mo Bcus tr s: Tr s: ( + mo ( + mo Bcus ( m T y propos B.: ( ( m (+ mo m (+ mo W ( m W (( m W (( m (+ mo (+ mo... m... m (+ mo (+ mo + ( B.. By (B.. (B.. (B.. tr st: W ((... W ((... + W ((... W ( m ( B.. c I. So y (B.. (B.. (B..c W ( m tr st W (. Bcus vry prt o vry p mssg wors s s prmtr o t-p crculr st oc. Tro B. ms y rc pt DDA tr wll t lst gt t-p crculr st rc.
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