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Quite general transformation from SRS model to plain MIM model. Another positive application of non-black-box techniques. Generalize to other applications? more parties? c :&The Endc< /=PLFOCS4504-.2lFullT57?0@4-.>89;1= ` fff33` 3KI3ff` 33ff` /p` 3%*3|` Jy3fff3f` 3ff3̙` 33ff33` DDyq3f` ̙3n` w3ff` }ff>?" dd@,?nKd@ P nA@F`d n?" dd@   @@``PR"   @ ` `2p>>   + ( (    6 #" ``   ^*   T  6̵ #" `` `` H@___PPT9"@ r*&     &F X #"X  T@d#" `P H"0 C   <Hìd#" `U H"0 C   c $Ƭ"UY B D   s *ɬ"YW B D    s *̬"YU B D    s *Ϭ" B D    c $ Ӭ#" `SV H"0 C    c $׬"Y B D    s *,۬"X B D   <ݬ #" `  `  T Click to edit Master title style! !$  0 " `p  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     SN  68 #" `^ `` H@___PPT9"@ l*$    H  0޽h ? }ff80___PPT10. 07  Pixely   0 e(   F  "  Zd #"   H"0 C   s * "9)e  H"0 C b e  # "e   c $|"ie  H"0 C   c $h"9) H"0 C    c $`"0 H"0 C    c $h"?e  H"0 C    c $4") H"0 C    c $"?G H"0 C    c $T"oG H"0 C   c $"9G H"0 C   c $l"iA H"0 C   c $"A? H"0 C N  6 #" `` `` H@___PPT9"@ l*$      6 #" ``   `*   T  6 #" `` `` H@___PPT9"@ r*&       08  "P    T Click to edit Master title style! !  0, " P   W#Click to edit Master subtitle style$ $H  0޽h ? }ff80___PPT10. 07 0 x(    N`pFpF  #   |*  R))RR{{t  Nl%pFpF f#` H@___PPT9"@ *"    R))RR{{d  c $ ?69  4  N.pFpF  [  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  T>pFpF     |*  R))RR{{z  Tl>pFpF f` H@___PPT9"@ *"    R))RR{{H  0i ? 3380___PPT10.5Q h`0L(  Lr L S 0@   r L S  P   r L C JA2smalltree_text_bluetrans R L C *Aj0230415 rxH L 0޽h ? }ff___PPT10i.6+D=' = @B +  W O ` (  `z   ` j ,$@  0`R ` 0 P ` 0,p <P( 2z   ` @` ,$D  0`R ` 0 P ` 0p <P( 2L ` C $A woman@dw8 Z @ `` pP ` C A manz0 @ ` 0<Z z oRight2( 2cc  ` 0h` nLeft2( 2cc  ` 0 0 P  ,P  two party protocol4( 2c l   `0 j,$D 0` ` C 0A devilfinish  Z ` 0 @  pMiddle2( 2cc  ` 0Q ,$ 0  Adversary completely controls communication No shared secrets between left & right No trusted parties or public information (e.g., no PKI)2( 2cc r ` S    H ` 0޽h ? }ff@8___PPT10.F+J^D' = @B Do' = @BA?%,( < +O%,( < +D7' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*`D' =1:Bhidden*o3>+B#style.visibility<*`%(D#' =4@BB?BB%()?)?Dw' =.?7 BBBBBQM -3.33333E-6 -1.11111E-6 L 0.3 0.0007 *3>*B ppt_xB ppt_y=@0BBAApBB>Bֹr9<*`D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-g6B fade*<3<*`D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bwipe(up)*<3<*`D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bwipe(up)*<3<*`DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(+8+0+` +e  O G PT (  T~ T s *0 `    T ZA woman @  T fA devilfinishP   T 0p oLeft 2( 2cc  T 0P  pMiddle2( 2cc  T 0`@ oRight2( 2cc XR  T 0@` XR  T 0@ F P`   T `` N P   T P  T 0  h Left Session$ ( 2 g  `B T 0DpP N  P`  T  P`  T 0 `  i Right Session$( 2g  `B T 0Dp0P0  T 0( PO  BRelaying Strategy - Adversary is transparent Blocking Strategy - Adversary follows honest strategy independently in each session( 2gcgcIcc  T 6>"` ,$D 0 `Intuitive Goal: Design protocols s.t. adversay is essentially limited to unavoidable strategies.La( 2gQcg8!2  T VA manP H T 0޽h ? }ff___PPT10.F+iGRD2' = @B D' = @BA?%,( < +O%,( < +D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*TD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*TD' =-g6B fade*<3<*T+8+0+T +Y  `X(  Xx X c $  `    X 0pp oLeft 2( 2cc  X 04P  pMiddle2( 2cc  X 0@ oRight2( 2cc XR  X 0@` XR  X 0@ F P`   X `` N P   X P   X 0  h Left Session$ ( 2 g  `B X 0DpP N  P`  X  P`  X 0  `  i Right Session$( 2g  `B X 0Dp0P0  X 0h dInput: a8 ( 2c X 0j  w  nCom. Value: a8( 2 c X 0` `m  pCom. Value: a 8( 2 cb X 0 P  If Adv. relaying then a = a If Adv. blocking then a independent of a>G( 2cgccgcggccgF V X 01P P< Scheme is non-malleable [DDN91] if either a = a or a and a are (computationally) independenta( 2 c gccccg#c` L X C $A womanVpX X C 0A devilfinish J H X C A man&)l     X  ,$D 0 X <:GHA "`    <   X 0<  #Non-malleability = Intuitive goal$$( 2$g# H X 0޽h ?X }ffyq___PPT10Q.F+Y D%' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(Dg' =4@BB7BB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*XD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*XD' =-g6B fade*<3<*X+     +h& (  hx h c $R `   XR h 00 P XR h 00 L h C $A womanp$@X h C 0A devilfinish| lH h C A man u h 0(U0 6 XMIM Model: Adversary between 2 parties that want to talk to each other.  Preferred strategy: relayingTg( 2 cUcccf XR h 0 `XR h 0 [L h C $A woman X h C 0A devilfinish 4 ( H h C A man tpH %h C A man d` L (h C $A woman XB )h@ 0DԔp 4 pXB *h 0DԔp dp +h 0 _ P  bNM Model: Two sessions with 2 out of the 4 parties cooperating maliciously.  Preferred strategy: blocking Tl( 2cZccck H h 0޽h ? }ff___PPT10i.F+D=' = @B +_  vnP(  X  0   0kP0V  Our goal: construct protocols s.t. adversary is essentially restricted to use either blocking or relaying. Technically: same as non-malleabllity [DDN] However: we don t take a  moral stand which unavoidable strategy is  better .f( 2Vccccc8e V r  S t@   H  0޽h ? }ff___PPT10i.Ѕ++D=' = @B +  p \@(  \r \ S F `   r \ S G` 0   \ BH "` `  ` This Work: g   {  \ 6L Y p\TL___PPT9.&@ NM Commit w/ O(1) rounds NM Zero-Knowledge w/ O(1) rounds Different Techniques (e.g., Non-Black-Box Proof of Security) Generic transformation from SRS model to plain model. c gc gccc'cg6cN _  \ 0P`Z A* See next slide for works in shared reference string (SRS) model B( 2BcA H \ 0޽h ? }ff___PPT10i.dV+D=' = @B +    &`* (  `~ ` s *lP    ` ZAj0090112 G   ` 0mp %  ^Dealer ( 2c l @ `@,$D  0 ` 0p @ _r&( 2g `B ` 0D  `B ` 0De u`B `B 0D  ` 0t  @ _r&( 2g  ` 0vu @ _r&( 2g ? ` 0d|  ,$ 0 QNM Commit w/ 1-round [DIO98,DKOS01] NM Zero-Knowledge w/ 1-round [Sah99,DDOPS01] >Q  Qccl `0   #`0 ` ,$D  0@ `    ``0  `R  ` 0`  `R  ` 0   !` 0܂ `   Pref(r)L( 2c  "` 04@   Pref(r)L( 2c L $` C $A womanp` X %` C 0A devilfinishLV 6 H &` C A manv< H ` 0޽h ? }ff  ___PPT10 .F+R DU ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(Dc' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-o6Bwipe(up)*<3<*`D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#`%(D' =-o6Bwipe(up)*<3<*#`DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(+8+0+` +0F  4 (  4x 4 c $` `p    4 0p oLeft 2( 2cc J 4 H8c?"`p 0 ,$@  0 Coin-Tossing Output: rB( 2ccc x  4 Hܤ8c?"` 0  ,$@   0 Run Pref(r)p ( 2cc  b  4 H8c?"`p ,$D  0 .Coin-Tossing Output: r B( 2ccc z  4 H8c?"`  ,$D   0 Run Pref(r )p ( 2cc  J 4 H08c?"`p,$D  0 Coin-Tossing Output: rB( 2ccc x 4 H,8c?"` ,$D  0 Run Pref(r)p ( 2cc  n 4 0h  ,$  0 Informal Def: Coin-tossing is Non-Malleable if either r =r or r is (computationally) random & independent from rs( 2 cc g cccc0cccr Z 4 0` s ,$  0 FIf r =r : same as in SRS execution!d$( 2ggg 4 0p ,$  0 8`If r indp. from r: formally different from SRS1( 2gg ggg&% D 4 0Ts $ 0TL___PPT9.&@ TpHowever, if Pref is  Natural then it is still secure! J9( 2 g&gg(6   4 0"`` l,$D 0 +eThm: If 9 constant-round NM coin-tossing then 9 constant-round NM commitment scheme and ZK argument.f( 2ccc&cc5ccb L 4 C $A woman&`l  p  4p ,$D 0 4 6D p  pMiddle2( 2cc ` 4 C 0A devilfinish  }8 pp 4pp 4 6\pp oRight2( 2cc P 4 C A man`H 4 0޽h ? }ff--___PPT10-. d+YD)' = @B D)' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bwipe(up)*<3<*4D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bwipe(up)*<3<*4D1' =%(D~' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*4%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*4%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-g6B fade*<3<*4D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bwipe(up)*<3<*4D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bwipe(up)*<3<* 4D' =%( D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bwipe(up)*<3<* 4D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bwipe(up)*<3<* 4DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D ' =%(D ' =%(D6' =A@BB BB0B%(D' =-g6B fade*<3<*4D' =1:Bhidden*o3>+B#style.visibility<*4%(D6' =A@BB BB0B%(D' =-g6B fade*<3<*4D' =1:Bhidden*o3>+B#style.visibility<*4%(D6' =A@BB BB0B%(D' =-g6B fade*<3<*4D' =1:Bhidden*o3>+B#style.visibility<*4%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-g6B fade*<3<*4++0+4 ++0+ 4 ++0+ 4 ++0+ 4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 +    *l (  lr l S $ `p    l H<&8c?"` 0  Coin-Tossing Output: rB( 2ccc .  l H\,8c?"`  .Coin-Tossing Output: r B( 2ccc : l 0H2   Informal Def: Coin-tossing is Non-Malleable if either r =r or r is (computationally) random & independent from rs( 2 cc g cccc0cccr  l 0H="`  *dThm: If 9 constant-round NM coin-tossing then 9 constant-round NM commitment scheme and ZK argument.e( 2ccc%cc5cca e l BF| "` ,$D 0 GOur Goal: Design a constant-round non-malleable coin-tossing protocol.2H g?cG  #l 0Kp oLeft 2( 2cc L $l C $A woman`zF  p  %l p  &l 0P p  pMiddle2( 2cc ` 'l C 0A devilfinish  F pp (l pp )l 08Vpp oRight2( 2cc P *l C A man`H l 0޽h ? }ffT L ___PPT10, . d+r DX ' = @B D ' = @BA?%,( < +O%,( < +DJ ' =%(%(D' =%(D$' =A@BB@BB0B%()?)?Dk' =.37 BBBBBEM 0.0 -1.48148E-6 L 0.0 -0.12662 *3>*B ppt_xB ppt_y=@0BBAApBBBt偽<*lDJ' =A@BB@BB0B%()?)?)D' =.I7 BBBBB[M -3.33333E-6 1.11111E-6 L 0.00417 -0.15625 *3>*B ppt_xB ppt_y=@0BBAApBB;B<<*lD' =%(D' =A@BB7BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*lD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*lD' =-g6B fade*<3<*l++0+l ++0+l ++0+l +  `(  X  0   0d{0 <Our goal: construct a constant-round NM coin-tossing protocol. In the paper: we (define and) construct such a protocol. Now: we solve a related  toy problem and then an even more related  bigger problem ( 2 c6c c,ccPccr  S p   H  0޽h ? }ff___PPT10i.Ѕ++D=' = @B +  0!L (  L L Bg> "`  ,$D 0 RToy Problem: Design a coin-tossing protocol such that w.h.p. r rev(r)jG g1ccc86 : L 0o@F  Informal Def: Coin-tossing is Non-Malleable if either r =r or r is (computationally) random & independent from rs( 2 cc g cccc0cccr   L 0`{ ,$ 0 ^4rev(r1& rn) = rn rn-1 & r1 ( 2ckckckckck8   L H8c?"` 0  Coin-Tossing Output: rB( 2ccc . L H̋8c?"`  .Coin-Tossing Output: r B( 2ccc  L 0p oLeft 2( 2cc L L C $A woman`zF  p  L p  L 0 p  pMiddle2( 2cc ` L C 0A devilfinish  F pp L pp L 0pp oRight2( 2cc P L C A man`r !L S ,0   H L 0޽h ? }ffr j ___PPT10J .y@C+ZD ' = @B Di ' = @BA?%,( < +O%,( < +D' =%(DW' =%(D' =A@BB"BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D ' X=+4 . B(-#ppt_w/2)0B(#ppt_x)*Y3>B ppt_x<*L%(D' =+4 . B00B -1.0*[3>Bxshear<*L%(X))?)?D' =0l9 BBBBBB*<3<*L%(X))?)?D2' =+4 )B-(#ppt_h/3+#ppt_w*0.1)*Y3>B ppt_x<*L%(X))?)?D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* L%(+p+0+L ++0+ L +P  u!m!)C(P (  ( ( 0@  {Left >( 2aac z   (  N,$D  0`  ( 0    ( 0   Comm(r1)\ ( 2ckc z  J ( P ,$D 0h (B s *"`Z J ( 0@ r 2J( 2ck &z @  (  ~,$D  0` ( 0 4 ( 0H@@:  r= r1r2 ( 2ckck l   2( ,$D  0r ( BGAH0   ( 6p *  T