crypto-public - D @ Ciph Pft h D 7 cHSe gBCA986 5 BpY8 h D...

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Unformatted text preview: D @ Ciph Pft h D 7 cHSe gBCA986 5 BpY8 h D IF c Bc @ 7 Dh 8 6B 3 pui4 2 iy 0 {pC 1puQ ) {i ( i g%Gjr2 g 6 3 dRA986 5 f D c DPhP g D B @ 7 P6 i B6 c DPhP g W y`Aojr2 g Q6 3 R 6 C8BIFctoPD eiD ct00BtPQi$p` toP2i`tGPCW i P c c D cB h c e c D i D B 6 c D i c h B e @ g 86 iy G @ TH hH @ G 97 I ! H G F r kP q 5 1 !P tyda f f cP6 i D 6 g i D i Q6DjoPjp8 6 3 6jP 3 CD m Cph pfSc i 7 Pc g6 iQ6 i6jr2 Ec8 U6 f P D `osn SgS 8sW DPhP gB Pc cH 7 cB c H e B m 7 l6 B yA sx kj ih I gesW f fw6 Bc 2ic gDb8 D rBcSB dWy y Q sW g B h c H e 6 B ! 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D fB 3 pb9W Pc c cB h H t2b8 6 3 cP g t2b8 6 3 W cP g 6tP ͤi s tP Ct W c 6 ic yA b t2b8 6 3 cP g dWy t2b8 6 3 W cP g g6 h D 7 ȤipB 3 8 W7 ȤphB 3 8 R g6 i D W d dWy U6 h U6tfB 3 Ĥ 7 f c F cPc D W B h @Bc EpbH ASc 6 c tP fcDc D H 3 Ssc 2i QF Uh U6 4Stᥢ Q D H e B g c B h ߩ c H P cP g P g B c h PP i h 7 B c DB c 6 P j$ɷ8 Q6 3 0 dU 3 Erh U"pQ6 W7 Ao f W c DBc i 9GE Uh 3 6 TUcSgI 7 B 7 6 cF e6 i P6H D @ 6 2oPSe 6 i H 3 CS f0B 3 pj gi Uh f DH e Pc c cB h H e6 i Diffie-Hellman Key Exchange A pick X n,g,g g compute Y X (g mod n) mod n = g XY mod n X mod n mod n compute Y X (g mod n) mod n = g XY mod n B pick Y Y To break, attacker must solve discrete logarithm problem Susceptible to Bucket Brigade Attack (Man in the Middle) Main Problem: Key exchange but NO AUTHENTICATION!! h ot&8vAS l g W T x~w X W T d f f aYa}}3 X X ` !c{3 k ! f vT n ` X gaus b t d ` i5c{ n aX n Q 4d g vX f ` X paus U T X U d f T f T $fhvg U p U 5d m n l r8s n d 5! y U X g W a||q n aX U d b 5ut n q q k q X T W U ` X W zzra5ruaYxq U q b T U T ` (4ivaVub W is n d 5! U 4 R Q S&P g vX d m l k q s T q X xFac` ` d 5Q T q s t VFiFb X 4 n X us k ! n s X W t s T ` W f T aYFvwwf U q 1(rop X g W f T g ioafW l k W ` b ` X g W d X g W f T X g f W g jjihagyfeidW Q d d b uYf 7 ' U 4 H E E IGF R U X g W ai C DB @ A# 9 U 7 86 U T X T q X vVaes d W U Y$VT U X X w W X s Q q X f ` X g f X f d b ` X W U a!yxvutraYpaihDY4ecaY$VT 2 ) ' % # 10(&$" ! ' 5043 Diffie-Hellman Bucket Brigade Attack A pick X X n,g,g mod n C pick Z n,g,g g g Z mod n Computes K1 and K2 a B pick Y Z mod n Y mod n t hv&e v h Y Computes K1 Computes K2 V l X f f 5uDX X g W W b k ` X ~Bija! g W T x~w U d q 54 U g W T x~ w 1p X W ` X U X Yuaia5 X W b k ` U aYiijaiaX G8i5 s d W f X f YD}it X f f $3uDX p G8i5 X W t Yb DFq n d 5! U s T vvFb U X g aW k ! n f q q X w f Vay U X g aW n X g W g T g w v~i U X a}f n s U X g aW l f f X a}D!! s q p rr Y g f T q s t b k fVF! 7 ' n H E E GIi U X g W X f t f T X d s eai!aYB(v15eSX C Di @ # 9 # d W X U d k U ` d Y~5d5Q n X g f W f ` X g W Q ai}cFri&P 7 6 # " 8&i7 Diffie-Hellman Public Key Encryption A B n ,g ,g Y mod n Publishes info B B B B ... pick X compute K = X Y (g mod n ) mod n B B B XY =g mod n B B Encrypt M with K X {M}k,gB mod nB compute K = Y X (gB mod nB ) mod nB XY =g mod n B B Decrypt {M}K with K e vo Sp G8B q s p U VT f 3 X ` c X W T ` YxwFb X g iW U s p q S(I T q s t VFiFb X g iW X ` X g cai~w vdD ` T VFb k X v X W rw VFiFB T ` b T q s t b s p q Sj(I n ` X W U d q f g q b T U T ` uaYI4B$h3ivaVwFb H # " 6 % $(|AE 2 E ' H 0' E H 0' g v E " ' 7 % # E 4 uASg' V l ts U g W T r~w U d q W U X f f B$h$a}vT X f f e53}DX n X ig m p G8i5 k s v U X aig m X W t aYb s r n d f 5!fT X ` t W U T c{rf g W T x~w X W U X W U d aYaY5! p Q 4d G8i5 X W t aYFb Ц q n d 5! 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