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Table All7Table<$paranumonly>, <$paratext>, on page<$pagenum>Table Number & Page'Table<$paranumonly> on page<$pagenum> Handout DateJanuary 7, 1999Heading <$paratext>AHTMLHeadingsA;;==??Ac5y??? 5 5*> 1.Bd.?*???"?$?& ?( ?* ?, ?. ?0 ?2 ?4 ?6 ?8 ?: ?< ?> ?@ ?B ?D ?F ?H ?J ?L ?N ?P ?R ?T ?V B4.>+>a.?X ?Z ?\ ?^ ?` ?b D{ D} ?f ?h ?j ?l ?n ?p ?r ?t ?v ?x D D ?| ?~ ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? D D ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? E7 E9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Ek Em ? ? ? @ @ @ @ @ @  @  @ @ @ @ @ @ @ @ @ @  @" @$ ABADAFAH AJ AL AN APAR AT@& @( @* @, @. @0 @2 @4 @6 @8 @: @< @> @@ @B @D @F @H @J @L @N @P @R @T @V @X @Z @\ @^ @` @b @d @f @h @j @l @n @p @r @t @v @x @z @| >b.@~ @ @ @@B6.B5.Ba.@@ @ @ @ AVAX AZ@ @ @ @ @ A\A^ @ @ @ @ @ @ @ @ @ @@@@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ Ae@ @ @ @ @ @ @ @ @ @ @ @ F? FA FL @@@@ @ @ @ A A CC C A AAAA A A A A A A  A" A%A'A)A+ A- A/ A1 A3 A5 A6Br2.Bsa.Bb.By3.Bza.Ba.B|b.B}c.Bb.Bc.Bc.Ba.Bb.Bd.Be.C C C C Bf.C C  C" C$ C& BC( C* C, C. C0 C2 C4 C6 C8 C C C C C C C FN FP FR FT FV FX FZ F\ F^ F` Fb Fd Ff Fh Fj Fl Fn Fp Fr Ft Fv Fx Fz F| F~ F F F F F F F F F F >b.F F F F F F F F F F GT GV GX GZ G\ G^ rdq}? C~5I? FWCe d? HmR? HmRHRHRFootnote Hr@? Hr@HzHz Single LineH? Footnote ?   HD?  HDHH Double LineH? Double Line? ? H?  Single Line? HZ?  TableFootnote EGxR?EGxREPwEPw TableFootnoted5p HHˆ5xHHˆGe HHˆ5zHHˆld?d?dHl d?d9(x(oje`[^adgjmpvy| #'+/ADOL963W3Bm       }d ?!d WeHTML Mapping Table }Hd ?Hd We }Hd ?Hd We HUV 5HUV Ge HUV 5HUV l H$ 5H$ Ge H$ 5H$ l HHˆ5HHˆ ))( `Outline for April 25, 2000 `What is a cryptosystem? )`B( M ,  C ,  K ,  D ,  E ) L`=attacks: known ciphertext, known plaintext, chosen plaintext 4P`Transposition ciphers 5\`"Show rail-fence cipher as example `Show anagramming 7v`Simple substitution ciphers 8`Do Csar cipher :`Present Vigenre tableau ;`&Discuss breaking it (Kasiski method). `Go through one-time pads '`DES 9``Product cipher with 64 bits in, 64 bits out, and 16 48-bit round keys generated from 56 bit key <`)Note S-boxes are real heart of algorithm >`Complementation property: DES k ( m ) = (DES k  ( m )) where  x  is the bitwise complement of  x ; !A kDifferential cryptanalysis: first version unusable as at 16 rounds, more plaintext/ciphertext pairs needed ythan exhaustive key trial; but for 15 rounds, cuts this time. Later versions cut it to 2 47  tries. Works by comjparing xors of results with xors of corresponding plaintext.. Designers of DES knew about this one, hence @the design of the S-boxes !B rLinear cryptanalysis drops required chosen plaintext/ciphertext pairs to 2 42 ; not known to designers of @DES. G`Triple DES and EDE mode S:` Public Key ?F`%based on NP-hard problems (knapsack) @`5based on hard mathematical problems (like factoring) R``Do RSA 1Tl WExponentiation cipher:  C  =  m e  mod  n ,  M  =  C d  mod  n ;  d  is private key, ( e ,  n ) is public key; must choose  d  @Ofirst, then  e  so that  ed  mod  f ( n ) = 1. 6 Why? as  ed  mod  f ( n ) = 1,  ed  =  t f ( n ) + 1 for some integer  t . Then #YC d  mod  n  = ( M e  mod  n ) d  mod  n ""=  M ed  mod  n ==  M t f ( n ) + 1  mod  n V=  M ( M t f ( n )  mod  n ) mod  n Q= M( M f ( n )  mod  n ) t  mod  n )=  M (1) t  mod  n =  M  mod  n @by Fermats Little Theorem != .Example:  p  = 5,  q  = 7,  n  = 35,  f ( n ) = 24; choose  e  = 11, then  d  = 11. HELLO WORLD is 07 04 11 11 14 22 @14 17 11 03; enciphering is  C  = 07 11  mod 35 = 28,  etc . so encipherment is 28 09 16 16 14 08 14 33 16 12. 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