Vernam Cipher
Project Preliminaries
CSC112
March 14, 2011
Oskars J. Rieksts
Computer Science Department
Kutztown University
Early/Simple Examples
Steganography
 Caesar cipher
 Substitution cipher
 Transposition cipher
 Vigenere cipher
 Vernam cipher

2008
Kutztown University
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Steganography

Merriam-Webster: The art or practice of concealing a
message, image, or file within another message, image, or
file
 from Greek
» steganos = covered
» grafo = write

Histiaeus – tyrant of Miletus
 shaved head of most trusted slave
 tattooed a message
 hair grew back covering message

Advantage – does not draw attention to
 itself
 messenger
 recipient

Often combined with cryptography
2008
Kutztown University
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Steganography Example
You may have seen the TV show – In Plain Sight –which is
based entirely on the federal witness protection program.
The show is about people who have testified or will be
testifying soon as witnesses in criminal cases but whose
lives are in danger as a result. For their protection they
are given new identities and are moved to a new
community. Ergo they are all hidden “in plain sight”. And
if you think this would not work, according to the U.S.
Marshalls extant website, no program participant who
follows security guidelines has ever been harmed while
under the active protection of the Marshals Service.
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Kutztown University
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Caesar Cipher

Example of a shift cipher
 Encryption – forward shift by 3
 Decryption – backward shift by 3

Shift ciphers






Private key
Symmetric key
Key = shift amount
Keyspace = 25
Plain text – IHAVEASECRET
Cipher text – LKDYHDVHFUHW
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Kutztown University
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Caesar Cipher – Example
L KDYH D GUHDP WKDW RQH GDB WKLV QDWLRQ ZLOO ULVH XS DQG OLYH
RXW WKH WUXH PHDQLQJ RI LWV FUHHG: "ZH KROG WKHVH WUXWKV WR
EH VHOI-HYLGHQW: WKDW DOO PHQ DUH FUHDWHG HTXDO."
L KDYH D GUHDP WKDW RQH GDB RQ WKH UHG KLOOV RI JHRUJLD WKH VRQV
RI IRUPHU VODYHV DQG WKH VRQV RI IRUPHU VODYH RZQHUV ZLOO EH
DEOH WR VLW GRZQ WRJHWKHU DW WKH WDEOH RI EURWKHUKRRG.
L KDYH D GUHDP WKDW RQH GDB HYHQ WKH VWDWH RI PLVVLVVLSSL, D
VWDWH VZHOWHULQJ ZLWK WKH KHDW RI LQMXVWLFH, VZHOWHULQJ
ZLWK WKH KHDW RI RSSUHVVLRQ, ZLOO EH WUDQVIRUPHG LQWR DQ
RDVLV RI IUHHGRP DQG MXVWLFH.
L KDYH D GUHDP WKDW PB IRXU OLWWOH FKLOGUHQ ZLOO RQH GDB OLYH LQ
D QDWLRQ ZKHUH WKHB ZLOO QRW EH MXGJHG EB WKH FRORU RI WKHLU
VNLQ EXW EB WKH FRQWHQW RI WKHLU FKDUDFWHU.
L KDYH D GUHDP WRGDB.
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Kutztown University
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Substitution Cipher

Randomly generated substitution

Example






AF
BK
CD
DJ
etc.
Characteristics




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Private & symmetric key
Monoalphabetic
Key = alphabet of substitutions
Keyspace = 26!
Kutztown University
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Substitution Cipher – Analysis
Keyspace = 26! =
403291461126605635584000000 = 4.03 x
1026
 But other factors make it insecure

 Letter frequency
N-grams
 Strong elimination coefficient
 With patience, can be decoded by hand
Plain text – BOOKKEEPINGROCKS
 Cipher text – JXXTTZZDOYBEXATU

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Kutztown University
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Substitution Cipher – Example
HPFAIFJZIFYTPFTUVIJFBTPHWVFTHUVGHXXZHWIEMFVJXHAIUETTPITZ
EIYIFVHVNUCHTWDZIIJGIPUXJTPIWITZETPWTUKIWIXCIAHJIVTTPFT
FXXYIVFZIDZIFTIJIOEFXHPFAIFJZIFYTPFTUVIJFBUVTPIZIJPHXXWUC
NIUZNHFTPIWUVWUCCUZYIZWXFAIWFVJTPIWUVWUCCUZYIZWXFA
IUGVIZWGHXXKIFKXITUWHTJUGVTUNITPIZFTTPITFKXIUCKZUTPIZP
UUJHPFAIFJZIFYTPFTUVIJFBIAIVTPIWTFTIUCYHWWHWWHMMHFWT
FTIWGIXTIZHVNGHTPTPIPIFTUCHVREWTHDIWGIXTIZHVNGHTPTPIPI
FTUCUMMZIWWHUVGHXXKITZFVWCUZYIJHVTUFVUFWHWUCCZIIJU
YFVJREWTHDIHPFAIFJZIFYTPFTYBCUEZXHTTXIDPHXJZIVGHXXUVIJ
FBXHAIHVFVFTHUVGPIZITPIBGHXXVUTKIREJNIJKBTPIDUXUZUCTPI
HZWSHVKETKBTPIDUVTIVTUCTPIHZDPFZFDTIZHPFAIFJZIFYTUJFBH
PFAIFJZIFYTPFTUVIJFBJUGVHVFXFKFYFGHTPHTWAHDHUEWZFDHW
TWGHTPHTWNUAIZVUZPFAHVNPHWXHMWJZHMMHVNGHTPTPIGUZ
JWUCHVTIZMUWHTHUVFVJVEXXHCHDFTHUVUVIJFBZHNPTTPIZIHV
FXFKFYFXHTTXIKXFDSKUBWFVJKXFDSNHZXWGHXXKIFKXITURUH
VPFVJWGHTPXHTTXIGPHTIKUBWFVJGPHTINHZXWFWWHWTIZWFVJ
KZUTPIZWHPFAIFJZIFYTUJFBHPFAIFJZIFYTPFTU
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Transposition Cipher
Generate permutation of n objects
 Transpose letters


Permutation of 0 through 7
6 – 3 – 7 – 1 – 4 – 8 – 5 – 2

Yields value transposition
16
23
37
41
54
68
75
82
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Kutztown University
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Transposition Cipher – Example

Cipher text
TYTSNHOAGTGERLUSHATEUAGNTIHVLBEAURRYTHHAOH
UUCGLGOATHYTNSUSGHTGREGNHLATUEEATAIHLVBEOT
LUAHHNERDWTAANRODESUHIEVNETAAMINYNFENNOTOR
TSTIHFLAEAHAINSNTDEHBGAEVSYTREHEENFIHMNOIARS
EPWDEEEEAUSRFPEALSYIBMMSAAIYTROINBNSYEOKNME
CCOOLUEDRYADMECRSAOEAECSNEHEWFNTLHONRDISBA
EYFOUOURTSSSPSTEOLFDHIFEELWEOHTIRETDHIWREAEIA
SNVVABKLRIEYMSHNEEEGANIRONPECLHFITNUFAAOIRNG
HCRBKOTAEHEUCKRGNNLSDEIAIMNTAGKSSMICELSOOTO
EFDLNTGHIIENNNIDMNNAAABSOYTETNNDEWOIRYOWWN
HLSLDIEAGYNECSHOCMTNETOSHIMTIIEGNHLTOHFNETRI
NMSCBLUHLOSOWWSYOBSWULLWEATSRTWTOHDOEKLS
NBLDRIARHEITMIGSBIEETRMTNHTGOAIEIAMNDREAGBIA
OSNSFTYLEIOONTNGHTIOAIEDTIRESRWAYVAMDEBTFIAL
EAONNGRENSDTEHIONRCDLWOIANDRSWWUNRTCCHOAL
SHLRWIGDAEIPNAYMNOSOAETHRTEUSTALUGEGNGIALHV
EATRBTTYHAHUCGULHORNRACDLIACRMCMUAOCHORYN
OPCRONYNOO
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Kutztown University
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Vigenere Cipher
 Polyalphabetic

substitution
Use n randomly generated substitutions
 1st letter is encoded by 1st substitution alphabet
 2nd letter is encoded by 2nd substitution alphabet
. . .
 nth letter is encoded by nth substitution alphabet
 n+1st letter is encoded by 1st substitution alphabet
 etc.
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Vigenere – Simple Example
Key = 3752
 Successive letters are shifted by 3, 7, 5, 2
 Plain text – BOOKKEEPINGROCKS
 Cipher text – EVTMNLJRLULTRJPU
 Eliminates double letters
 Scatters N-grams

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Kutztown University
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Vigenere Cipher

Advantages
 Creates confusion
 Same letter can be encoded n different ways
 Pretty much eliminates n-grams
 Keyspace > 26!
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Kutztown University
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Vigenere Cipher
 le
chiffre indéchiffrable
 Named for Blaise de Vigenère
 Invented by Giovan Battista Bellaso
ca. 1550
 Broken by
 Charles Babbage in 1854 (unpublished)
 Major Friedrich Kasiski in 1863
» Prussian infantry office
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Kutztown University
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Vigenere Cipher – Example
T KRCS L GILOX WYHH ZQV KOJ WYPG YDKPCY ZZSZ CLJL IA DEK ZTYV VIE WYL HCXV
TSLQZUU ZI ZAG NUVLR: "HH YVZO WYLGP WIBHSV KV PP VVST-PYZKSYW: KOOE DCS
APQ RYS NUVHHPG VXILO."
Z OOGH R KFPDD AVLW FUS ODP VB EKV YSO KZSZD RW NSZUXPO EKV ZCYV FM TZUDLF
DORCSD DEK HSH JVBD RW MCCPVY GWDML CHQVYG HLCS PP DSSS ER JPH ORNU
HZJVAVPU RA HSH KHPWH FM PCRKOSCKFVR.
T KRCS L GILOX WYHH ZQV KOJ HMLB EKV ZHLWV VT XLJZWDVZWDT, D JAOEH
JDSWWVYWYJ NPHS WYL VPDK VT TQABGELTL, GHHCASCLEN KTWY AVP KVHH ZI
FWDCHJZWZQ, NPZW EV AFLQJMCCPVK WYWF HB ZDJPG ZI WYSPGFT OYG ABGELTL.
W SDML O OUVHA EKRA AJ IFBF WLKAZP FYPZOUVU KTOC VBP GRF ZTYV PB L QRAWZQ
NOSCH KOSJ ZZSZ YRK IS UXUNSO EP AVP FFSCC RW AVPLI ZYTQ SBH MB KOS
NREASYW FM HSHZY QSDIHQEHI.
P VLYV H RCHRT HZGRF.
W SDML O OUVHA EKRA CYH UHM, ORNU WY DCHPLPR, DWEK ZAG GLTPCFV IHQTVKZ,
KTWY PHD JFCSCQFY VLYZUU SLJ SWAV UYWASZUU HLKO HSH NVFOV FM
WYWVYDZVZAWZQ RUR YXCSWQLTHHTRE; VBP GRF FTJYA HSHIL WY DCHPLPR,
SWEWCL PWDTR PZBJ HBO ECHQV JZYZD ZZSZ MH RIZP WF QCTQ YHBOV NPHS
OZAHWH NOWEH SVMD DEK KSLKL UTUCZ OD VZZHPUJ HBO EIVHSHIZ.
W SDML O OUVHA ERUHM.
T KRCS L GILOX WYHH ZQV KOJ HMLFJ YRSZPB JOOWO SL SIDCASO, HMLFJ KZSZ LQU
TCFQKHWY VYHZW EV TOOH
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Kutztown University
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Vigenere Cipher – Example Analysis
TKRCSLGILOXWYHHZQVKOJWYPGYDKPCYZZSZCLJLIADEKZTYVVI
EWYLHCXVTSLQZUUZIZAGNUVLRHHYVZOWYLGPWIBHSVKVPPVVST
PYZKSYWKOOEDCSAPQRYSNUVHHPGVXILOZOOGHRKFPDDAVLWFUS
ODPVBEKVYSOKZSZDRWNSZUXPOEKVZCYVFMTZUDLFDORCSDDEKH
SHJVBDRWMCCPVYGWDMLCHQVYGHLCSPPDSSSERJPHORNUHZJVAV
PURAHSHKHPWHFMPCRKOSCKFVRTKRCSLGILOXWYHHZQVKOJHMLB
EKVZHLWVVTXLJZWDVZWDTDJAOEHJDSWWVYWYJNPHSWYLVPDKVT
TQABGELTLGHHCASCLENKTWYAVPKVHHZIFWDCHJZWZQNPZWEVAF
LQJMCCPVKWYWFHBZDJPGZIWYSPGFTOYGABGELTLWSDMLOOUVHA
EKRAAJIFBFWLKAZPFYPZOUVUKTOCVBPGRFZTYVPBLQRAWZQNOS
CHKOSJZZSZYRKISUXUNSOEPAVPFFSCCRWAVPLIZYTQSBHMBKOS
NREASYWFMHSHZYQSDIHQEHIPVLYVHRCHRTHZGRFWSDMLOOUVHA
EKRACYHUHMORNUWYDCHPLPRDWEKZAGGLTPCFVIHQTVKZKTWYPH
DJFCSCQFYVLYZUUSLJSWAVUYWASZUUHLKOHSHNVFOVFMWYWVYD
ZVZAWZQRURYXCSWQLTHHTREVBPGRFFTJYAHSHILWYDCHPLPRSW
EWCLPWDTRPZBJHBOECHQVJZYZDZZSZMHRIZPWFQCTQYHBOVNPH
SOZAHWHNOWEHSVMDDEKKSLKLUTUCZODVZZHPUJHBOEIVHSHIZW
SDMLOOUVHAERUHMTKRCSLGILOXWYHHZQVKOJHMLFJYRSZPBJOO
WOSLSIDCASOHMLFJKZSZLQUTCFQKHWYVYHZWEVTOOHCVKEKVYC
FJYWZLFVZKTOCISXDULDWDZUOYGKOSNUFVYPGGSONHJDWWOSLA
LGVZHCDZNVEDEKHSHXSCCBFMHSHCVFOVYHZWEVYSGHRSSODEKO
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Kutztown University
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Vigenere Cipher – Example Analysis
TKRCSLGILO
XWYHHZQVKO
JWYPGYDKPC
YZZSZCLJLI
ADEKZTYVVI
EWYLHCXVTS
LQZUUZIZAG
NUVLRHHYVZ
OWYLGPWIBH
SVKVPPVVST
PYZKSYWKOO
EDCSAPQRYS
NUVHHPGVXI
LOZOOGHRKF
PDDAVLWFUS
ODPVBEKVYS
OKZSZDRWNS
ZUXPOEKVZC
YVFMTZUDLF
DORCSDDEKH
SHJVBDRWMC
CPVYGWDMLC
HQVYGHLCSP
PDSSSERJPH
ORNUHZJVAV
PURAHSHKHP
WHFMPCRKOS
CKFVRTKRCS
LGILOXWYHH
ZQVKOJHMLB
EKVZHLWVVT
XLJZWDVZWD
TDJAOEHJDS
WWVYWYJNPH
SWYLVPDKVT
TQABGELTLG
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Kutztown University
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Vigenere Cipher – Example Analysis
HHCASCLENK
TWYAVPKVHH
ZIFWDCHJZW
ZQNPZWEVAF
LQJMCCPVKW
YWFHBZDJPG
ZIWYSPGFTO
YGABGELTLW
SDMLOOUVHA
EKRAAJIFBF
WLKAZPFYPZ
OUVUKTOCVB
PGRFZTYVPB
LQRAWZQNOS
CHKOSJZZSZ
YRKISUXUNS
OEPAVPFFSC
CRWAVPLIZY
TQSBHMBKOS
NREASYWFMH
SHZYQSDIHQ
EHIPVLYVHR
CHRTHZGRFW
SDMLOOUVHA
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Kutztown University
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Deciphering Vigenere

Determine the number of alphabets
 Compute distances between matching sequences
 Compute GCD of distances


Treat cipher text as n separate texts
For each separate text & each of 25 possible shifts
 Compute Index of Coincidence
 based on frequencies found in cipher text
 using table of frequencies of letters in English

Index of Coincidence formula
 fee = S {relFreqTab(k, ciphLet) *
charFreq(ciphLet)}
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Kutztown University
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Frequency Table – English
A 0.08; B 0.015; C 0.03; D 0.04; E 0.13;
F 0.02; G 0.015; H 0.06; I 0.065; J 0.005
K 0.005; L 0.035; M 0.03; N 0.07; O 0.08
P 0.02; Q 0.002; R 0.065; S 0.06; T 0.09
U 0.03; V 0.01; W 0.015; X 0.005; Y 0.02
Z 0.002
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Vigenere – Final Step

Produce possible plain texts
 using combination of
 highest ranking fee table values


Choose best plain text
This step can be automated
 Rate each possible plain text
 using n-gram information
 or list of 5 letter words in English
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Kutztown University
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Vernam Cipher

Gilbert Sandford Vernam – inventor
 Also known as one-time pad
 Invented ca. 1919

Proven unbreakable by Claude Shannon
 Communication Theory of Secrecy Systems
 1949

Unbreakable if and only if
 Key is same length as plain text
 Key is never re-used
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Vernam Cipher
Basic operation – bitwise XOR
 XOR table

 0 xor 0 = 0
 0 xor 1 = 1
 1 xor 0 = 1
 1 xor 1 = 0
Plain text is represented as bit stream
 Key is random bit stream of same length
 Cipher text is produced via bitwise XOR of
plain bit stream and key bit stream.

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Vernam Cipher – Example
Plain text :: Grade = A – Great!
 Plain text in ASCII

 71 114 97 100 101 32 61 32 65 32 45 32
71 114 101 97 116 33

Plain text as bit stream
01000111 01110010 01100001 01100100
01100101 00100000 00111101 00100000
01000110 00100000 10010110 00100000
01010011 01101111 01110010 01110010
01111001 00100001
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Vernam Cipher – Example

Key as bit stream
11000001 01110000 11011110 10111001 01100001
10001000 01101100 11111010 00110011
01001110 01111001 00011110 00001000 10010001
10100100 01000000 10000000 01000010

Cipher text as bit stream
10000110 00000010 10111111 11011101 00000100
10101000 01010001 11011010 01110010
01101110 01010100 00111110 01001111 11100011
11000001 00100001 11110100 01100011
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Kutztown University
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Vernam Cipher – Why Unbreakable
Try attack by exhaustive search
 Among possible keys

11000001 01110000 11011110 10111001
01100001 10001000 01101100 11111010
00110100 01001110 01111001 00011110
00011100 10001100 10110011 01010011
10001101 01000010
Produces this recovered plain text:
 Grade = F – Sorry!

2008
Kutztown University
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Vernam Cipher – Why Unbreakable
Exhaustive search will produce every
possible combination of 18 characters.
 And there is no way to distinguish between
them
 Among the possible recovered texts:

 Tickle me Elmo now
 Jabberwocky Rocks!
 Attack tomorrow am
 Attack tomorrow pm
 Grade = C++ & Java
2008
Kutztown University
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Vernam Cipher – Why Look
Elsewhere?

Key distribution problem
 Every sender/recipient must have same pad
 N sender recipient pairs require O(N2) pads
 Pad distribution is security risk

Key coordination problem
 Sheets on pad must match exactly
 Messages must arrive in order sent

Key generation problem
 High quality random numbers hard to generate

Bottom line – has some limited use
2008
Kutztown University
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