In Lectures 11-12, we continue our course schedule with a studyof fascinating cipher systems known as the "Viggy" based onmultiple alphabets - Polyalphabetic Substitution systems.
We will continue developing our subject via an overview basedon the Op-20-GYT course notes (Office of Chief Of NavalOperations, Washington) [OP20]. We will revisit polyalphabeticcipher systems using Friedman's detailed analysis. We willcover the Viggy, Variant, PORTA systems and other familymembers. [FRE4], [FRE5], FRE6], [FRE7], [FRE8]. We will takematerial from ACA's Practical Cryptanalysis Volume V by WilliamG. Bryan on "Periodic Ciphers - Miscellaneous: Volume II"[BRYA] and Sinkov's [SINK] text to discover Viggy's secrets.We will look at [ELCY's] treatment of these systems.
In Lecture 12, we will describe the difficult aperiodicpolyalphabetic case and give a diagram of topics considered inLectures 10 - 12. [FR3] We will complete the Viggy family.I will also cover decimation processes in detail.
I have again updated our Resources Section with many referenceson these systems - focusing on the cryptanalytic attack andareas of historical interest. Kahn has some wonderful storiesabout the Viggy family. [KAHN]
In Lectures 1- 10, I have purposely stayed away from theheavier mathematics of cryptography (subject to change).Everything I am presenting can and has been reduced tomathematical models and computerized for ease of work. For myreaders who can not live without the math diet, there areplenty of guru' s like [SCHN] and [SCH2] to have breakfastwith. There are plenty of computer aids at the Crypto Drop Boxto help you do the setup work.
BUT those who embark on a course of "only the computer" do thiswithout knowing the real effort -the brain power - theshortcuts - the tradecraft - the historical implications, inmy opinion, have lost the real heart of Cryptography. The "ahha's" of inspiration are what make the difference. First, thereis a fundamental problem in that computer models do not applyto all variant cases. Simple changes to the system can fooleven the most adept computer program. For example, placingclever nulls will defeat many a statistical based model.
Second, we lose the sense of urgency that was required forwartime cryptography. If President Kennedy's Playfair message[that's right it was not English as in the movie PT-109] onthe back of a coconut had been intercepted and deciphered bythe Japanese [which they very capable of doing], we might nothave had the graceful light of his Presidency or who knows themoon landings. As another case in point, the solution ofENIGMA during the mid - final Atlantic Campaigns of World WarII, reduced the operational effectiveness of the U-Boat to oneday and hence saved allied tonnage and warships supplingEurope. The American and British Crypee's 'thought' more liketheir German counterparts than their counterparts. Computersolutions were bulky, machine dependent [the solution "stops"]and not reliable until 1945. People made the difference.
There are three fundamental steps to solve a Periodic cipher.
Step one is finding the period. Bryan reminds us that thereare at least two ways to find the period. The short approachmakes use of the distances between patent cipher textrepetitions and factors the differentials. The long approachis used when there are no patent repetitions to factor. Inthis case we set up a possibilities matrix and factor everycombination looking for the highest probable common factor.[BRYA]
As an example of the first case take:
10 20 30 40BGZEY DKFWK BZVRM LUNYB QNUKA YCRYB GWMKC DDTSP 50 60 70 80OFIAK OWWHM RFBLJ JQFRM PNIQA VQCUP IFLAZ HKATJ 90 100 110 120UVVQE EKESZ DUDWE KKESL IZQAT SBYUZ UUVAZ IXYEZ 130 140JFTAJ EMRAS QKZSQ FOPHM W.We tabulate the repetitions and the cipher text letterdifferences between repetitions.
Delta FactorsBG 29 -RM 45 3,5,9KA 53 -MR 77 7,11QA 39 3,13VQ 17 -AZ 40 4,5,8,10AT 26 13UV 31 -EK 9 3,9KES 10 5,10 .... this trigraph more importantSQ 4 4 than QA or AT digraphs. Suggest that the period is either 5 or 10. Practice dictates that the larger number is the proper.But suppose there are no repeats or those that do exist do notestablish a period. What then?
Given: 10 20 30 40RNQJH AUKGV WGIVO BBSEJ CRYUS FMQLP OFTLC MRHKB 50 60 70 80BUTNA WXZQS NFWLM OHYOF VMKTV HKVPK KSWEI TGSRB 90 100 110 120LNAGJ BFLAM EAEJW WVGZG SVLBK IXHGT JKYUC HLKTUMWWK.We set up the following vertical tally. We note theactual position of every letter.
Table 11-1 3 4 5 6 7 8 9 10 11 12 -------------------------------A 3 1 1 1 1 1 2 1B 9 7 4 5 3 7 4 2 1 2C 1 1 1 1 1DE 1 1 1 1 1 1 1F 2 3 3 1 2 1 1 1 1G 5 5 4 1 4 3 2 1 3 1H 6 3 2 2 3 1 1 2 1I 1J 3 1 2 1 1 1 3 1K 13 10 4 9 8 5 3 1 2 3L 4 3 4 1 4 1 3 1 2M 4 2 3 2 6 3 1 1N 1 1 1 1 3 1 1O 1 3 1 1 1 1P 1Q 1 1 1R 5 1 1 3 2 1 1S 4 4 2 3 2 1 1 1 1T 4 3 1 1 2 1 1 2 2U 5 1 2 5 1 2 3 1 2 2V 5 6 2 2 1 2 3 1 1W 9 4 5 3 8 1 4 4 3 1XY 2 2 3 2 1 2 1 3 1Z 1 --------------------------------- 87 61 47 43 57 30 35 21 25 16 Columns totalX 3 4 5 6 7 8 9 10 1 112 times period ---------------------------------- 261 244 235 258 399 240 315 210 275 192 Total ===The period is 7.
The Viggy (or more correctly the Vigenere) Family is group ofciphers. Included in this group are: Vigenere, Variant,Beaufort, Gronsfeld, Porta, Portax, and Quagmires I-IV.Other ciphers may be included in the group. They are NihilistSubstitution, Auto - Key, Running Key and Interrupted ciphers.Bryan includes the Tri-square, the periodic FractionatedMorse, the Seriated Playfair and the Homophonic in the sameclass of ciphers.
These ciphers were invented at different times by differentauthors, sometimes with confusion of authorship, and indifferent countries. They are similar in that they representpermutations of the same cryptographic concept and can becracked with the same general methodology, albeit with slightvariations in procedure. What is also interesting is thatthese ciphers can be viewed in tableaux form, in slide form ormatrix form.
The theory of polyalphabetic substitution is simple. Theencipherer has at his disposal several simple substitutionalphabets, usually 26. He uses one such alphabet to encipheronly one letter, another alphabet for the second letter,and so forth, until some preconcerted plan has been followed.The earliest known ciphers of this kind, the Porta (1563), theVigenere (1586) used tableau's for encipherment, in which allthe alphabets were written out in full below each other. TheGronsfield (1655) had a mental key, and the Beaufort (1857)which came two hundred years later, again used the tableaux.The process was reduced to strips or slides in 1880 at theFrench military academy of Saint-Cyr. The polyalphabeticdeciphering slides now bear that name. [ELCY]
To know thoroughly any of these ciphers is to understand thefundamental principles of all. Lets look at the papa bear.
The father of the Viggy family is the Vigenere Cipher. Likemost of the periodic ciphers, the 'Viggy' is actually a seriesof monoalphabetic substitutions such as Aristocrats, and sincea keyword is used, under each letter of the keyword, there is aseparate simple substitution cipher - each one different- using all the letters, in such a manner, that the resultingcipher is a combination of several such substitutions.
Attributed to Blaise de Vigenere, the cipher named for him wasinvented by him in 1586. In his "Traicte des Chiffres"he did invent an autokey system which used both a priming keyand did not recommence his plaintext key with each word, butkept it running continuously. He described a second autokeysystem which was more open but still secure. Both systems wereforgotten and were re-invented in the 19th century. Historianshave credited Vigenere with the simpler polyalphabeticsubstitution system. Legend grew around this cipher that itwas "impossible of translation" as late as 1917. [KAHN]
The original Viggy was composed of an enciphering anddeciphering tableaux. Letters were enciphered and decipheredone letter at a time. The modern Vigenere tableaux isshown in Figure 11-1.
Figure 11-1 a b c d e f g h i j k l m n o p q r s t u v w x y zA A B C D E F G H I J K L M N O P Q R S T U V W X Y ZB B C D E F G H I J K L M N O P Q R S T U V W X Y Z AC C D E F G H I J K L M N O P Q R S T U V W X Y Z A BD D E F G H I J K L M N O P Q R S T U V W X Y Z A B CE E F G H I J K L M N O P Q R S T U V W X Y Z A B C DF F G H I J K L M N O P Q R S T U V W X Y Z A B C D EG G H I J K L M N O P Q R S T U V W X Y Z A B C D E FH H I J K L M N O P Q R S T U V W X Y Z A B C D E F GI I J K L M N O P Q R S T U V W X Y Z A B C D E F G HJ J K L M N O P Q R S T U V W X Y Z A B C D E F G H IK K L M N O P Q R S T U V W X Y Z A B C D E F G H I JL L M N O P Q R S T U V W X Y Z A B C D E F G H I J KM M N O P Q R S T U V W X Y Z A B C D E F G H I J K LN N O P Q R S T U V W X Y Z A B C D E F G H I J K L MO O P Q R S T U V W X Y Z A B C D E F G H I J K L M NP P Q R S T U V W X Y Z A B C D E F G H I J K L M N OQ Q R S T U V W X Y Z A B C D E F G H I J K L M N O PR R S T U V W X Y Z A B C D E F G H I J K L M N O P QS S T U V W X Y Z A B C D E F G H I J K L M N O P Q RT T U V W X Y Z A B C D E F G H I J K L M N O P Q R SU U V W X Y Z A B C D E F G H I J K L M N O P Q R S TV V W X Y Z A B C D E F G H I J K L M N O P Q R S T UW W X Y Z A B C D E F G H I J K L M N O P Q R S T U VX X Y Z A B C D E F G H I J K L M N O P Q R S T U V WY Y Z A B C D E F G H I J K L M N O P Q R S T U V W XZ Z A B C D E F G H I J K L M N O P Q R S T U V W X YThe normal alphabet at the top of the tableaux is for plaintextand the keyletters are shown at the extreme left under the 'A'of the top row. Where the two lines intersect in the body ofFigure 11-1, the ciphertext is found.
For example using the keyword TENT, we encipher "COME AT ONCE"
We have: TENT TENT ---- ---- COME VSZX (ciphertext) ATON TXBG CE VI--The enciphering and deciphering problem are done as a group ofletters to improve speed and accuracy of the process.
Another way to look at this is that the Viggy is really a twodimensional slide problem. We can construct (or purchase forabout $2.00 from ACA) a set of two Saint-Cyr slides thatoperate the same way as the tableaux shown in Figure 11-1.What is useful is that each slide bears the standard normalalphabet from A-Z with high frequency letters colored orshaded. Each slide is a double-alphabet to allow flexibility.
Figure 11-2 ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ GHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEF * *Figure 2 shows the Saint- Cyr slide at a key of G. Check withFigure 11-1 to see that the results are the same for Nplain =Tcipher or Iplain = Ocipher.
The practical use of the Saint Cyr slide is that the wholecolumn of plaintext is enciphered as a unit. So C A C would beenciphered as V A V, plaintext O T E becomes S X I, etc.This eliminates mistakes. The cipher is taken off in 5 lettergroups by rows, so we would have VSZXT XBGVI for our previousexample.
Friedman points out that the sliding components produce thesame type of cipher with the circular disks like the old U. S.Army version. [FRE7]
Koblitz [KOBL] describes the Viggy as follows:
Konheim's description is worse than Koblitz's. [KONH]
Seberry and Pieprzyk describe the Viggy as made up ofkey sequence k= k1...kd where ki , (i=1,d) gives the amount ofshift in the ith alphabet, fi(a) = a+ki(mod n) and theciphertext is described as fi**(-1) = (ki -c) mod n so that:
Does it matter with the Viggy, that we encipher S by B (Balphabet or Key B) to find cipher T or encipher B by S (Salphabet or Key S) to find T? No. This is an interestingcharacteristic not shared by all in the Viggy family. It maybe its downfall.
For instance, the message:
Key : BEDB EDBEDBED BE DBEDBED BEDBEDBPlain : SEND SUPPLIES TO MORLEYS STATIONCipher: TIQE WXQTOJIV US PPVOFCV TXDUMROThe modern Saint-Cyr slide encipherment of the above would be:
Key B E D B E D B E D Plain S E N D S U P P L Cipher T I Q E W X Q T O I E S T O M O R L J I V U S P P V O E Y S S T A T I O F C V T X D U M R N Owhich gives: 5 10 15 20 25T I Q E W X Q T O J I V U S P P V O F C V T X D U 30M R O X X (two ending nulls and a bad choice at that)With the Saint Cyr slide, we would encipher S, I, E, N; thenD, T, S, and finally P, O , T by setting the B key on thebottom slide under the A key of the top slide and reading offthe equivalents. [SINK], [ELCY]
Refer to Figure 11-3:
Figure 11-3Deciphering with the Key:Key : B E D B E D B E D B E D ........Cipher: T I Q E W X Q T O J I V ........Plain : S E N D S U P P L I E S ........Deciphering with the Message:Plain : S E N D S U P P L I E S ........ (trial key)Cipher: T I Q E W X Q T O J I V ........Key : B E D B E D B E D B E D ........ (true key)Figure 11-3 indicates a possible solution method. The messagefragment works well as a trial key, and if applied in thesame manner as the true key, the true original key will berevealed. The Vigenere Cipher works equally well in reverse.It is this peculiarity that portends the use of a probable wordattack.
Suppose we have the cryptogram:
U S Z H L W D B P B G G F S ...in which we suspect the presence of the word SUPPLIES.We decipher the first 8 letters using this probable word as atrial key, and obtain the jumbled series: C Y K S A O Z J,which is unsatisfactory. We next drop the first U, and obtaingroup : A F S W L V X X. We fail again on the third andfourth trials. The fifth decipherment obtains the seriesTCOMETCO. We see the TCO repeats and the key word COMET.[ELCY]
F. R. Carter of the ACA shows us a more organized approach inFigure 11-4:
Figure 11-4Cryptogram Fragment: U S Z H L W D B P B G G F S ......Probable Word: * S C A H P T E L J X J O O N A U Y F N R C J H V H M M L Y P K S W H O M A M R R Q D P S W H O M A M R R Q D L A L S Q E Q V V U H I O V T H T Y Y X K E Z X L X C C B O S O *Look down at an angle between the stars to find the key wordCOMET. The first letter S was used to decipher every possiblekey letter which can produce S. The entire row of equivalentswere produced at the same time. The resulting rows ofdecipherment indicate all the possible keyletters that couldproduce S, then U, then P, and so on. Carter actuallyshortened the procedure to three full rows and then partialsthereafter. He assumes that the keyword is readable anddiscards non readable text.
For the case where we have no probable word or the sequence isvery short, we may use Ohaver's Trigram Method. We start witha list of usual trigrams THE, AND, THA, ENT, ION, TIO. The keyfragments deciphered by these will be short and numerous, somecorrect and some incorrect to bring out the repeating keysequence. A secondary worksheet is used to test the variousfragments as keys. If any one of them is a fragment of theoriginal key, it must bring out fragments of plaintext atregular intervals.
A scheme like Carters can be used with the trigrams THE, AND..replacing the word SUPPLIES. Refer to Figure 11-5.
Given: 10 20 26 L N F V E O L N V M R N G Q F H H R N H I R V F E BThe cipher text is only 26 letters long. Every letter exceptthe final two might begin a cipher trigram. So we have 24cipher trigrams. Write them out in full on two worksheets.
Figure 11-5ION Trial 1 LNF NFV FVE VEO EOL OLN LNV NVM VMR MRN RNG NGQ AZS FRI XHR NQB WAY GXA DZI FHZ NYE EDA JZT FSD --- GQF QFH FHH HHR HRN RNH NHI HIR IRV RVF VFE FEB YCS IRU XTU ZTE ZDA ZJU FTV ZUE ADI JHS NRR XQOEDA Trial 2 LNF NFV FVE VEO EOL OLN LNV NVM VMR MRN RNG NGQ HKF JCV BSE RBO ALL KIN HKV JSM RJR ION NKC JDQ --- GQF QFH FHH HHR HRN RNH NHI HIR IRV RVF VFE FEB CNF MCH BEH DER DON NKH JEI DFR EOV NSF RCE BBBTrial 1 tests for THA, THE, AND fail but ION gives us FRI andWAY. But anyone of these 24 decipherments on the second rowmight be a fragment of the original key. Trial 2 fails toconfirm FRI or WAY but test of key-fragment EDA yields ION.If this sequence is actually a portion of the original key,then the plaintext will be brought out at some constantdistance apart. The point we found the trigram is the tenthcryptogram letter; that is every trigram presents only one newletter so to find a completely different trigram in eitherdirection, we must count backwards or forwards a distance ofthree trigrams.
Beginning at the tenth trigram we examine every third trigramin both directions. The following is found: HKF, RBO, HKV,ION,CNF, DER,JEI, NSF. These are incoherent. This would beequivalent to a period of three - not likely. Try every fourthdecipherment: JCV,KIN,ION,MCH,NKH,NSF. Not usable for aconsecutive sequence, continuously written cryptogram.Trying the decipherments at a proposed period of 5, we get ALL,ION, BEH, DFR. This possibility is good. We try todecipher the T before ION and get the letter C. We now havefour letters in our key C E D A. With a little anagraming wehave the word D A * C E. A probable word FRIDAY comes to mind.
William G. Bryan shows us how to use the high frequency letterson the Saint-Cyr slide to good use.
Given the Viggy with a known period of 7 based on a similareffort used in Table 11-1:
PXIZH GVGEU UOXIX MYEEJ ZCOCM OWZCL FMTOR ISIGH LKWPSMSIDX WCFBR KPYXO PRJIL HFMCR IHUDU LVRLJ FVVVS HTYFRRGPHQ WIIBL XQXMM TDVGU EITFM QEEJH WUHFW.We reset the problem in groups of 7: 1234567 PXIZHGV GEUUOXI XMYEEJZ COCMOWZ CLFMTOR ISIGHLK WPSMSID XWCFBRK PYXOPRJ ILHFMCR IHUDULV RLJFVVV SHTYFRR GPHQWII BLXQXMM TDVGUEI TFMQEEJ HWUHFWNow each column represents a separate simple substitutioncipher. They will not produce consecutive plaintext, butmerely show isolated letters in that particular substitution,to be coupled with those letters that fall on either side inother substitutions, to make a true plain text sequence. Here'swhere the underlined high-frequency letters on the slide comein:
We go down column 1 and tabulate all the letters whichappear more than once. P-2, G-2, X-2, C-2, I-3, T-2. Werearrange them in their normal sequence = C G I P T X.The lower slide is moved successively so that the first letterC is under the high frequency letters, in turn, A E H I N O R ST, and a reading is made of the number of 'hits' , the numberof other cipher text letters G I P T X that fall below the highfrequency letters. If they do then the letter under A of thetop slide is the key letter for that column. If they don'tfurther trials are necessary.
High frequency letters don't always show up. Some times mediumfrequency letters may be required. So with C under A: G-E, I-G,P-N, T-R, X-V; With C under E:G-I, I-K, P-R, T-V, X-Z; With Cunder the H: G-L, I-N, P-U, T-Y, X-C; with C under the I: G-M,I-O,P-V, T-Z, X-D; and with C under the N: G-R, I-t, P -A, T-E, X-I (six hits); and we have found the setting. So we set Punder the A in the top slide, and decipher the entire column AR I N N T H I A T T C D R, and write it into a blank column ascolumn 1.
Proceeding with Column 2, we have no results. Column shows 2passable results at P and U, Column 4 seems to go with Y,column 5, setting B has 4 hits, Column 6 has 5 hits indicatingan E, and Column 7, R gives six hits.
The keyword thus recovered is P P Y B E R. We choose todecipher the ending B E R as the ending of a keyword toproduce:
B E R ----- G C E N T R O F I N S I S K A G H T R E M A N T O N S L Y A T H E U R E E N A V E R W I V T A R D A S E S -These are almost all good fragments. The GHT must have an I orU before it. Since cipher letter G is involved, we place the Gunder the I which results in the Y we already had and putting Gunder the U gives us M under the A, we choose the latter.
Now we have MBER has a key fragment. Deciphering column 4with M adds N I I S A A U A T C T R T M E E U E V to theevidence.
There are several possibilities NGCE preceded by an O, UGHTpreceded by an O, TANT preceded by an OR; TLYA preceded by anN; UTAR preceded by an O or A; and EWIV preceded by R/H.
With the Viggy cipher, remember to read the setting for thekeyword letter below the A of the Stationary slide; and theplain text appears on the same slide as this A, while thecipher text is in the lower slide.
At this juncture, I wondered how our Viggy solver at the CDBwould do on this problem. I brought up my faithful computerprogram and entered the cipher text into Vigenere.exe withouttelling it the period and found the following:
We have seen that equivalents obtainable from use of squaretables may be duplicated by slides or revolving disks [FR2],[FR7] or computer models. Cryptographically, the results maybe quite diverse from different methods of using suchparaphenalia, since the specific equivalents obtained from onemethod may be altogether different from those obtained fromanother method. But from the cryptanalytic point of view thediversity referred to is of little significance.
There are, not two, but four letters involved in every case offinding equivalents by means of sliding components;furthermore, the determination of an equivalent for a givenplaintext letter is represented by two equations involving fourequally important elements, usually letters.
Consider this juxtaposition:1. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z2. F B P Y R C Q Z I G S E H T D J U M K V A L W N O XQuestion - what is the equivalent of Pplain when the Key letteris K? Answer - without further specification, the cipherequivalent can not be stated. Which letter do we set K againstand in which alphabet? We have previously assumed that the Kcipher would be put against A in the plain. But this is only aconvention.
Figure 11-6 Index Plain * * 1. Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ 2. Cipher:FBPYRCQZIGSEHTDJUMKVALWNOXFBPYRCQZIGSEHTDJUMKVALWNOX * * Key CipherWith this setting Pplain = Zcipher.
The four elements are:
(I) Kk = A1 ; Pp = Zc k=key, p=plain, c=cipher, 1= initialThere is nothing sacred about the sliding components. ConsiderFigure 11-6b.
Figure 11-6b Index Cipher * *1. Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ2. Cipher:FBPYRCQZIGSEHTDJUMKVALWNOXFBPYRCQZIGSEHTDJUMKVALWNOX * * Key Plainthus (II) Kk = A1; Pp = KcSince equations (I) and (II) yield different results even withthe same index, key and plain text letters, it is obvious thata more precise formula is required. Adding locations to theseequations does the trick.
(I) Kk in component (2) =A1 in component (1); Pp in component (1) = Zc in component (2).(II) Kk in component (2) =A1 in component (1); Pp in component (2) = Zc in component (1).In shorthand notation: (1) Kk/2 = A1/1; Pp/1 + Zc/2 (2) Kk/2 = A1/1; Pp/2 + Zc/1Employing two sliding components and four letters impliestwelve different resulting systems for the same set ofcomponents and twelve enciphering conditions. Theseconstitute the Viggy Family:
Table 11-2(1) 0k/2=01/1; 0p/1=0c/2 (7) 0k/2=0p/1; 01/2=0c/1(2) 0k/2=01/1; 0p/2=0c/1 (8) 0k/2=0c/1; 01/2=0p/1(3) 0k/1=01/2; 0p/1=0c/2 (9) 0k/1=0p/2; 01/1=0c/2(4) 0k/1=01/2; 0p/2=0c/1 (10) 0k/1=0c/2; 01/1=0p/2(5) 0k/2=0p/1; 01/1=0c/2 (11) 0k/1=0p/2; 01/2=0c/1(6) 0k/2=0c/1; 0p/1=0p/2 (12) 0k/1=0c/2; 01/2=0p/1The first two equations (1) and (2) define the Vigenere type ofencipherment and are widely used. Equations (5) and (6) definethe Beauford type and Equations (9) and (10) define theDelastelle type of encipherment. [FR7]
I have said that the three steps in the cryptanalysis ofrepeating key systems are : 1) Find the length of the period,2) Allocate or distribute the letters of the ciphertext intotheir respective alphabets, thereby reducing the polyalphabetictext to monoalphabetic terms, and 3) analysis of the individualmonoalphabetic distributions to determine the plain text valuesof their cipher equivalents in each distribution or alphabet.
As a direct result of using a repeating key (no matter howlong) certain phenomena are manifested externally to thecryptogram. Regardless of what system is used, identical plaintext letters enciphered by the same cipher alphabet with singleequivalents must yield identical cipher letters. This happenseach time the same key letter is used to encipher identicalplaintext letters.
Since the number of columns or positions with respect to thekey are limited, and there is a normal redundancy in thelanguage, it follows that there will be in a message of fairlength many cases where identical plain text letters must fallinto the same column. This will be enciphered by the samecipher alphabet, resulting in many repetitions. There are twotypes of repetitions: causal and accidental (random)repetitions. The former we can trace back to the key. Thelatter occurs when different plaintext letters fall indifferent columns and by chance produce identical cipher textletters.
Accidental repetitions will occur frequently with individualletters, less frequently with digraphs (because the accidentmust occur twice in succession, much less in the case oftrigraphs and very much less in the case of a tetragraph.The probability of chance repetition decreases significantly asthe repetition increases in length. Friedman has developedstatistical tables based on the binomial and Poissondistributions to determine the individual and cumulativeprobabilities for expected number of repetitions in n lettertext to occur x or more times in samples of random text.
The use of these tables is important. They tell us whenwe are dealing with cryptographically maneuvered text versusrandom noise designed to fool the listener. They indicatewhat may be a hoax (Beale or Bacon - Shakespeare controversies)versus valid enciphered text.
Tables 11-3 to 11-6 show the above theory.
Table 11-3Number Expected Number of Digraphs Occurringof Exactly x TimesLetters E(2) E(3) E(4) E(5) E(6) E(7) E(8) E(9) E(10)--------------------------------------------------------------100 6.21 .298 .011200 21.8 2.12 .154 .009300 42.5 6.23 .683 .060 .004400 65.3 12.8 1.87 .220 .022 .002500 88.1 21.6 3.97 .582 .071 .008600 110. 32.3 7.11 1.25 .184 .023 .003700 129. 44.3 11.4 2.35 .403 .059 .008 .001800 145. 57.1 16.8 3.96 .777 .130 .019 .003900 158. 70.1 23.2 6.16 1.36 .257 .043 .006 .0011000 169. 83.0 30.6 9.03 2.21 .466 .085 .014 .002By way of illustration, of the use of these tables, from Table11-3, we obseve that in a sample of 300 letters of random text,we may expect 43 digraphs to occur twice, 6 digraphs to occurthree times and 1 digraph to occur four times. If we sum thevalues under E(2) through E(6) we have the cumulativeprobability in the 300 letter sample. The sum is 49.477, whichindicates that in a sample of 300 letters or so, 49 digraphswill occur two or more times.
Table 11-4Number Expected Number of Trigraphs Occurringof Exactly x TimesLetters E(2) E(3) E(4)--------------------------100 .269 .001200 1.10 .004300 2.48 .014400 4.40 .033500 6.85 .064600 9.81 .111 .001700 13.3 .175 .002800 17.3 .261 .003900 21.8 .371 .0051000 26.8 .505 .008
Table 11-5Number Expected Number of Tetragraphs Occurringof Exactly x TimesLetters E(2) E(3)--------------------------100 .010200 .043300 .096400 .171500 .270600 .389700 .530800 .693900 .8771000 1.08 0.001
Table 11-6Number Expected Number of Pentagraphs Occurringof Exactly x TimesLetters E(2)----------------100200 .002300 .004400 .007500 .011600 .015700 .021800 .027900 .0341000 .042
The second step in the solution of periodic ciphers is todistribute the cipher text into the component monoalphabets.The period once established tells us the number of cipheralphabets. By rewriting the message in groups corresponding tothe length of the key (period) in columnar fashion, weautomatically have divided up the text so that lettersbelonging to the same cipher alphabet occupy similar positionsin the groups or in the same columns.
If we make separate uniliteral frequency distributions for theisolated alphabets, each of these resulting distributions istherefore, a monoalphabetic frequency distribution. Were thisnot so, if they did not have the characteristic crest andtrough appearance including the expected number of blanks,if the observed values of Phi are not sufficiently close to theexpected value of Phi plain, or do not yield I.C.'s in theclose vicinity of the expected value, then the entire analysisis fallacious.
The I.C. values of these individual distributions may beconsidered an index of correctness of the factoring process.Both theoretically and practically, the correct hypothesis withrespect to these distributions will tend to conform moreclosely to the expected I.C. of a monoalphabetic frequencydistribution.
Friedman demonstrates the above with an example: [FR7]
Plaintext Message:The artillery battalion marching in the rear of the advanceguard keeps its combat train with it insofar as practical.Keyword BLUE using direct standard alphabets.Cipher AlphabetsPlain: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ---------------------------------------------------1. B C D E F G H I J K L M N O P Q R S T U V W X Y Z A2. L M N O P Q R S T U V W X Y Z A B C D E F G H I J K3. U V W X Y Z A B C D E F G H I J K L M N O P Q R S T4. E F G H I J K L M N O P Q R S T U V W X Y Z A B C D B L U E B L U E B L U E B L U E B L U E B L U E ... T H E A R T I L L E R Y B A T T I L I O N M A R ...Cipher TextUSYES ECPMP LCCLN XBWCS OXUVD SCRHTHXIPL IBCIJ USYEE GURDP AYBCX OFPJWJEMGP XVEUE LEJYQ MUSCX JYMSG LLETALEDEC GBMFIFriedman gives a useful formula for monographic I.C. of a 26character text:
I.C. = 26 sum f(f-1)/N(N-1) = Phi(o) / Phi (r)and since Phi (p) for English is 0.0667N (N-1)and Phi (r) = 0.0385 N ( N-1) where N is the total number ofelements in the distribution. I.C. for English plain = 1.73and 1.0 for random text. We may apply the I.C. test to thedistributions of periodic polyalphabetic ciphers to confirmthe monoalphabeticity of their character. This also confirmsthe period length and correctness. If the correct period isassumed, then the Phi test applied to each of the alphabetsshould approximate closely and consistently the value of Phi(p)and conversely, if the incorrect period is assumed, then thePhi(o) should approximate the value of Phi(r). Deviation fromthis hypothesis must be statistically significant. [FR7]
So we break down the four alphabets:
4 1 4 1 1 1 1 1 3 1 1 1 1 1 4 Phi =42A B C D E F G H I J K L M N O P Q R S T U V W X Y Z I.C.=1.681 2 4 1 2 1 4 4 1 1 2 2 Phi=44A B C D E F G H I J K L M N O P Q R S T U V W X Y Z I.C.=1.911 5 1 1 1 1 5 2 1 1 2 1 1 2 Phi=46A B C D E F G H I J K L M N O P Q R S T U V W X Y Z I.C.=1.99 1 6 2 2 1 1 1 1 2 2 1 1 3 1 Phi=44A B C D E F G H I J K L M N O P Q R S T U V W X Y Z I.C.=1.91It is seen that all these distributions are monoalphabeticsince their observed Phi's are closer to the Phi (p) = 40.rather than Phi (r) = 23. Any other period assumed at fouror a multiple of four, will not yield monoalphabeticdistributions.
In light of the foregoing principles, we now look at twoadditional cryptanalytic techniques for the Viggy family.The first compares the distributions to the normal and thesecond is very important - completing the plain-component.
Given message text A:
5 10 15 20 25A. A U K H Y J A M K I Z Y M W M J M I G X N F M L XB. E T I M I Z H B H R A Y M Z M I L V M E J K U T GC. D P V X K Q U K H Q L H V R M J A Z N G G Z V X ED. N L U F M P Z J N V C H U A S H K Q G K I P L W PE. A J Z X I G U M T V D P T E J E C M Y S Q Y B A VF. A L A H Y P O I X W P V N Y E E Y X E E U D P X RG. B V Z V I Z I I V O S P T E G K U B B R Q L L X PH. W F Q G K N L L L E P T I K W D J Z X I G O I O IJ. Z L A M V K F M W F N P L Z I O V V F M Z K T X GK. N L M D F A A E X I J L U F M P Z J N V C A I G IL. U A W P R N V I W E J K Z A S Z L A F M H SThe period is 5 and the I.C. confirms this hypothesis.
We make uniliteral frequency distributions for the 5 alphabetsto determine if we have standard alphabets.
Figure 11-70 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z1 W X Y Z A B C D E F G H I J K L M N O P Q R S T U V2 H I J K L M N O P Q R S T U V W X Y Z A B C D E F G3 I J K L M N O P Q R S T U V W X Y Z A B C D E F G H4 T U V W X Y Z A B C D E F G H I J K L M N O P Q R S5 E F G H I J K L M N O P Q R S T U V W X Y Z A B C DApplying these values to the first groups of our message:A U K H Y J A M K I Z Y M W M J M I G X N F M L XE N C O U N T E R E D R E D I N F A N T R Y E S TLook at the I.C.'s for these alphabets. The expected is1.73. The third alphabet is almost exact. Three alphabets seemlow and one is high or are they? Actually these deviations arewithin one sigma of the samples of these sizes 55 tallies, sothe deviations are not abnormal. The standard deviations maybe calculated with:
For plain text: Sigma (O) = Sqrt[ (0.0048)N**3 + (.1101)N**2- (.1149) N] Sigma(I.C.)= 26/(N-1)sqrt(N) * sqrt[ (0.0048)N**2 + (.1101)N- (.1149) ]The more important deviation is from random rather thanobserved: Sigma(Phi) = 0.2720 sqrt[ N (N-1)] Sigma(I.C.)= 7.0711/sqrt[N(N-1)] where: sqrt is the square root functionThe latter two equations apply to a 26 letter alphabet only.
Since simage is defined as a difference between the observedand the expected number, divided by the standard deviation, itmay be shown that the I.C. of Alphabet 1 is 1.44-1.00/.13 =3.38 sigma over random; for this type of distribution whichfollows the Chi squared distribution, this amounts to 1 chancein 300 of being random.
In the foregoing example, standard alphabets were used.We could easily of used reversed standard alphabets. The U.S.Army Cipher Disk produces just this type of cipher. It is knownas the Beaufort Cipher. The direction of the crests andtroughs is reversed when fitting the distributions to thenormal.
When direct standard alphabets are used we can mechanicallysolve the cipher by completing the plain component. The plaintext reappears on only one generatrix and this generatrix isthe same for the whole message. It is the only generatrix thatyields intelligible text. This same process can be modified towork with the alphabets of a Viggy. In this case the correctgeneratrix should be distinguishable from the others because itshows a more favorable assortment of high frequency letters,and thus can be selected by eye from the whole set ofgeneratrixes.
Using the previous example, we let the first ten cipher lettersin each alphabet be set down in a horizontal line and theassumption is made that the alphabets are direct standard withnormal sequences. See Figure 11-8.
We use the following selection rules:
Figure 11-8Gen./ Alphabet 1 Alphabet 2 Alphabet 3 Alphabet 4 1 AJZJNEZAIJ 2 UAYMFTHYLK 2 KMMIMIBMVU HKWGLMHZMT 2 BKAKOFABJK VBZNGUIZML LNNJNJCNWV 5 ILXHMNIANU 3 0 CLBLPGBCKL 4 WCAOHVJANM MOOKOKDOXW JMYINOJBOV 4 0 DMCMQHCDLM XDBPIWKBON 2 NPPLPLEPYX KNZJOPKCPW 5 * 7 ENDNRIDEMN YECQJXLCPO OQQMQMFQZY LOAKPQLDQX 6 7 FOEOSJEFNO ZFDRKYMDQP 7 PRRNRNGRAZ 3 MPBLQRMERY 7 2 GPFPTKFGOP AGESLZNERQ 7 QSSOSOHSBA NQCMRSNFSZ 8 HQGQULGHPQ 5 BHFTMAOFSR 6 RTTPTPITCB *8 ORDNSTOGTA 9 5 IRHRVMHIQR 4 CIGUNBPGTS SUUQUQJUDC 4 PSEOTUPHUB 10 JSISWNIJRS DJHVOCQHUT 4 TVVRVRKVED QTFPUVQIVC 11 KTJTXOJKST 4 EKIWPDRIVU 3 UWWSWSLWFE RUGQVWRJWD 12 LUKUYPKLTU FLJXQESJWV VXXTXTMXGF SVHRWXSKXE 13 MVLVZQLMUV GMKYRFTKXW 1 WYYUYUNYHG 3 TWISXYTLYF 14 4 NWMWARMNVW HNLZSGULYX XZZVZVOZIH UXJTYZUMZG 15 OXNXBSNOWX 4 IOMATHVMZY 5 YAAWAWPAJI VYKUZAVNAH 16 3 PYOYCTOPXY JPNBUIWNAZ ZBBXBXQBKJ 3 WZLVABWOBI 17 QZPZDUPQYZ KQOCVJXOBA 2 ACCYCYRCLK XAMWBCXPCJ 18 RAQAEVQRZA 1 LRPDWKYPCB BDDZDZSDML YBNXCDYQDK 19 5 SBRBFWRSAB MSQEXLZQDC *8 CEEAEATENM ZCOYDEZREL 20 4 TCSCGXSTBC *6 NTRFYMARED 2 DFFBFBUFON 4 ADPZEFASFM 21 2 UDTDHYTUCD 5 OUSGZNBSFE 2 EGGCGCVGPO 4 BEQAFGBTGN 22 4 VEUEIZUVDE 4 PVTHAOCTGF 0 FHHDHDWHQP 2 CFRBGHCUHO 23 2 WFVFJAVWEF 1 QWUIBPDUHG GIIEIEXIRQ 3 DGSCHIDVIP 24 XGWGKBWXFG RXVJCQEVIH HJJFJFYJSR EHTDIJEWJQ 25 YHXHLCXYGH SYWKDRFWJI IKKGKGZKTS FIUEJKFXKR 26 ZIYIMDYZHI TZXLESGXKJ 2 JLLHLHALUT GJVFKLGYLS Alphabet 5 1 YIMXXIRMEG 2 ZJNYYJSNFH 3 AKOZZKTOGI 4 2 BLPAALUPHJ 5 CMQBBMVQIK 6 4 DNRCCNWRJL 7 EOSDDOXSKM 8 5 FPTEEPYTLN 9 GQUFFQZUMO 10 4 HRVGGRAVNP 11 4 ISWHHSBWOQ 12 JTXIITCXPR 13 KUYJJUDYQS 14 LVZKKVEZRT 15 3 MWALLWFASU 16 NXBMMXGBTV 17 3 OYCNNYHCUW 18 PZDOOZIDVX 19 QAEPPAJEWY 20 RBFQQBKFXZ 21 4 SCGRRCLGYA 22 3 TDHSSDMHZB 23 *8 UEITTENIAC 24 VFJUUFOJBD 25 WGKVVGPKCE 26 XHLWWHQLDFThe high frequency generatrixes are selected and their lettersare juxtaposed in columns, the consecutive letters ofintelligible plain text present themselves. If reversedstandard alphabets are used, we must convert the cipher lettersof each isolated alphabet into their normal, plain componentequivalents, and then proceed as in the case of direct standardalphabets.
Friedman describes a graphical method for generatrixdevelopment in [FR7] and [FR8].
Time to move on to other family members. We shall identify thesystems and peculiarities of each, but remember that thesolution techniques presented for the papa bear apply equallywell to the children and cousins.
The Variant Cipher is just that, a variant of the Vigenere,except that if the Viggy procedure is followed through, apeculiar keyword appears, like JYUWFT. Going back to theslides, In the Variant, the plaintext appears in the oppositeslide from the one containing the key letter: Vigenere belowthe 'A' and Variant above the 'A'. The application of the highfrequency letters is the same. The keyword is obtained in adifferent fashion. For the simple encipherment of COME ATONCE with the keyword TENT:
T E N T T E N T ------- ------- C O M E J K Z L A T O N H P B U C E - - J A - -The setting of the slides for say , the initial T of thekeyword is:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z H I J K L M N O P Q R S T U V W X Y Z A B C D E F GThe decipherment of a Variant is the same as a Vigenere.
From our trusty CDB, I found Variant.exe and applied it to thefollowing cryptogram:
UALOT SILKH RWEBN NRHNL THURD VPVCH DLSUC OABSM YMXFO QAUBR NFHFR IBAOH YTMWT ENJVQ UPZHF AQWGZ MVHTB OENJD IGIMF SULUA BPMLZ RNFNX SMJTG DJHAF EKKSZ QWDZQ CLVRN FZXBZ WISTJ LMRNH RZ.The solution was found in two steps with a period of 7, keyword"RABBVTS" which is RABBITS, and reads: Lamp black isextensively in the manufacture of printing inks, as a pigmentfor oil painting and also for waxing and lacquering of leatheras well as in darkening a furniture polish. Total time 2 or3 minutes.
A third member of the Viggy family, the Beaufort, and while thesame procedure is applied, the slides (or tables) aredifferent. One is a normal alphabet, extending double lengthA-Z; the other is reversed, double length Z-A. So if I = T atone setting, then T=I at the same setting. It does not matterwhat the index for the key is, the results are the same.
So:
ABCDEFGHIJKLMNOBQRSTUVWXYZABCDEFGHIJKL TSRQPONMLKJIHGFEDCBAZYWXVUTSRQPONMLKJI * *Again the simple example. T E N T T E N T ------- ------- C O M E R Q B P A T O N T L Z G C E - - R A --
I found BEAUFORT.exe at the CDB and applied it two thefollowing message:
LDYUP AKUPT LVDTO BXUFW SERZP QMQPD NITHA NXUHE UGZTG HMGSMSRCUF LBQPZ XRYOB FDMNZ TGCUP QQUFB PANAQ HBOON XOOQP DJCJKTPFDV TBRKL TTSZG ODUFB TETEL POIEB HRTSM DBGGA YUT.Not so successful this time. It croaked at period = 6.The best i could get was "light-" I then reran the program witha wider key range and found that the true period was 10. Aftersome trial and error,the keyword is LIGHTHOUSE and the message starts:
LEDGE points out some interesting relationships between theVigenere, Variant and Beaufort. Let A=0, B=1, C=2 .. Z=25,then:
For Vigenere and Variant if key letter = A, since A=0,thecipher text = plain text. If we reconstruct a cipher assumingit is a Vigenere, but it is actually a Variant, we will get thetrue plain text but strange keyword. By subtracting theVariant equation from the Vigenere equation and setting ciphertext (Viggy) = ciphertext (Variant) and similarly plaintext(Viggy) = plaintext (Variant), we get the keyletter (Variant)= - keyletter(Vigenere) the same relationship as that betweenciphertext and plaintext when the keyletter is A in theBeaufort (since A=0). Hence, we encipher our strange keywordwith the A Beaufort alphabet to get the Variant key. The sameholds true if we have a Variant and assume it a Viggy.
If we have a Vigenere and a fragment of the same messageenciphered with the same key in Variant (or visa versa) then:
Table 11-7 defines the PORTA Cipher. In this table thealphabets are all reciprocal, for example Gplain(Wkey) =Rcipher, Rplain(Wkey)=Gcipher. They are called complementaryalphabets. Either of two letters may serve as a key letterindifferently: Gplain(Wkey) or Gplain(Xkey) = Rcipher.
Table 11-7 A B C D E F G H I J K L M AB N O P Q R S T U V W X Y Z A B C D E F G H I J K L M CD O P Q R S T U V W X Y Z M A B C D E F G H I J K L M EF P Q R S T U V W X Y Z N O A B C D E F G H I J K L M GH Q R S T U V W X Y Z N O P A B C D E F G H I J K L M IJ R S T U V W X Y Z N O P Q A B C D E F G H I J K L M KL S T U V W X Y Z N O P Q R A B C D E F G H I J K L M MN T U V W X Y Z N O P Q R S A B C D E F G H I J K L M OP U V W X Y Z N O P Q R S T A B C D E F G H I J K L M QR V W X Y Z N O P Q R S T U A B C D E F G H I J K L M ST W X Y Z N O P Q R S T U V A B C D E F G H I J K L M UV X Y Z N O P Q R S T U V W A B C D E F G H I J K L M WX Y Z N O P Q R S T U V W X A B C D E F G H I J K L M YZ Z N O P Q R S T U V W X YThe Porta Cipher permits 13 different ways to disguise a plainletter.
Again our simple encipherment:
T E N T T E N TC O M E Y M S NA T O N W E I EC E - - Y T - -A peculiarity of this system is that since half the alphabetis represented by the half of the alphabet, there never will befound the letters A-M of the plaintext appearing as A-M in theciphertext; no N-Z plaintext appearing as the N-Z ciphertext.This helpful in placing a tip. THE shows up as a (A-M) (N-Z)(N-Z) combination. [BRYA]
Table 11-8 shows a different view of the PORTA Cipher
Table 11-8 Plain Text A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ---------------------------------------------------A,B N O P Q R S T U V W X Y Z A B C D E F G H I J K L MC,D O P Q R S T U V W X Y Z N M A B C D E F G H I J K LE,F P Q R S T U V W X Y Z N O L M A B C D E F G H I J KG,H Q R S T U V W X Y Z N O P K L M A B C D E F G H I JI,J R S T U V W X Y Z N O P Q J K L M A B C D E F G H IK,L S T U V W X Y Z N O P Q R I J K L M A B C D E F G HM,N T U V W X Y Z N O P Q R S H I J K L M A B C D E F GO,P U V W X Y Z N O P Q R S T G H I J K L M A B C D E FQ,R V W X Y Z N O P Q R S T U F G H I J K L M A B C D ES,T W X Y Z N O P Q R S T U V E F G H I J K L M A B C DU,V X Y Z N O P Q R S T U V W D E F G H I J K L M A B CW,X Y Z N O P Q R S T U V W X C D E F G H I J K L M A BY,Z Z N O P Q R S T U V W X Y B C D E F G H I J K L M AUsing the message text A from page 20 as an example with keyword WHITE , the distribution of 5 alphabets is:
2 6 2 1 6 1 5 3 1 6 5 1 2 3 3 3 2 2 11. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 4 2 5 1 3 4 4 1 2 3 1 2 4 9 1 2 52. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 5 3 3 2 5 1 1 3 4 7 2 2 4 8 1 1 23. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 1 4 4 2 2 3 3 1 9 2 2 3 1 1 3 3 2 2 44. A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 5 2 2 2 4 3 2 1 6 2 4 9 1 3 7 15. A B C D E F G H I J K L M N O P Q R S T U V W X Y ZNow we can divide the M and N distributions, and each half maybe used to fit a normal distribution. In alphabet 1, thesequence CDEFGHIJ cipher may easily be recognized as NOPQRSTUplain; this would fix the keyletters as WX, and therefor theA...Mplain sequence should begin with Ycipher. In alphabets2,3, and 5 the RSTplain sequence may be spotted at BCDcipher,ABCcipher, and CDEcipher, respectively, whereas in alphabet 4,if Ncipher = Eplain, then Ecipher = Nplain; therefore theoriginal assumptions for the first halves will be confirmed bythe goodness of fit of the distributions for the second halves.The keys fore these 5 alphabets are derived as (W,X), (G,H)(I,J), (S,T), and (E,F); from these letters we get WHITE.
In completing the plain component sequence for the Portaencipherment, the cipher letters are first converted to theirPorta plain-component equivalents and then these letters areused for the decipherment. EXCEPT, cipher letters A-M arecompleted in a downward direction and cipher letters N-Z arecompleted in an upward direction.
Reference [FR7] gives the example:
P K T F F C D V I T O B V Z X C V R E E G I V J ET P R K T O Q C F L P B V P X ....The conversion process and plain component completion of thefirst three alphabets are shown below using the generatrixelimination and weighting scheme developed earlier:
Alphabet 1 Alphabet 2 Alphabet 3 P C O C G T O P K D B V I P Q B T V V R V R C V --------------- --------------- ---------------1 C P B P T G B C X Q O I V C D O 6 G I I E I E P I3 D O C O S H C D 3 W P N J U D E N H J J F J F O J6 E N D N R I D E V O Z K T E F Z I K K G K G N K F Z E Z Q J E F 2 U N Y L S F G Y J L L H L H Z L0 G Y F Y P K F G T Z X M R G H X 2 K M M I M I Y M H X G X O L G H 3 S Y W A Q H I W L A A J A J X A3 I W H W N M H I R X V B P I J V M B B K B K W B J V I V Z A I J Q W U C O J K U 1 A C C L C L V C K U J U Y B J K 3 P V T D N K L T 0 B D D M D M U D L T K T X C K L 3 O U S E Z L M S 7 C E E A E A T E2 M S L S W D L M 5 N T R F Y M A R 1 D F F B F B S F5 A R M R V E M A Z S Q G X A B Q 2 E G G C G C R G B Q A Q U F A B 1 Y R P H W B C P 0 F H H D H D Q HThe generatrixes with the highest scores are the correct ones.
Just as the Vigenere table consisting of direct standardalphabets has its complementary table of reversed standardalphabets, a variant of the Porta table can be constructedwhere the lower halves of the sequences run in oppositedirection to the upper half. For example:
A,B A B C D E F G H I J K L M Z Y X W V U T S R Q P O N C,D A B C D E F G H I J K L M N Z Y X W V U T S R Q P O
The probable word method is very easy way to attack a Portacipher. Let 1 = any letter in the A-M sequence, and 2 equalany letter in the N-Z sequence.
P K T F F C D V I T O B V Z X C V R E E G I V J E2 1 2 1 1 1 1 2 1 2 2 1 2 2 2 1 2 2 1 1 1 1 2 1 1T P R K T O Q C F L P B V P X ....2 2 2 1 2 2 2 1 1 1 2 1 2 2 2Use the probable word INFANTRY, which has the class notation of12112222, but in encipherment is reversed to 21221111 pattern.At position 15, X C V R E E G I, we find:
plain I N F A N T R Y cipher X C V R E E G I key E W G I S E W G derived F X H J T F X HRead diagonally, we see WHITE repeated.
At the trusty CDB is a program called PORTA.exe. Using it onthe following cipher message found a period of 9 with apossible key of KL/IJ/CD/MN/AB/OP/OP/EF/QR. I came up with thekeyword: LIDNAOOER:
EYWRR MOTJJ QOHFA LTYQV SQFPG EPWTG RVGUC DVVBT EMLMN BYSOE OHFKW YARQL PEBSB ETVXM WVBCV XRTIT JJAMX EHADX VCAXN MMWZR WALFY BTJSP RTLLP LZDVD FZHGE PBKQR RUKWQ AEAOP Yand behold the message cracked to:
The GRONSFELD Cipher uses a numerical key and restricts theViggy table to just ten alphabets. We can construct a slidewith one normal alphabet and numbered one like this:
... 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 ...One half the digits are used for encipherment and the otherhalf for decipherment. For example the key is derived asfollows:
C O N S T I T U T I O N 1 6 4 8 9 2 10 12 11 3 7 5The first duplicate letter carries the lower number.
So back to:
6 2 3 4 6 2 3 4 C O M E I Q P I A T O N G V R R C E - - I G - -Slide method: put the 0 over the C, take the letter to theright in juxtaposition of the 6 = I, same for A which is Gand so on. We decipher by looking to the left.
A typical decipherment might look like this for the test word"YOUR":
0 2 4 7 0 2 4 7 0 2 4 7 0 2T S V H Y Q B V Y I G L M G U X A S R M F K C I A A O V I Z-----------------------------------------------------------S R U G Y O U R X F H K M E N T Z R Q L F I V E Z Z N U I X ------- ------- ------- ---R Q T F W G E J Y Q P K Y Y M TQ P S E V F D I X P O J W W K RT S V H Y Q B V Y I G L M G U X A S R M F K C I A A O V I Z-----------------------------------------------------------Y 9 0 3 0 8 8 2 7 4 2 2O 2 7 6 4 0U 7 4 3 1R 4 9
11.1 Viggy.SYCVT HFXEQ DPTLN KTGMP FHMPA SRVIT LSEXH DPITXKELIQ WDXEC VNLIP HPWXD XXIXH UTRIH.11.2 Beaufort.SXSXZ IYLEQ AWEQF EZEPP QZQRD VANKH HLZJX OQSEUYSOVS SZKLE DRMRU THTUW SCLOX NEHLA OPEEU GAZIAUUOQG OJX.11.3 Variant.JQRSB YBKNF WWTGK UXDTK ZAOAA MCVJU KBCEX GUYLBUASWY TIENQ XLPYX CWASU VAKOM XIGIK XHWZT SWGOPWRTSJ NAWG.11.4 Gronsfeld.ZRWQU IKLMS IXAWI UQMWP KFQEL RBWJG XHIXT NLVKS ZHVHSZRUEK KWPIM GSXIA XVUEL RHZPI SLBWT NHU.11.5 Viggy or Beaufort; same message and key starts ONOIHT.ORQGX HPNKW QQCHI ABIFZ NQCHR VLVLU HYUDT MCYJN WAUHPHLVIN BZCCB GCGKZ JNLMM WTVLY DYCCV JPUVG KLKQX YTTKIXOQYB JJMHJ BYHQY LFQWF NRYUC XCECN GPCBW TPAXE ABKGCPVHKL OIKQW TPKOW KNCMM HFFAV A.
Thanks to JOE O for a fine analysis of all three problems.
QQ-1 QUAGMIRE I Travelogue. (Ends:SINGOUTOFTHESEA) RHIZOME1234567 1234567 1234567 1234567 1234567 1234567 1234567THEFIRS TIMEaVI SITOREX CLAIMSA HROMANT ICVENIC ESINKINKKQHPQR KTYOiTA TLGAWBM XORKTAT BSOOIYI CGICEJV UCYZRJPALNSFRZ UCQDXIS TDRBFYS YTFDZBD USQWKMT CPPDOAI CAAKEHKUAYFHQA TLNIFSI SIGJHAS V.QQ-1 Quagmire I Solution. VERDICT/nose. Period =7.The first time visitor exclaims "Ah, romantic Venice sinkinginto the sea." The seasoned traveler exclaims,"Ah, stinkingVenice rising out of the sea. 0 A B C D F G H I J K L M P Q R T U V W X Y Z N O S E 1 V W X Y Z A B C D E F G H I J K L M N O P Q R S T U 2 E F G H I J K L M N O P Q R S T U V W X Y Z A B C D 3 R S T U V W X Y Z A B C D E F G H I J K L M N O P Q 4 D E F G H I J K L M N O P Q R S T U V W X Y Z A B C 5 I J K L M N O P Q R S T U V W X Y Z A B C D E F G H 6 C D E F G H I J K L M N O P Q R S T U V W X Y Z A B 7 T U V W X Y Z A B C D E F G H I J K L M N O P Q R SQQ-2 QUAGMIRE III Tedious. (CRYPTANALYTIC METHODS)DOPPELSCHACHPeriod= 612345 61234 56123 45612 34561 23456 12345 61234 56123THETI MEREQ UIRED BYS.......PNATV SJBAQ WGMTR BZYLU ACACR GBNTQ FGGCN APNID ULMVDSCEPB AMCQF BBPVR EOBSL AFSAN HFYVV MCYTF LEMAO MFHVUKBAAU ATTEA NGOHU GTQEX ISUGU SAKCC TLIRT TLSZM PBMGVAPYRV YIIGL WGNUF JFROG SNQGN HBOTU TACUO JUVQH HUGWWWBIMT WNHVO GTLSZ MPYQZ BNCEN UWLC.HARDER/decorative. Period = 6. The time required by somecryptanalytic methods grows extremely rapidly as key length ormessage length increases. All possible keys for a columnartransposition instead of making an entry by building up afrom a pair of columns is an example.0 D E C O R A T I V B F G H J K L M N P Q S V W X Y Z1 H J K L M N P Q S V W X Y Z D E C O R A T I V B F G2 A T I V B F G H J K L M N P Q S V W X Y Z D E C O R3 R A T I V B F G H J K L M N P Q S V W X Y Z D E C O4 D E C O R A T I V B F G H J K L M N P Q S V W X Y Z5 E C O R A T I V B F G H J K L M N P Q S V W X Y Z DQQ-3 QUAGMIRE IV Economics Lesson. EDNASANDE (BUSINESSACTIVITYDURINGAPERIOD)THEEC ONOMY OFTHE NATIO ..........TDNSE PMBSV FURMQ UFYSJ PAGGY FVIKT GYVLV FBTPH IIIADHVIUY QSAFA VQVFU HPIHE BIXNN HBSTN IRMQH IIIAD OVIXTCTNOW EOJOZ BOWBU ONLFN GOBJS HBOQS VZMOU JSFQH SAHPSJBBJT AAMIE XILRA TOTVL TUAML FLNEJ PPMNT XHVQV FCYSBJODNF XJSFT UIUTM ONKDO UMMSB NWUL. EXCHANGE/stock/MARKET. The economy of the Nation is built on supply and demand, the result of inflation. Recession is a temporary falling off of business activity during a period when such activity has been generally increasing..0 S T O C K A B D E F G H I J L M N P Q R U V W X Y Z1 E T B C D F G H I J L N O P Q S U V W X Y Z M A R K2 X Y Z M A R K E T B C D F G H I J L N O P Q S U V W3 C D F G H I J L N O P Q S U V W X Y Z M A R K E T B4 H I J L N O P Q S U V W X Y Z M A R K E T B D E F G5 A R K E T B C D F G H I J L N O P Q S U V W X Y Z M6 N O P Q S U V W X Y Z M A R K E T B D E F G H I J L7 G H I J L N O P Q S U V W X Y Z M A R K E T B D E F8 E T B C D F G H I J L N O P Q S U V W X Y Z M A R K
[ACA] ACA and You, "Handbook For Members of the American Cryptogram Association," ACA publications, 1995.[ACA1] Anonymous, "The ACA and You - Handbook For Secure Communications", American Cryptogram Association, 1994.[ACM] Association For Computing Machinery, "Codes, Keys and Conflicts: Issues in U.S. Crypto Policy," Report of a Special Panel of ACM U. S. Public Policy Committee (USACM), June 1994.[AFM] AFM - 100-80, Traffic Analysis, Department of the Air Force, 1946.[ALAN] Turing, Alan, "The Enigma", by A. Hodges. Simon and Schuster, 1983.[ALBA] Alberti, "Treatise De Cifris," Meister Papstlichen, Princeton University Press, Princeton, N.J., 1963.[ALEX] Alexander, D. 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English trans. by Warren T, McCready of the University of Toronto, 1964[KOBL] Koblitz, Neal, " A Course in Number Theory and Cryptography, 2nd Ed, Springer-Verlag, New York, 1994.[KONH] Konheim, Alan G., "Cryptography -A Primer" , John Wiley, 1981, pp 212 ff.[KORD] Kordemsky, B., "The Moscow Puzzles," Schribners, 1972.[KOTT] Kottack, Phillip Conrad, "Anthropology: The Exploration Of Human Diversity," 6th ed., McGraw-Hill, Inc., New York, N.Y. 1994.[KOZA] Kozaczuk, Dr. Wladyslaw, "Enigma: How the German Machine Cipher was Broken and How it Was Read by the Allies in WWI", University Pub, 1984.[KRAI] Kraitchek, "Mathematical Recreations," Norton, 1942, and Dover, 1963.[KULL] Kullback, Solomon, Statistical Methods in Cryptanalysis, Aegean Park Press, Laguna Hills, Ca. 1976[LAFF] Laffin, John, "Codes and Ciphers: Secret Writing Through The Ages," Abelard-Schuman, London, 1973.[LAI] Lai, Xuejia, "On the Design and Security of Block Ciphers," ETH Series in Information Processing 1, 1992. (Article defines the IDEA Cipher)[LAIM] Lai, Xuejia, and James L. Massey, "A Proposal for a New Block Encryption Standard," Advances in Cryptology - Eurocrypt 90 Proceedings, 1992, pp. 55-70.[LAKE] Lakoff, R., "Language and the Women's Place," Harper & Row, New York, 1975.[LANG] Langie, Andre, "Cryptography," translated from French by J.C.H. Macbeth, Constable and Co., London, 1922.[LAN1] Langie, Andre, "Cryptography - A Study on Secret Writings", Aegean Park Press, Laguna Hills, CA. 1989.[LAN2] Langie, Andre, and E. A. 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And, it has one of the better illustrations of the Soviet one-time pad with example, with three errors in cipher text, that I have corrected for the author.][MARS] Marshall, Alan, "Intelligence and Espionage in the Reign of Charles II," 1660-1665, Cambridge University, New York, N.Y., 1994.[MART] Martin, James, "Security, Accuracy and Privacy in Computer Systems," Prentice Hall, Englewood Cliffs, N.J., 1973.[MAST] Lewis, Frank W., "Solving Cipher Problems - Cryptanalysis, Probabilities and Diagnostics," Aegean Park Press, Laguna Hills, CA, 1992.[MAU] Mau, Ernest E., "Word Puzzles With Your Microcomputer," Hayden Books, 1990.[MAVE] Mavenel, Denis L., Lettres, Instructions Diplomatiques et Papiers d' Etat du Cardinal Richelieu, Historie Politique, Paris 1853-1877 Collection.[MAYA] Coe, M. 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Merriam Co., Norman, OK. 1982.[RAND] Randolph, Boris, "Cryptofun," Aegean Park Press, 1981.[RB1] Friedman, William F., The Riverbank Publications, Volume 1," Aegean Park Press, 1979.[RB2] Friedman, William F., The Riverbank Publications, Volume 2," Aegean Park Press, 1979.[RB3] Friedman, William F., The Riverbank Publications, Volume 3," Aegean Park Press, 1979.[REJE] Rejewski, Marian, "Mathematical Solution of the Enigma Cipher" published in vol 6, #1, Jan 1982 Cryptologia pp 1-37.[RELY] Relyea, Harold C., "Evolution and Organization of Intelligence Activities in the United States," Aegean Park Press, 1976.[RENA] Renauld, P. "La Machine a' chiffrer 'Enigma'", Bulletin Trimestriel de l'association des Amis de L'Ecole superieure de guerre no 78, 1978.[RHEE] Rhee, Man Young, "Cryptography and Secure Commun- ications," McGraw Hill Co, 1994[RIVE] Rivest, Ron, "Ciphertext: The RSA Newsletter 1, 1993.[RIV1] Rivest, Ron, Shamir, A and L. 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Montgomery, "Room 3603, The Story of British Intelligence Center in New York During World War II", New York, Farrar, Straus, 1963.[ROSE] Budge, E. A. Wallis, "The Rosetta Stone," British Museum Press, London, 1927.[RSA] RSA Data Security, Inc., "Mailsafe: Public Key Encryption Software Users Manual, Version 5.0, Redwood City, CA, 1994[RUNY] Runyan, T. J. and Jan M. Copes "To Die Gallently", Westview Press 1994, p85-86 ff.[RYSK] Norbert Ryska and Siegfried Herda, "Kryptographische Verfahren in der Datenverarbeitung," Gesellschaft fur Informatik, Berlin, Springer-Verlag1980.[SADL] Sadler, A. L., "The Code of the Samurai," Rutland and Tokyo: Charles E. Tuttle Co., 1969.[SACC] Sacco, Generale Luigi, " Manuale di Crittografia", 3rd ed., Rome, 1947.[SALE] Salewski, Michael, "Die Deutscher Seekriegsleitung, 1938- 1945, Frankfurt/Main: Bernard and Graefe, 1970- 1974. 3 volumes.[SANB] Sanbohonbu, ed., "Sanbohonbu kotokan shokuinhyo." 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J., "How To Insure that Data Acquired to Verify Treaty Compliance are Trustworthy, " in "Authentication without secrecy: A secure communications problem uniquely solvable by asymmetric encryption techniques.", IEEE EASCON 79, Washington, 1979, pp. 661- 62.[SINK] Sinkov, Abraham, "Elementary Cryptanalysis", The Mathematical Association of America, NYU, 1966.[SMIH] Smith, David E., "John Wallis as Cryptographer", Bulletin of American Mathematical Society, XXIV, 1917.[SMIT] Smith, Laurence D., "Cryptography, the Science of Secret Writing," Dover, NY, 1943.[SOLZ] Solzhenitsyn, Aleksandr I. , "The Gulag Archipelago I- III, " Harper and Row, New York, N.Y., 1975.[SPAN] Barker, Wayne G. "Cryptograms in Spanish," Aegean Park Press, Laguna Hills, CA., 1986.[STAL] Stallings, William, "Protect Your Privacy: A Guide for PGP Users," Prentice Hall PTR, 1995.[STEV] Stevenson, William, 'A Man Called INTREPID', Macmillan, London 1976.[STIN] Stinson, D. 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Thompson, The Outcome;(Mid 1943 to 1945), Department of the Army, Office of the Chief of Military History, USGPO, Washington,1956 -1966.[THEO] Theodore White and Annalee Jacoby, "Thunder Out Of China," William Sloane Assoc., New York, 1946.[THOM] Thompson, Ken, "Reflections on Trusting Trust," Communications of the ACM 27, 1984.[TILD] Glover, D. Beaird, Secret Ciphers of The 1876 Presidential Election, Aegean Park Press, Laguna Hills, Ca. 1991.[TM32] TM 32-250, Fundamentals of Traffic Analysis (Radio Telegraph) Department of the Army, 1948.[TORR] Torrieri, Don J., "Principles of Military Communication Systems," Artech, 1981.[TRAD] U. S. 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D., Traffic Analysis and the Zendian Problem, Agean Park Press, 1984. (also available through NSA Center for Cryptologic History)Text converted to HTML on June 29, 1998 by Joe Peschel.Any mistakes you find are quite likely mine. Please let me know about them by e-mailing:
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Joe Peschel