In Lecture 3, we continue our look into substitution ciphers,and move into the multiliteral substitution case, we field moretools for cryptanalysis, look at some fascinating historicalvariations, we review "the unbreakable cipher" and solvehomework problems.
Monoalphabetic substitution methods are classified asuniliteral and multiliteral systems. Uniliteral systemsmaintain a strict one-to-one correspondence between the lengthof the units of the plain and those of the cipher text. Eachletter of plain text is replaced by a single character in thecipher text. In multiliteral monoalphabetic substitutionsystems, this correspondence is no longer one plain to onecipher but may be one plain to two cipher, where each letter ofthe plain text is replaced by two characters in the ciphertext; or one plain to three cipher, where a three-charactercombination in the cipher text represents a single letter ofthe plain text. We refer to these systems as uniliteral,biliteral, and triliteral, respectively. Ciphers in which oneplain text letter is represented by cipher characters of two ormore elements are classed as multiliteral. [FR1], [FR2],[FR5]
Friedman gives some interesting examples of biliteralmonoalphabetic substitution. [FR1] Many cipher systemsstart with a geometric shape. Using the square in Figure 3-1:
W H I T E ********************** W * A B C D E * H * F G H IJ K * I * L M N O P * T * Q R S T U * E * V W X Y Z Figure 3-1
The alphabet derived from the cipher square or matrix isreferenced by row and column coordinates, respectively.
The key to this system is that when a message is enciphered bythis biliteral alphabet, the cryptogram is still monoalphabeticin character. A frequency distribution based upon pairs ofletters will have all the characteristics of a simpleuniliteral distribution for a monoalphabetic substitutioncipher.
Numbers can be used as effectively as letters in the biliteralcipher. The simplest form is A=01, B=02, C=03,...Z=26. So,the plain text letters have as their equivalents two-digitnumbers indicating their position in the normal alphabet.
Other dinome (two digit) cipher matrices are previewed:
1 2 3 4 5 6 7 8 9 0 ................................. Figure 3-2 1 . A B C D E F G H I J 2 . K L M N O P Q R S T 3 . U V W X Y Z . , : ;
Note that frequently-used punctuation marks can be encipheredin the above matrix.
Another four examples are:
Figure 3-3 Figure 3-4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 .................... ............................ 1 . A B C D E F 1 . A B C D E F G H I 2 . G H IJ K L M 2 . J K L M N O P Q R 3 . N O P Q R S 3 . S T U V W X Y Z * 4 . T UV W X Y Z Figure 3-5 Figure 3-6 M U N I C H A B C D E F G H I .................... ............................. B .A 7 E 5 R M A . A D G J M P S V Y E .G 1 N Y B 2 B . B E H K N Q T W Z R .C 3 D 4 F 6 C . C F I L O R U X 1 L .H 8 I 9 J 0 D . 2 3 4 5 6 7 8 9 0 I .K L O P Q S N .T U V W X Z
It is possible to generate false or pseudo-code or artificialcode language by using an enciphering matrix with vowels as rowindicators and consonants as column indicators.
Figure 3-7 B C D F G .............. A . A B C D E E . F G H IJ K I . L M N O P O . Q R S T U U . V W X Y Z
Enciphering the word RAIDS would be OCABE FAFOD. [FR5]
Another subterfuge used to camouflage the biliteral ciphermatrix is to append a third character to the row or columnindicator. This third character may be produced through theuse of cipher matrix shown in Figure 3-8 (wherein A=611,B=612, etc.) or the third character can be the "sum checking"digit which is the non-carrying sum (modulo 10) of thepreceding two digits such as trinomes 257, 831, and 662. Itmay also involve self summing groups such as 254, 830, 669 allwhich sum to the constant 1, or finally the third digit can berandom, inserted solely for the pleasure of the cryptanalyst.
Figure 3-8 1 2 3 4 5 .................. 61 . A B C D E 72 . F G H IJ K 83 . L M N O P 94 . Q R S T U 05 . V W X Y Z A=611 , B=612 X=053
All the above matrices are bipartite. They can be divided intotwo separate parts that can be clearly and cleanly defined byrow and column indicators. This is the primary weakness ofthis type of cipher. [FR1]
Sinkov presents a good description of the modulo arithmeticrequired to solve biliteral cipher challenges. [SINK] A moreinvolved look at the statistics involved can be found in[CULL].
Consider the following cipher matrix:
Figure 3-9 1 2 3 4 5 .................. 09 . H Y D R A 15 . U L IJ C B 21 . E F G K M 27 . N O P Q S 33 . T V W X Z
We can produce a biliteral cipher alphabet in which theequivalent for any letter in the matrix is the sum of the twocoordinates which indicate its cell in the matrix:
Plain A B C D E F G H I J K L MCipher 14 20 19 12 22 23 24 10 18 18 25 17 26Plain N O P Q R S T U V W X Y ZCipher 28 29 30 31 13 32 34 16 35 36 37 11 38 A = 9+5 =14, E = 21 + 1 =22
The cipher units are biliteral but they are not bipartite.Cipher text equivalent of plain text letter "A" is 14 anddigits 1 and 4 have no meaning per se. Plain text letterswhose cipher equivalents begin with 1 may be found in twodifferent rows of the matrix and those of whose equivalents endin 4 appear in three different columns. [FR1]
Another possibility lends itself to certain multiliteralciphers in the use of a word spacer or word separator. Theword space might be represented by a value in the matrix;i.e., the separator is enciphered as a value (dinome 39 inFigure 3-4). The word space might be an unenciphered element.
Lets break from the theory and look at four interestingmultiliteral historical ciphers before discussing the generalcryptanalytic attack on the multiliteral cipher.
The abbot Trithemius, born Johann von Heydenberg (1462-1516)invented one of the first multiliteral ciphers. It wasfashioned similar to the Baconian Cipher and was a means fordisguising secret text. His work "Steganographia" published in1499 describes several systems of 'covered writing.' [TRIT][WATS], [FR1] The science of steganography is named afterhim. Several Internet discussion groups currently discuss theuse of steganography to hide messages in graphics files. (.GIFfiles)
His alphabet, modified to include 26 letters of present-dayEnglish, is shown in Figure 3-10, below; it consists of allthe permutations of three things taken three at a time or3 ** 3 = 27 in all.
Figure 3-10A - 111 G - 131 M - 221 S - 311 Y - 331B - 112 H - 132 N - 222 T - 312 Z - 332C - 113 I - 133 O - 223 U - 313 * - 333D - 121 J - 211 P - 231 V - 321E - 122 K - 212 Q - 232 W - 322F - 123 L - 213 R - 233 X - 323
The cipher text does not have to be restricted to digits; anygroupings of three things taken three at a time will do.
Sir Francis Bacon (1561-1626) invented a cipher in which thecipher equivalents are five-letter groups and the resultingcipher is monoalphabetic in character. Bacon uses a 24 lettercipher with I and J, U and W used interchangeably.
A = aaaaa I/J = abaaa R = baaaa B = aaaab K = abaab S = baaab C = aaaba L = ababa T = baaba D = aaabb M = ababb U/V = baabb E = aabaa N = abbaa W = babaa F = aabab O = abbab X = babab G = aabba P = abbba Y = babba H = aabbb Q = abbbb Z = babbb
Bacon described the steganographic effect of message enfoldingin an innocent external message. Suppose we let capitals bethe "a" element and lower-case letters represent the "b"elements. The message "All is well with me today" can be madeto convey the message "Help." Thus: A L l i s W E l L W I t H m E T o d a Y a a b b b a a b a a a b a b a a b b b a H E l P
Bacon describes many several variations on the theme. [FR1],[DEAU] Note the regularity of construction of Bacon'sbiliteral alphabet, a feature which permits its reconstructionfrom memory.
Probably the most corrupt political election occurred onNovember 7, 1876 with the election of President Rutherford B.Hayes (Republican). He defeated Samuel Jones Tilden(Democrat). Tilden had won the popular vote by 700,000 votesbut because of frauds surrounding the electoral college, he wasdeprived of the high office of President. Actually, bothcandidates were involved with bribery, election tampering,voter fraud, conspiracy and a host of other goodies. Tildenran on a law and order ticket that credited him with convictingBoss Tweed and the Tweed Ring in New York City, whichcontrolled the city through Tammany Hall. For two years intoHayes Presidency, the scandals persisted.
With the help of New York Tribune, Republicans finished theTilden 'honesty' horse. They published the Tilden Ciphers andkeys. There were about 400 of them representing substitutionand transposition forms. We will revisit the transpositionforms at a later juncture. They represented secret and illegaloperations by Tilden's men in Florida, Louisiana, SouthCarolina and Oregon. The decipherments were done byinvestigators of the Tribune. Here are two examples and theirsolution. [TILD] , [FR1] , [TRIB]
GEO. F. RANEY, Tallahassee.
P P Y Y E M N S N Y Y Y P I M A S H N S Y Y S S I T E P A A EN S H N S P E N N S S H N S M M P I Y Y S N P P Y E A A P I EI S S Y E S H A I N S S S P E E I Y Y S H N Y N S S S Y E P IA A N Y I T N S S H Y Y S P Y Y P I N S Y Y S S I T E M E I PI M M E I S S E I Y Y E I S S I T E I E P Y Y P E E I A A S SI M A A Y E S P N S Y Y I A N S S S E I S S M M P P N S P I NS S N P I N S I M I M Y Y I T E M Y Y S S P E Y Y M M N S Y Y SS I T S P Y Y P E E P P P M A A A Y Y P I I TL' Engle goes up tomorrow. Daniel
Examination of the message discloses a bipartite alphabetcipher with only ten different letters used. Dividing themessages by twos, assigning arbitrary letters for pairs ofletters and performing a triliteral frequency distribution willyield a solution.
PP YY EM NS NY YY PI MA SH NS YY SS etc A B C D E B F G H D B I etc
Message reads:
Have Marble and Coyle telegraph for influential men fromDelaware and Virginia. Indications of weakening here. Pressadvantage and watch board.
Here is another Tilden cipher using numerical substitutes:
S. PASCO AND E. M. L'ENGLE
84 55 84 25 93 34 82 31 31 75 93 82 77 33 55 4293 20 93 66 77 66 33 84 66 31 31 93 20 82 33 6652 48 44 55 42 82 48 89 42 93 31 82 66 75 31 93 DANIEL
There were several messages of this type. They disclosed thatonly 26 different numbers were used.Message reads:
Cocke will be ignored, Eagan called in. Authority reliable.
The Tribune experts gave the following alphabets:
AA = O EN = Y IT = D NS = E PP = H SS = NAI = U EP = C MA = B NY = M SH = L YE = FEI = I IA = K MM = G PE = T SN = P YI = XEM = V IM = S NN = J PI = R SP = W YY = A-------------------------------------------------------20 = D 33 = N 44 = H 62 = X 77 = G 89 = Y25 = K 34 = W 48 = T 66 = A 82 = I 93 = E27 = S 39 = P 52 = U 68 = F 84 = C 96 = M31 = L 42 = R 55 = O 75 = B 87 = V 99 = J
William F. Friedman correlated these alphabets with the resultsbeing amusing:
H I S P A Y M E N T 1 2 3 4 5 6 7 8 9 0 ------------------------------- H 1 . . I 2 . K S D . S 3 . L N W P . P 4 . R H T . A 5 . U O . Y 6 . X A F . M 7 . B G . E 8 . I C V Y . N 9 . E M J . T 0 . . ------------------------------
The blank squares may have contained proper names and moneydesignations. Key = HISPAYMENT for bribery seems to beappropriate. [HIS1], [TRIB], [TILD], [FR1]
One of the most fascinating stories of the American Civil War(1861-65) is about communications using flag telegraphy or alsoknown as the wigwag signal system.
Wigwag is a system of positioning a flag (or flags) at variousangles that indicate the corresponding twenty-six letters ofthe alphabet. It was created in the mid-1800s by three menworking at separate locations: Navy Captain Phillip Colomb and,Army Captain Francis Bolton, in England, and Surgeon-inventorAlbert J. Meyer in America. [WRIX] Meyer observed therailroad electromagnetic telegraph, developed by AlexanderBain, and invented a touch method of communication for the deafand later the wigwag system. He developed companion methodswith torches and disks. The name "wigwag" derived from theflag movements.
Three main color combinations were used in flags measuring two,four and six feet square. The white banners had red squarecenters while the black or red flags had white centers. Myersmethod required three motions (elements) to be used for eachletter. The first position always initiated a messagesequence. Motion one went from head to toe and back on rightside. Motion 2 went from head to toe and back on left side.Motion three went from head to toe and back in front of theman. Each motion made quickly. Chart 3-1 indicates themultiliteral alphabet and directional orders required to conveya message.
Chart 3-1 A - 112 H - 312 O - 223 V - 222 B - 121 I - 213 P - 313 W - 311 C - 211 J - 232 Q - 131 X - 321 D - 212 K - 323 R - 331 Y - 111 E - 221 L - 231 S - 332 Z - 113 F - 122 M - 132 T - 133 G - 123 N - 322 U - 233
Myers Signal Directions
For night signals, Myer applied his system with torches on thesignal poles and lanterns. A foot torch was used as areference point. Thus the direction of the flying wave couldbetter be seen. Compare this to the semaphore system used byships at sea when radio silence is a must.
Myer continuously improved his invention through 1859 andpresented his findings gratis to the Union Army (which gave hima luke warm yawn for his trouble). Alexander Porter, his chiefassistant joined the Confederate Army and used the wigwagsystem in actual combat. Porter was able to warn ColonelNathan Evans at Manassas Junction - Stone Bridge that the UnionArmy had reached Sudley Ford and was about to surprise GeneralBeauregard's best Division. Porter sent from his observationtower, the following message to Colonel Evans at the StoneBridge defenses: "Look out for your left, you are turned."
Colonel Evans turned his cannons and musket fire toward theFederal troops before they could initiate their attack. Porterwas credited later (and decorated), for his vigilance led tochanges in the tactics of the entire struggle around ManassasJunction. The application of the new signal system haddirectly influenced the shocking Union defeat that eventfulJuly day.
Myers signaling system was catapulted into use at the Battle ofGettysburg. General Lee had invaded northern soil in June1863. His Potomac crossing was relayed by flag system to theWar Department. General Joseph Hooker resigned under fire onJune 28. General George Meade (of NSA grounds fame) took overcommand of the Army of the Potomac. His headquarters were atTaneytown, MD. Startling news came via signalmen on July 1.A skirmish on the Maryland border indicated that General Bufordwas facing a major force not in Maryland but in Pennsylvania.Lee was himself in command at Gettysburg. Signalmen of eacharmy unit sent out calls for help. Reinforcements from dozensof units several miles away were committed to the fray. ByJuly 1, 73,000 gray and 88,000 blue met in one of history'smost decisive battles. Rarely, if at all, do textbooks evenhint that the secret message system of flags affected thesehistory changing events. Yet the crucial sightings by Unionobservers directly tipped the scales against Lee's besttactics. The most famous incident was when Captain Castle onCemetery Ridge, refused to submit to Confederate artillerybarrage as General George Pickett charged the "thin blue line",used a wooden pole and a bedsheet to make a makeshift flag toalert Union forces under General Meade who ordered counter-measures. Pickett's charge was stopped short of breaching theUnion lines. General Lee's gamble failed. Previouslydisregarded flagmen enabled George Meade to enter the shrine ofheros. [BLUE], [ANNA], [MYER], [NIBL], [TRAD], [WRIX], [KAHN]
Multiliteral ciphers are often recognized by the fact that thecryptographic text is usually composed of but a very limitednumber of different characters. They are handled in the sameway as are uniliteral monoalphabetic substitution ciphers. Solong as the same character or number is used to represent thesame plain text letter, and so long as a given letter ofplain text is always represented by the same character orcombination of characters, then the substitution is strictlymonoalphabetic and can be handled by methods in my Lectures 1and 2.
In the case of biliteral ciphers where the row and columnindicators are not identical, the direction of reading thecipher pairs is chosen at will for each succeeding cipher pair,and analysis of contacts of the letters comprising the cipherpairs will disclose that there are two distinct families ofletters, and the cipher pair will never consist of two lettersof the same family. We reduce by further substitution touniliteral terms and solve by known methods.
If a multiliteral cipher includes a provision for theencipherment of a word separator, the cipher equivalent of thisword separator may be readily identified because it will havethe highest frequency of any cipher unit.
Friedman presents data on word separators:
For English, the average word length is 5.2 letters. The wordseparator will be close to 16% frequency. [FR1] The lettersof the alphabet take on new percentage frequencies as follows: One of the first steps to solving a multiliteral cipher with acipher matrix, is to anagram the letters comprising the row andcolumn indicators in an attempt to disclose the key words used.When the anagraming process does disclose any key word(s), askeleton reconstruction matrix which is the duplicate of theoriginal enciphering matrix is made to show the order of therow and column indicators. Partial recovery of plain text maybe possible at this point in the analysis. Looking at thefrequency analysis (and location of the crests and troughs) maytell us something about the enciphering alphabet as normal orkeyed. Cipher alphabets whose cipher components consist of numbers arepracticable for telegraph or radio transmission. They may takeforms corresponding to those employing letters. Standard numerical cipher alphabets are those in which thecipher component is a normal sequence of numbers. Mixed numerical cipher alphabets are those that have been keyedby a key word turned into numerical cipher equivalents or havea random combination of two or more digits for each letter ofplain text. Figure 3-3 and 3-4 could be arranged for simple numericalequivalents like this: Reference [NIC4] on Russian Cryptography describes the VICCipher and the one-time pad. Both involve mathematicaltreatment to numerical based ciphers. TheHill Cipher is another good example of the use of mathematical transformation processes on ciphers and is presented in David Kahn's book.[KAHN] In modern cryptographic systems, the DES family of ciphers usesimple S-Boxes [substitution boxes] that are reorganized byordered non-linear mathematical rules applied several timesover (know as rounds). [NIC4], [OP20], [RHEE], [HILL], [IBM1] The question of 'unbreakable' mathematical ciphers might bepoised at this juncture. Lets look at the famous one-time padand see what it offers. [NIC4] The one-time pad is truly an unbreakable cipher system. Thereare many descriptions of this cipher. One of the betterdescriptions is by Bruce Schneier. [SCHN] It consists of anonrepetitive truly random key of letters or characters that isused just once. The key is written on special sheets of paperand glued together in a pad. The sender uses each key letteron the pad to encrypt exactly one plain text letter orcharacter. The receiver has an identical pad and uses the keyon the pad, in turn, to decrypt each letter of the ciphertext.[SHAN] Each key is used exactly once and for only one message.The sender encrypts the message and destroys the pad's page.The receiver does the same thing after decrypting the message.New message - new page and new key letters/numbers - each time. The one-time pad is unbreakable both in theory and in practice.Interception of ciphertext does not help the cryptographerbreak this cipher. No matter how much ciphertext the analysthas available, or how much time he had to work on it, he couldnever solve it. [KAHN] The reason is that no pattern can be constructed for the key.The perfect randomness of the one time system nullifies anyefforts to reconstruct the key or plain text via horizontal orlengthwise analysis, via cohesion, via re-assembly (such asKasiski or Kerckhoff's columns) via repeats or via internalframework erection. [KAHN] [KAH1], [WRIX], [NIC4], [SCHN] Brute force (trial and error) might bring out the trueplaintext but it would also yield every other text of the samelength, and there is no way to tell which is the right one.The worst of it is that the possible solutions increase as themessage lengthens. Supposing the key were stolen, would this help to predictfuture keys? No, because a random key has no underling systemto exploit. If it did, it would not be random. [KAHN] A random key sequence XOR 'ed with a nonrandom plain textmessage produces a completely random ciphertext message and noamount of computing will change that. [SCHN] The one-timepad can be extended to encryption of binary data. Instead ofletters, we use bits. [SCHN] The one-time pad has a drawback - the quantities of fresh keyrequired. For military messages in the field (a fluidsituation) a practical limit is reached. It is impossible toproduce and distribute sufficient fresh key to the units.During WWII, the US Army's European theater HQ's transmitted,even before the Normandy invasion, 2 million five (5) lettercode groups a day! It would have therefore, consumed 10million letters of key every 24 hours -the equivalent of ashelf of 20 average books. [KAH1] , [FRAA] The real issue for the one-time pad, is that the keys must betruly random. Attacks against the one-time pad must be againstthe method used to generate the key itself. [SCHN] Pseudo-random number generators don't count; often they have nonrandomproperties. Reference [SCHN], Chapter 15, discusses in detailrandom sequence generators and stream cipher. I take exceptionto his remarks regarding keyboard latency measurement.People's typing patterns are anything but random (especially ustwo finger types). [SCHN] [MART] Begin with a cipher (A=1, B=2 ...) Many variations exist. Note in the cipher text T1 .ne. T2.ne. T(i) and A1 .ne. A2 .ne. A(i), etc. [MARO] The one-time pad originated from the work of Gilbert Vernam in1917. Vernam worked for ATT. He got his idea from the Frenchtelegrapher Emile Baudot. Baudot code replaced letters withelectrical impulses, called units. Every character was given 5units that either signified a pulse of electrical current("marks") or its absence ("spaces") during a given time period.[ 32 combinations in all]. In 1917, paper tape was used andthe marks and spaces were read by metallic fingers. Vernamessentially automated the process and devised a cipher on it. In modern computer terms, key bits were added modulo 2 toplaintext bits on a bit by bit basis. If X = x1, x2, x3..denotes the plain text, and K = k1, k2, k3 .. the keystream,Vernam's cipher produces a cipher text bit stream Y = Ek(X) =y1, y2, y3. [VERN] Other countries conducted similar research. Between 1918-1920,other one-time pad methods were developed. The German ForeignOffice employed the one-time pad in 1920. The Russians firststole and then improved the German system. It was fullydeployed in 1925 for diplomatic use! OSS and SOE operatives inWWII had special grid one-time pad's. By 1944, OSS technicianshad developed pages made of film that were read with a handmagnifying glass. By 1960, Russian pads were the size of apostage stamp or scrolls the size of a large eraser. TheRussians were first to conceal the one-time pad in microfilm.One-time pads were made of cellulose nitrate for rapiddestruction. [RHEE] ,[VERN], [TERR], [KAHN] So why classify the one-time pad with Russian Ciphers? Becausethey have been serious about using it since 1925! Before 1917,Russian diplomatic and military systems could be expressed bythe old axiom: After her loss of trade information to the British in 1920, anddefeats of her Army in WWI because of poor cipher handling, shewoke up. By 1916, Russia's intercept service at Nicolaieffwas in full service against the Germans. From 1920 throughtoday, Russia has targeted stealing other countries codes with"great vigor" as Kennedy once said. Code stealing was donethrough the COMINT efforts of the former KGB and GRU. TheSpets-Odel (Special Department) was a primary agency involvedwith Ciphers and Cryptanalysis. Section 6 grew 400% over a 10year period prior to WWII. The Soviet Union has employed the one-time pad to protect ALLher diplomatic missions from 1930 on. Consequently hercrucial Foreign Office messages were not read by foes,neutrals, nor allies. The GRU and the Soviet Spy rings -"LUCY", "RED ORCHESTRA, and "Sorge's Net" all used the one-time pad. They also used a straddling checkerboard variant(not unbreakable). The one-time pad is used in the old fashioned form in theSoviet Mission - diplomatic , secret police, military,commercial, political (Communist Party) - all have their ownkeys. All cables coming into a legation look alike: simplegroups of five digits. Letters that are photographed,codenames are applied and then enciphered in one-time padsystem. [COVT], [BLK], [BARR] Agents in the field use the one-time pad. Radio links toMoscow, are encrypted via one-time pads. The main Soviet spycipher today still employs the one-time pads. The most dramatic spy stories (Klaus Fuchs, Iger Gouzenko,Vladimir Petrov, Colonel Zabotin, Rudolf Abel, GregoryLiolios, Eleftherious Voutsas, the Krogers, Guiseppe Martelli,Ali Abbasi, Reino Hayhanen, Aldridge Ames ...) all have usedthe one-time pads. Such is cryptology in the Soviet Union - complex, enigmatic,focused, state-of-the-art, applying the one-time pad principlesto other ciphers. Do you remember when the diplomatic ciphersin use at the American embassy in Moscow were solved? Russiahas a profound understanding of cryptography and cryptanalysis.[VOGE], [SUVO], [KAHN] The U.S. history was different. Some would argue that the U.S.became serious and superplayers in 1953. Some would argue1943. But not many will argue 1925 (we still had SIGTOT then).[SISI] In Lecture 4, we will complete our look into Englishsubstitution ciphers, by describing multiliteral substitutionwith difficult variants. The Homophonic and GrandPre Cipherswill be covered. A synoptic diagram of the substitutionciphers presented in Lectures 1-4 will be presented. We will cover recognition and solution of XENOCRYPTS (languagesubstitution ciphers) in detail. BOZOL gets the kudo for best solution on the homework. Bothproblems were unkeyed. Message reads: Sanity is the great virtue of the ancientliterature; the want of that is the great defect of the modern,in spite of its variety and power. Matthew Arnold Try the A=e, Q=t, e=h, O=r, and I=n. Look for words offer,battles, death, country. Message reads: "I offer neither pay nor quarters norprovisions. I offer hunger, thirst, forced marches, battlesand death. Let him who loves our country in his heart and notwith his lips only, follow me." Made famous by Girabaldi. Solve the following cipher problems. Any mistakes you find are quite likely mine. Please let me know about them by e-mailing: Thanks.A - 6.2 J - 0.16 S - 5.1B - 0.84 K - 0.25 T - 7.7C - 2.6 L - 3.0 U - 2.2D - 3.5 M - 2.1 V - 1.3E - 11.0 N - 6.6 W - 1.3F - 2.3 O - 6.3 X - 0.41G - 1.3 P - 2.3 Y - 1.6H - 2.9 Q - 0.25 Z - 0.08I - 6.2 R - 6.4
On the other hand, if the word separator is a single character,this character may be identified by its positional appearancespaced 'wordlength-wise' in the cipher text and by the factthat it never contacts itself.ANAGRAMING
NUMERICAL CIPHERS
Plain - A B C D E F G H I J K L MCipher - 11 12 13 14 15 16 17 18 19 20 21 22 23Plain - N O P Q R S T U V W X Y ZCipher - 24 25 26 27 28 29 30 31 32 33 34 35 36
We could easily have started the cipher alphabet with A= 01,B=02,..., Z=26 with the same results.Plain - A B C D E F G H I - J K L MCipher - 76 88 01 67 04 80 66 99 96 96 02 69 90Plain - N O P Q R S T U V W X Y ZCipher - 77 05 87 60 39 79 03 78 68 98 86 70 97
The computer whizzes are now thinking that the example hasall numbers less than 100. Therefore, a brute force attackon all combinations of two letter-equivalents of the aboveciphertext numerical values taken two at a time in combinationwith the digram frequency data could be a good approach to thecipher matrix construction problem. The ASOLVER computerprogram at the CDB does this kind analysis and adds thresholdlimitations on the search. Figure 3-3a Figure 3-4a 1 2 3 4 5 1 2 3 4 5 6 7 8 9 ................ ............................ 1 . A B C D E 1 . A B C D E F G H I 2 . F G H IJ K 2 . J K L M N O P Q R 3 . L M N O P 3 . S T U V W X Y Z * 4 . Q R S T U 5 . V W X Y Zwhere: A = 11, R=42 Z=55
Numerical cipher values lend themselves to treatment by variousmathematical processes to further complicate the cipher systemin which they are used. These processes, mainly addition orsubtraction, may be applied to each cipher equivalentindividually, or to the complete numerical cipher message byconsidering it as one number. [OP20]ONE-TIME PAD
FRESH KEY DRAWBACK
RANDOMNESS
ONE-TIME PAD SIMPLE EXAMPLE W/O SUPERENCIPHERMENT OR XOR
PT: T A X A T I O N I S T H E F TCE: 20 1 24 1 20 9 15 14 9 19 20 8 5 6 20
From a table of truly random numbers: 10480 15011 01536 02011 81647 91646 69719 22368 45673 25595 85393 30995 89198 27982 24130 48360 22527 97265 76393 64809 15179 42167 ....
Add the cipher equivalent to the random key: T A X A T I 20 1 24 1 20 9 10480 15011 01536 02011 81647 91646 ----- ----- ----- ----- ----- ----- ... 10500 15012 01560 02012 81667 91655
Transmit new cipher text: 10500 15012 01560 02012 81667 91655 69734 .....
Receiver subtract key out of message and decodes equivalents.ONE-TIME PAD HISTORICAL CONSIDERATIONS
CONCURRENT DEVELOPMENTS
RUSSIAN IMPLEMENTATION OF THE ONE-TIME PAD
LECTURE 4
LECTURE 5 - 6
SOLUTION TO HOMEWORK PROBLEMS FROM LECTURE 2
Pd-1. DanielH Z K L X A L H X P N C I N Z X F L I X G N W Q XP N Z K T L N K X O L X N I Z X G I N X P N E Z KX W Q X P Z X L H X P N C I N Z X S N Q N T X W QX P N W V S N I K L K H B L X N W Q L X H F Z I LN X A Z K S B W E N I.
Problem 1 breaks down as follows:High frequency (top 7%), count = 8 : XNLZIMedium frequency letters: : KPWHQSLo frequency (less than 3) : ABCEFGTOVZero (0) frequency : DJMRUYBy "N" Gram Count 6 gram Count CT FrequencyHXPNCI 2 5 19 6 17 2 8LHXPNC 2 10 5 19 6 17 2NCINZX 2 17 2 8 17 9 19PNCINZ 2 6 17 2 8 17 9XPNCIN 2 19 6 17 2 8 175 gramsCINZX 2 2 8 17 9 19HXPNC 2 5 19 6 17 2LHXPN 2 10 5 19 6 17NCINZ 2 17 2 8 17 9PNCIN 2 6 17 2 8 17WQXPN 2 6 5 19 6 17XPNCI 2 19 6 17 2 8XWQXP (THATS)? 2 19 6 5 19 64 gramsCINX 2 2 8 17 9HXPN 2 5 19 6 17INZX 2 8 17 9 19LHXP 2 10 5 19 6NCIN 2 17 2 8 17PNCI 2 6 17 2 8QXPN 2 5 19 6 17WQXP 2 6 5 19 6YPNC 2 19 6 17 2XWQX (THAT)? 2 19 6 5 193 gramsCIN 2 2 8 17HXP 2 5 19 6INZ 2 8 17 9LHX 2 10 5 19LXN 2 10 19 17NCI 2 17 2 8NWQ 2 17 6 5NZX 2 17 9 19PNC 2 6 17 2QXP 3 5 19 6WQX 3 6 5 19XPN 5 19 6 17XWQ 2 19 6 52 grams Count CT FrequencyCI 2 2 8HX 2 5 19IN 3 8 17KL 2 7 10KX 2 7 19LH 2 10 5LN 2 10 17LX 4 10 19NC 2 17 2NI 2 17 8NW 3 17 6NX 2 17 19NZ 3 17 9PN 5 6 17QX 3 5 19SN 2 3 17WQ 4 6 5XA 2 19 2XG 2 19 2XN 2 19 17XP 6 19 6XW 2 19 6ZK 4 9 7ZX 4 9 19 Frequency * Variety = ContactsA 2 3 6 XLZB 2 4 8 HLSWC 2 2 4 NID 0 0 0E 2 3 6 NZWF 2 4 8 XLHZG 2 3 6 XNIH 5 6 30 ZLXKBFI 8 7 56 CNLXZGKJ 0 0 0K 7 8 56 ZLTNXIHSL 10 11 110 KXAHFITNOBQM 0 0 0N 17 13 221 PCIZGWLKXESQTO 1 2 2 XLP 6 3 18 XNZQ 5 4 20 WXNLR 0 0 0S 3 5 15 XNVKBT 2 4 8 KLNXU 0 0 0V 1 2 2 WSW 6 6 36 NQXVBEX 19 15 285 LAHPZFIGQKONWSTY 0 0 0Z 9 9 81 HKNXIEPFA
From above data we try X= t and N=e, P=h. Then E=y, L=i,W=o, S = D.Pd-2. Join the army. DanielF L B B A O I A F Q E A O M Z U I L O N R Z O Q AO P I L O M O L S F P F L I P F L B B A O E R I CA O Q E F O P Q B L O W A V H Z O W E A P X Z Q QG A P Z I V V A Z Q E G A Q E F H T E L G L S A PL R O W L R I Q O U F I E F P E A Z O Q Z I V I LQ T F Q E E F P G F M P L I G U B L G G L T H A.Problem 2 breaks down as follows:High frequency (top 7%), count = 10 : LOAFQEIMedium frequency letters: : PZGBRVHMTUWLo frequency (less than 3) : SCNXZero (0) frequency : DJKYBy "N" Gram Count 6 gram Count CT FrequencyFLBBAO 2 12 15 6 6 14 155 gramsFLBBA 2 12 15 6 6 14LBBAO 2 15 6 6 14 154 gramsBBAO 2 6 6 14 15FLBB 2 12 15 6 6LBBA 2 12 6 6 143 gramsBAO 2 6 14 15BBA 2 6 6 14EFP 2 11 12 10FLB 2 12 15 6FQE 2 12 12 11ILO 2 11 15 15LBB 2 15 6 6PFL 2 10 12 15QEF 2 12 11 12ZIV 2 8 11 4ZOQ 2 8 15 122 grams Count CT. FrequencyAO 5 14 15AP 3 14 10AZ 2 14 8BA 2 6 14BB 2 6 6BL 2 6 15EA 3 11 14EF 4 11 12FL 3 12 15FP 3 12 10FQ 2 12 12GA 2 7 14GL 2 7 15IL 3 11 15IV 2 11 4LB 2 15 6LG 2 15 7LI 2 15 11LO 3 15 15LR 2 15 4LS 2 15 2OM 2 15 3OP 2 15 10OQ 3 15 12OW 3 15 3PF 2 10 12PL 2 10 15QE 5 12 11RI 2 4 11ZI 2 8 11ZO 3 8 15ZQ 2 8 12 Frequency * Variety = ContactsA 14 14 196 BOIFEQCWVPGZSHB 6 5 30 LBAQUC 1 2 2 IAD 0 0 0E 11 12 132 QAORFWGTLIPEF 12 13 156 LAQSPEOHUITGMG 7 9 63 QAELPFIUGH 3 5 15 VZFTAI 11 13 143 OAULPRCZVQFEGJ 0 0 0K 0 0 0L 15 12 180 FBIOSEGPRWQTM 3 4 12 OZFPN 1 2 2 ORO 15 13 195 AIMLNZQPEFWRUP 10 11 110 OIFQAXZLEGMQ 12 12 144 FEOAPBZQGILTR 4 6 24 NZEILOS 2 3 6 LFAT 3 5 15 HEQFLU 3 6 18 ZIOFGBV 4 4 16 AHIVW 3 4 12 OAELX 1 2 2 PZY 0 0 0Z 8 10 80 MUROHQXPIA
BOZOL tried the crib word World from "Join the Army ..see theworld" The crib failed but did show him some possibilities.LANAKI's caveat - Forget the tip, it is usually a red hering.HOMEWORK LECTURE 3
Mv-1. From Martin Gardner. 8 5 1 8 5 1 9 1 1 9 9 1 3 1 6 1 2 5 1 1 2 1 6 8 1 2 5 2 0 9 3 3 1 5 4 5 2 0 8 1 2 0 9 2 2 5 1 4 5 2 2 5 1 8 1 9 5 5 1 4 2 5 6 1 5 1 8 5 1 3 1 2 5 2 5 2 5 1 5 2 1 3 1 1 4 2 1 1 9 5 9 2 0 9 1 4 2 5 1 5 2 1 1 8 3 1 5 1 2 2 1 1 3 1 4 1 3 1 1 8 2 0 9 1 4 7 1 1 8 4 1 4 5 1 8 8 5 1 4 4 5 1 8 1 9 1 5 1 4 2 2 9 1 2 1 2 5 1 4 1 5 1 8 2 0 8 3 1 1 8 1 5 1 2 9 1 4 1
Solve and reconstruct the cryptographic systems used.Mv-2.0 6 0 2 1 0 0 5 0 1 0 1 0 5 1 5 2 2 0 2 0 6 0 8 23 2 5 1 0 0 8 0 4 0 2 2 1 0 9 0 8 0 4 0 8 2 2 1 10 8 0 4 1 7 1 5 1 3 1 4 2 2 2 1 0 2 2 4 0 2 0 1 22 0 2 0 2 0 1 0 8 1 9 0 6 1 5 1 7 0 8 0 1 1 1 2 21 4 0 2 0 1 1 9 0 6 0 5 1 0 0 2 0 2 1 1 2 2 1 4 06 2 3 1 9 0 5 1 5 0 1 2 2 1 3 0 2 0 5 0 6 1 3 0 20 5 0 1 1 0 0 5 2 3 0 6 2 1 0 2 2 2 1 4 0 6 0 2 02 2 2 1 4 0 6 0 2 0 2 2 6 0 2 0 6 0 5 2 1 1 9 0 20 2 1 1 2 2 0 3 0 2 1 7 2 4 0 2 1 9 0 2 0 6 1 5 05 1 1 0 6 0 2 1 9 0 5 0 6 2 2 0 1 0 5 0 5 0 1 1 90 5 2 1 1 5 2 2 1 5 0 5 0 1 2 2 0 5 1 8 0 5 0 6 06 0 5 0 3Mv-3.5 3 2 4 1 5 4 5 3 2 2 4 4 3 2 5 1 2 4 3 2 4 2 3 15 4 4 4 5 4 5 3 2 5 1 4 3 4 4 1 4 1 5 2 1 4 1 1 54 3 4 5 3 5 2 1 2 3 3 5 1 2 5 1 1 4 2 1 5 3 3 3 45 3 2 4 4 2 3 1 5 4 5 4 5 2 4 4 3 2 4 1 4 4 4 3 21 2 5 3 2 4 4 3 4 4 2 4 1 5 4 4 4 5 2 4 4 3 3 5 21 5 3 3 3 1 3 1 4 4 4 1 5 4 5 4 4 5 1 4 3 2 5 1 52 3 2 4 1 5 5 2 2 4 4 3 1 5 3 1 3 3 1 3 3 1 4 5 53 2 4 1 3 4 5 2 1 2 5 3 3 5 2 2 4 3 4 1 3 1 2 4 54 4 5 2 3 3 4 4 3 3 2 2 3 3 3 5 3 3 4 5 2 1 3 5 24 4 4 4 4 4 5 3 2 1 5 1 3 1 5 5 2 2 4 4 3 1 5 3 12 4 5 1 1 3 1 4 2 4 4 4 3 3 4 3 1 5 2 2 3 5 2 4 25 3 5 2 1 3 3 1 3 3 1 2 3 1 2 1 3 1 4 3 3 4 5 3 31 2 1 3 4 4 4 1 2 4 4 3 3 3 1 2 1 4 3 2 2 4 3 3 31 3 2 4 5 1 2 2 5 3 5 1 2 5 3 2 3 3 5 1 2 5 1 1 44 4 1 5 4 5 4 1 4 3 2 4 4 4 2 4 1 3 4 5 1 5 2 2 12 5 1 4 5 1 2 1 3 2 4 4 5 3 2 1 2 5 1 4 4 1 5 1 31 4 2 5 2 4 2 4 4 5
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Joe Peschel