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This article was downloaded by: [Northeastern University] On: 20 November 2014, At: 05:04 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Cryptologia Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/ucry20 Reading Encrypted Diplomatic Correspondence: An Undergraduate Research Project Jeffrey D. Adler , Ryan W. Fuoss , Michael J. Levin & Amanda R. Youell Published online: 10 Jan 2008. To cite this article: Jeffrey D. Adler , Ryan W. Fuoss , Michael J. Levin & Amanda R. Youell (2008) Reading Encrypted Diplomatic Correspondence: An Undergraduate Research Project, Cryptologia, 32:1, 1-12 To link to this article: http://dx.doi.org/10.1080/01611190701498212 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms- and-conditions

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Page 1: Reading Encrypted Diplomatic Correspondence: An Undergraduate Research Project

This article was downloaded by: [Northeastern University]On: 20 November 2014, At: 05:04Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

CryptologiaPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/ucry20

Reading Encrypted DiplomaticCorrespondence: An UndergraduateResearch ProjectJeffrey D. Adler , Ryan W. Fuoss , Michael J. Levin & Amanda R.YouellPublished online: 10 Jan 2008.

To cite this article: Jeffrey D. Adler , Ryan W. Fuoss , Michael J. Levin & Amanda R. Youell (2008)Reading Encrypted Diplomatic Correspondence: An Undergraduate Research Project, Cryptologia,32:1, 1-12

To link to this article: http://dx.doi.org/10.1080/01611190701498212

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.

This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Reading Encrypted Diplomatic Correspondence: An Undergraduate Research Project

Reading Encrypted Diplomatic Correspondence:An Undergraduate Research Project

JEFFREY D. ADLER, RYAN W. FUOSS, MICHAEL J. LEVIN,AND AMANDA R. YOUELL

Abstract We describe the cryptanalysis of a collection of sixteenth-centurySpanish diplomatic correspondence, performed by undergraduates who did notknow Spanish.

Keywords cryptanalysis, diplomacy, Renaissance, Spain, undergraduate research

1. An Undergraduate Research Program

In the summer of 2005, the Department of Theoretical and Applied Mathematics atThe University of Akron began a Research Experiences for Undergraduates pro-gram. Two of the present authors were among nine participants recruited fromaround the United States. The other two authors directed or consulted for one ofthe three available research projects: the cryptanalysis of some sixteenth-centurySpanish diplomatic correspondence.

One of the authors came upon this correspondence while conducting research atthe State Archive at Simancas, Spain. Unfortunately, portions of many of the lettersare encrypted, and at the time, it was not clear whether any written key still existed.For some documents, plaintext versions are available, so for the purposes of histori-cal research it made sense to concentrate on those. However, future trips to thearchive would be potentially more productive if a recipe for producing keys couldbe concocted. Thus, the present project’s goal was to produce such keys and recipes.(We have since learned of the existence of many keys in [3]. In particular, we nowknow that the students’ work was extremely accurate.)

We began the project with a microcourse on the history of cryptography, andcontinued with a description of the historical role of the documents at our disposal(see x2). The students were provided with photocopies of all these documents, exceptthe associated plaintext was sometimes deliberately withheld. Since the studentscould not always read even the unencrypted portions on their own, the faculty advi-sors provided a cast of characters, as well as the common abbreviations in Table 1.

After the initial stages of work, all students were allowed to choose between thisproject and others. Although such a degree of choice created more work for the

Research supported by the National Science Foundation, grant DMS-0354022, ResearchExperiences for Undergradates at The University of Akron.

Address correspondence to Dr. Jeffrey Adler, Department of Mathematics and Statistics,American University, 4400 Massachusetts Avenue NW, Washington, DC, 20016-8050, USA.E-mail: [email protected]

Cryptologia, 32:1–12, 2008Copyright � Taylor & Francis Group, LLCISSN: 0161-1194 printDOI: 10.1080/01611190701498212

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organizers, it led to a high level of student enthusiasm, which was necessary tosustain the project through many hours of labor.

2. Historical Background

Cryptography, and its counterpart cryptanalysis, came of age in the Italian Renais-sance.1 This development was directly related to the rise of modern diplomacy anddiplomatic practice, which also originated in Renaissance Italy.2 In the mid- tolate-fifteenth century, various Italian city-states developed networks of permanentresident embassies, which were perceived as tools to help maintain a balance ofpower in the peninsula. The practice spread across the Alps to the rest of WesternEurope. Ferdinand ‘‘the Catholic’’ of Spain was one of the first monarchs to adoptthe Italian diplomatic system, and in the period 1480–1500 established residentembassies in Rome, Venice, London, Brussels, and the itinerant court of the HolyRoman Emperor.3

Ferdinand’s successors, Charles V (r. 1516–1556) and Philip II (1556–1598),inherited this diplomatic system and quickly realized its benefits as a source forthe gathering and dissemination of political intelligence.4 This was especially criticalin Italy, one of the main battlegrounds between Spain and France in the sixteenthcentury. In particular, the Spanish resident embassies in Rome and Venice, thetwo most powerful states in Italy, became spy centers.5. The ambassadors reportedon the intentions and actions of Venice and the Papacy, and whether they would aidor thwart Spanish efforts to establish control of the Italian peninsula. Recognizingthe need to keep secrets, the Spanish Crown developed means of protecting its com-munications with the ambassadors, and Spanish cryptography became increasinglyimportant.

The Crown of Aragon had been using ciphers since the beginning of the fifteenthcentury.6 However, some of the codes were so difficult to use that in 1504 the

Table 1. Some common abbreviations.

VMd vuestro Majestad Your Majesty_qq que[curly-Q] quetp _oo tiempop _aa parapucas publicasobpo Obispo bishopRepca RepublicaSusd Su Santidad His Holiness

1[10], pp. 18–22; [6], chapter four.2See the classic work by Garrett Mattingly [8], and, more recently, [5].3[4], p. 132.4[8], p. 160.5See [7], chapter six.6See [1], pp. 171–176. We thank one of our anonymous referees for providing this

citation.

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Spanish Crown replaced them with simpler systems.7 When Philip II came to thethrone, he overhauled Spain’s secret services. The Spanish spy network was greatlyexpanded, and new emphasis was placed on developing effective codes.8 In fact, oneof Philip’s first actions as king was to scrap all the codes his father had employed infavor of new, more sophisticated ciphers (that were nonetheless easier for us tocrack). Philip instructed all his ambassadors that they were now to use two differentcode systems: a ‘‘general cipher’’ (cifra general) for ordinary correspondencethroughout the diplomatic network, and a separate code that was unique to eachambassador (cifra particular) for more sensitive material. Furthermore, all codeswere changed every few years.9 Despite these precautions, the effectiveness ofSpanish codes is a matter of debate among modern historians. David Kahn, forexample, claims that the Spanish ‘‘apparently knew little about cryptanalysis,’’and that Spain’s opponents, or at least the Papacy and the French, easily brokeSpain’s codes.10 On the other hand, Geoffrey Parker writes that the evidence isambiguous. Spain’s enemies obtained the keys to a number of their codes by chance,force, or treachery, but it is not clear if they actually broke any codes without suchhelp.11

In any case, the Spanish ambassadors featured in this study had plenty to besecretive about. Don Diego Guzm�aan de Silva (d. 1578), for example, the residentambassador in Venice from 1571 to 1576, struggled to understand the intricaciesof Venetian politics. In 1571, Spain, Venice, and the Papacy formed a militaryalliance against the Ottoman Turks, who, being Muslim, were seen as enemies ofGod. Beyond their fear and hatred of the Turks, however, these three powers hadlittle in common. Although they enjoyed initial success (climaxing with the greatnaval victory of the Battle of Lepanto), the alliance collapsed in 1573. Much tothe Spaniards’ disgust, the Venetians signed a separate truce with the Turks.Guzm�aan de Silva’s correspondence throughout this period reflects his uncertaintyabout what the Venetians would do next.12 His letters run the gamut from exhilar-ation to despair, depending on the latest events—and much of it had to be in code,for he trusted the supposedly friendly Venetians little more than Spain’s outrightenemies. It is these coded letters, along with those of other contemporary Spanishambassadors, that were the basis of the present study.

3. Two Particular Letters

For the sake of brevity, we limit our attention here to one letter and only briefly lookat a second.

In 1572, as a follow up to the battle of Lepanto, Venice and the Papacy wantedto organize another campaign against the Turks. But King Philip was unwilling, andso the campaign never materialized. Guzm�aan de Silva did not know what the Kingwas trying to do. He only knew that the campaign was not happening and that it was

7[6], p. 114.8See the recent work by Carlos Carnicer and Javier Marcos [2].9[6], p. 115.10[6], p. 118.11[9], pp. 215–216. Parker does say that Spain suffered greatly due to intelligence failures

(or successes, from the point of view of its enemies). For example, Parker refers to the plansfor the Spanish Armada of 1588 as the ‘‘worst kept secret in Europe.’’

12[7], pp. 30–38, 160–165.

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Spain’s fault. The Venetians complained bitterly to him about this. The ambassadorwas thus in the difficult position of having to defend a government policy that hehimself did not understand.

In document E1331-69 (see Table 2 and [7, pp. 34–36]), he writes of how heresponds to Venetian comments, all of which are negative. He reminds the Venetiansof the maliciousness of the French and the friendship of the King of Spain, but theVenetians do not believe him.

Meanwhile, Philip had sent a huge army to the Netherlands to put down a revoltagainst Spanish control. The Venetians mention this as an example of how Spaintreats even its own subjects.

Guzm�aan de Silva simply replies that one cannot compare Philip’s treatment ofthe Dutch and his friendship with the Venetians. Like all diplomats, he must presenta forceful case while hiding his own doubts and suspicions.

At this point, the tone of the letter becomes less journalistic and more rhetorical.It is not clear whether the further conversations that Guzm�aan de Silva reports actuallyoccurred, or whether he has invented them as a device for indirect criticism of theKing. For example, after listing unattributed, negative comments about Spain, hereports arguing that Philip knows what he’s doing, and the Venetians have no rightto judge him. He then adds in code (cifra particular) that he only uses this argumentwith people of quality (i.e., nobles). He does not say such things in the college (a bodythat represents the middle classes), because that would only make them angry. Withthese people, he simply assures them of how much Philip cares for the common good.

For contrast, we now present the content of the coded portion of documentE1332-72 (see Table 2). Don Cesar de la Mara was outlawed from his native Naplesfor allegedly killing his mother, and now lives in Ragusa (modern-day Dubrovnik).Angry and virtually a captive there, he offers his services to both the Bishop of Aixand the King of France. However, he is actually a double-agent, working forGuzm�aan de Silva. Now Don Cesar is offering to procure a secret from a merchantwho will soon travel to Constantinople, but in return for his service to the King,he wants the outlaw decree against him lifted. Guzm�aan de Silva writes about allof this in (weak!) code, mentions how difficult it is to find good intelligence sources,and recommends that the King accept the deal.

Table 2. Documents analyzed.

Box and doc. # From Date

E1399-5 Venice� Jan 1570E1331-69 Venice Jul 1572E1332-40 Venice Apr 1573E1332-72 Venice Jul 1573E1334-53 Venice Jul 1575E1335-25 Venice Apr 1576

E922-34 Rome Jan 1573

IV 115. . . Paris�� Dec 1569

�Sent from Genoa, where the Venice ambassador was filling in.��Sent to the Ambassador in Rome, not to the King. This docu-

ment came from a different archive: Instituto de Valencia de DonJuan (Madrid).

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4. Introduction to the Cipher

In practice, an ambassador would compose a message with the help of a secretary,switching freely between plaintext and ciphertext, depending on the topics andpersons discussed (and the more or less flattering manner of discussing them). Uponreceipt in Spain, the message would be decoded by another secretary, who wouldoften write the plaintext in the margins and cross out the ciphertext.

Fortunately, the procedure of writing plaintext in the margins of these docu-ments has provided numerous examples in which a precise, word-for-word decryp-tion of a segment of coded text is available for purposes of comparison. Figure 1offers a typical example (with a transcription in Figure 2). This particular documentoffers an example of the cifra general of 1571.13

As Figure 1 illustrates, however, even the plaintext is far from clear—the docu-ments are, after all, over four hundred years old, the ink has leaked through, andsometimes one only has access to nth-generation photocopies. Scribes often usedabbreviations that would not be clear to a casual modern reader. Moreover, thehandwriting itself often requires some decryption.

Obviously, a basic knowledge of Spanish would be useful in decrypting thesedocuments, although much of the actual work is statistical. Sixteenth-centurySpanish is much closer to its modern form than English is to its own modern form,but spelling was much less standardized than today, and writers sometimes omittedbreaks between words.

By having the plaintext and the ciphertext written out side by side, it becomes asimple process of looking for commonalities, particularly noting distinctive repeti-tions of letters in close sequence: ‘‘los mismos,’’ for example, roughly correspondswith the in the ciphertext. This is the first step in creating a key forwhat is a relatively simple monoalphabetic substitution cipher—each symbol standsfor one letter of plaintext. In this case, 6 is l, 7 is m, and 15 is s, with separate non-numeric symbols for the intervening vowels. Continuing this process for the wholedocument, we see the correspondences and their relative frequencies as in Table 3.

There is a separate set of symbols for vowels that immediately follow consonants.These symbols sit either directly above or directly after those for the consonants.In addition, there are separate symbols for r (a dot below) and l (a dot above)when they are between another consonant and a vowel, as in the word ‘‘tratados’’in Figures 1 and 2. Table 4 gives examples of each vowel symbol and their relativefrequencies.

Figure 1. Section taken from document E1331-69, a message sent by Ambassador DiegoGuzm�aan de Silva from Venice in July of 1572.

13This key, along with many others, appears in [3], pp. 135–142.

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Finally, there are certain symbols that stand for words in and of themselves: gen-erally either short sequences of letters, or numbers whose large size suggests that theydo not stand for individual letters. For example, we see from Table 7 that thesymbols , , �4141, and �4242, all of which appear in Figure 1, mean hombre,siempre, mas, and menos, respectively.

Table 3. Numeric symbol frequencies in E1331-69.

Symbol Letter Freq

0 b 81 c 312 d 373 f 44 g 25 h 46 l 297 m 158 n 599 p 2413 qu 1214 r 3215 s 5916 t 3218 y 1319 z 220 a 2221 ha 122 e 1923 e 824 j 325 i 227 o 928 v 9

Figure 2. Transcription and translation of the plaintext in Figure 1.

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5. Breaking the Code

All the above is very well when the plaintext is available, but this would not be thecase for anyone who, having intercepted a diplomatic message, was faced with thetask of decrypting it. Sometimes, several documents from the same period wouldhave been encrypted with the same key (as in E1332-40 and E922-34) or strikinglysimilar keys (as in E1399-5 and IV-115). There are several methods for convertinga code such as is found in Figure 1 to the type of plaintext found in Figure 2, butthey generally begin with what is undoubtedly the slowest, most tedious part ofthe whole process: counting each individual letter-symbol or number-symbol combi-nation. Since it is common in Spanish to have syllables consisting of one consonantfollowed by one vowel, it is typical in the codes to have one small symbol (as in Table4, there ought to be five of them, although there are notable exceptions in more com-plex codes) accompanying the letters or numbers that stand for letters. By counting

, , , , , and separately, it becomes a simple matter of creating tablessuch as Table 3 and Table 4 (excluding, for now, the middle column). At this point,there are several strategies that can help one determine which symbols stand forwhich letters.

1. Frequency analysis. Among the consonants in these communiques, s and n areby far the most common, so their symbols will also be among the most common

Table 4. Vowel symbol frequencies in E1331-69.

Ciphertext Plaintext Vowel Freq

na 31

ne 61

ni 42

no 90

nu 21

Table 5. Letter frequencies, after decryption, in the coded sections of selecteddocuments listed in Table 2.

Letter Freq Letter Freq Vowels after consonants Freq

b 99 r 588 a 698c 318 s 785 e 1151d 615 t 319 i 441f 62 v 184 o 724g 86 x 15 u 142h 179 y 171j 39 z 30l 497 a 297m 250 e 572n 745 o 96p 256 ch 48qu 260

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(Table 5 provides a broad overview for quick reference). Among the vowel sym-bols, e, o, and a are the most common, followed by i, and u is by far the leastcommon. This step alone is generally enough to determine the symbols for i,and u; two mutually exclusive guesses for s and n; and three mutually exclusiveguesses for e, o, and a.

It is important to note that any frequency analysis with documents of thistype (including the ones in our collection) will necessarily be approximate.For various reasons including poor handwriting and deterioration over time,some symbols will be illegible.

2. Digraph frequency. Some consonants inevitably appear more frequently withsome vowels than with others, and each will have a distinctive pattern in thisregard. See Table 6 for reference.

3. The word ‘‘que.’’ In these documents, qu is generally given one symbol. In Span-ish the word ‘‘que’’ (‘‘that’’) is quite common, and the qu is relatively uncommonoutside this context (see Table 6). Thus, there will generally be one consonantsymbol that almost always appears with one and only one vowel symbol. Thisstep can therefore not only give the symbol for qu, but also selects the singlesymbol of the three from Step 1 that stands for e.

4. The alphanumeric vowel symbols. These are such symbols as 20, 22, 23, 25, and27 from Table 3. They are distinctive not in their commonality, but rather in

Table 6. Frequencies of consonant=vowel combinations for selected documentslisted in Table 2.

b 8 f 2 l 162 qu 3 v 23 bl 0 dr 0ba 13 fa 12 la 100 qua 5 va 36 bla 1 dra 2be 13 fe 10 le 58 que 238 ve 62 ble 1 dre 3bi 30 fi 15 li 11 qui 14 vi 52 bli 8 dri 1bo 4 fo 5 lo 115 quo 0 vo 11 blo 0 dro 0bu 14 fu 12 lu 4 quu 0 vu 0 blu 0 dru 0c 13 g 7 m 31 r 262 x 5 br 2 pr 1ca 61 ga 17 ma 46 ra 75 xa 4 bra 3 pra 0ce 38 ge 8 me 83 re 59 xe 0 bre 4 pre 4ci 69 gi 4 mi 41 ri 29 xi 0 bri 0 pri 3co 101 go 18 mo 27 ro 19 xo 6 bro 1 pro 13cu 23 gu 31 mu 29 ru 2 xu 0 bru 0 pru 1ch 0 h 5 n 451 s 435 y 159 cl 15 tr 1cha 7 ha 88 na 50 sa 38 ya 7 cla 4 tra 21che 0 he 26 ne 73 se 134 ye 1 cle 0 tre 7chi 2 hi 5 ni 41 si 52 yi 3 cli 2 tri 2cho 28 ho 4 no 91 so 29 yo 9 clo 0 tro 7chu 0 hu 2 nu 7 su 37 yu 4 clu 1 tru 0d 16 j 19 p 5 t 2 z 2 cr 0 pla 8da 59 ja 5 pa 67 ta 97 za 4 cra 1 fra 1de 312 je 0 pe 31 te 121 ze 21 cre 10 fre 2di 70 ji 0 pi 10 ti 63 zi 6 cri 9 gra 5do 141 jo 13 po 84 to 106 zo 0 cro 0 gro 3du 7 ju 5 pu 25 tu 10 zu 1 cru 0 gri 1

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that they will rarely be followed by vowel symbols in simple code systems.There are examples of systems in which this does not hold: in E1399-5, forinstance, symbols associated with 17 were ignored and in IV-115 symbols asso-ciated with 19 rendered the translation ch rather than a. Despite these addedcomplexities, alphanumeric vowels generally remain recognizable as theirappearances without appended symbols tend greatly to outnumber those withsuch symbols.

5. Other common short words. Such words as ‘‘el,’’ ‘‘es,’’ ‘‘los,’’ and ‘‘con’’ will gen-erally appear more than once if the document is long enough, as will frequentlyused related words like ‘‘esta’’ and ‘‘estos,’’ and Steps 1 and 3 should alreadyhave yielded good guesses for s, n, the small vowel symbol for o, the alphanu-meric symbol(s) for e, and perhaps t. Another such common word is ‘‘de,’’which will particularly appear between word symbols, as in Step 6.

6. Short sequences between obvious unique symbols. For example, in the cases of, and , we see a short sequence of letter symbols

between what are apparently distinct words. This provides clear word breaks inwhat is otherwise a seemingly endless stream of letters, numbers, and symbols.In these two cases, the intermediate words are ‘‘del’’ and ‘‘porque,’’ respectively.

Once one has identified or developed good guesses for several symbols using themethods listed above, a few additional methods become useful.

7. Ordering of alphanumeric symbols. Due to the surprising simplicity of the ciphersin these documents, it is fairly common to see a logical alphabetical or numericalordering of the cipher symbols roughly corresponding to the alphabetical orderof their plaintext translations. In E1399-5, E1331-69, and IV-115, the orderingsare in direct correspondence, in E1332-40 and E922-34 the first three letters arereversed and thereafter the correspondence is direct, in E1335-25 the orderingcorresponds directly but the symbols alternate between numbers and letters,and even in E1334-53 some vestiges of this ordering scheme remain, howeverobscured by transpositions.

8. Spanish grammar and syntax. Although fluency in Spanish is not necessary, someknowledge of parts of speech, verb forms, etc. can be useful in filling in gaps inthe code and recognizing both possible and impossible constructions.

9. Context. When deciphering the code, it often helps to bear in mind expectedwords or ideas such as ‘‘embiar’’ (‘‘to send’’) or ‘‘Duque’’ (‘‘duke’’). If ‘‘micro-waves’’ or ‘‘flowered tutus’’ appear in the text, it might be a clue that one is onthe wrong path.

10. Ordering of word symbols. As can be noted from Table 7, in the cases that certainwords in a document are enciphered with unique number symbols, the apparentcommon practice was to list the words that would be so enciphered in alphabeti-cal order and simply number them with respect to that ordering.

Taken as a whole, this approach, along with its requisite trial and error,should be sufficient to decrypt virtually the whole of the alphabet—and oncethe symbols have been counted, it is possible to do the bulk of the work in a mat-ter of minutes, although a few symbols may take much longer. This leaves onlysuch symbols as are listed at the end of Table 7, which would not slow down aSpanish-literate, sixteenth-century Venetian (with all the contextual clues at hisor her disposal) in the slightest, but which can be virtually impenetrable withoutsuch knowledge.

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6. Description of Tables

Except as indicated, each document listed in Table 2 is a letter written by the Spanishambassador at the listed city, sent to the king of Spain and eventually deposited inthe State Archive at Simancas, Spain. Table 6 gives letter, digraph, and (selected) tri-graph frequencies for much of the collection of documents taken together. (The lownumbers in the final two columns of the table reflect the fact that, at least in the earlypart of the project, the students could not distinguish between meaningful dots andmeaningless ink spots.)

The professors on this project were impressed by the accuracy achieved by thestudents. Although the latter developed keys for all documents listed in Table 2,we include here only the key for E1399-69, for illustrative purposes. This key, givenin Table 7, is remarkably similar to the corresponding table in [3], to which we hadno access. The differences are as follows:

1. Some ciphertext symbols never appeared in our particular collection of docu-ments and so are missing from our table.

Table 7. Key for document E1331-69, as constructed by the students. For eachsymbol, we provide the plaintext and frequency.

0 b 8 41 mas 2 ��See below1 c 31 42 menos 1 a 31

2 d 37 49 nuncio 1 e 61

3 f 4 60 occasiones 1 i 42

4 g 2 81 pa 1 o 90

5 h 4 82 par 1 u 216 l 29 83 porque 17 m 15 84 quando 1 dri

8 n 59 40 amigos 1 bli9 p 24 47 assi 2

13 qu(2) 12 50 aunque 114 r 32 85 cosapucas 115 s 59 cra siempre 116 t 32 cru Turco 118 y 13 fla respuesta 119 z 2 fro todo 220 a 22 gro VMd 321 ha 1 gri tiempo 222 e 19 g

�con 1

23 e 8 je francais 124 j(4) 3 vo hasta(3) 125 i(4) 2 quu hombre 127 o 9

Re fuerco(3) 1

28 v 9

Note: Numbers in parentheses refer to notes in x6.��This part of the table illustrates how alterations to a ciphertext character representing a

consonant (in this case ‘‘n’’) specify which vowel follows.

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2. In our analysis, a single symbol represents ‘‘qu’’. In [3], a single symbol represents‘‘q’’, and the next typically represents a digraph. Thus, this particular differencein the tables does not affect the translation scheme and so is not an error.

3. In a few instances, we misread the handwriting in the original documents. Forexample, we read ‘‘vo’’ instead of ‘‘ro’’ and

Re instead of le in the ciphertext,

and ‘‘fuerco’’ instead ‘‘fuerca’’ in the plaintext.4. We should have conflated the letters i and j when they are used as consonants, but

did not. This is an issue of sixteenth-century spelling.5. The next to last row of our key does not correspond to any part of the key in [3].

It is possible that we should have read ‘‘2þ’’ instead of ‘‘2� þ,’’ and ‘‘di’’ insteadof ‘‘dri.’’

Acknowledgements

It is a pleasure to thank the following: The University of Akron and the NationalScience Foundation, for sponsoring the REU program in which this work wasperformed; Judith Palagallo, Thomas Price, and Jeffrey Riedl, who were the otherdirectors of the program; Thomas Price (again), for help with graphics; AntonioQuesada, for help with Spanish; three anonymous referees, who suggested severalimprovements and brought [3] to our attention; and the other student participantsin the program, all of whom took part in the early stage of this project. They were:Anne Chmura, Jennifer Feder, Briana Foster-Greenwood, Jonathan Gross, SallyHall, Michael Holm, and Ryan Johnson.

About the Authors

Jeffrey Adler was an associate professor of mathematics at The University of Akronwhen this work was performed and is now at American University. His primaryresearch interest is harmonic analysis on p-adic groups.

Ryan Fuoss was an undergraduate at Taylor University when this work was per-formed. Following graduation, he spent a year working for Habitat for Humanitybefore attending law school at the University of Michigan.

Michael J. Levin is an associate professor of history at The University of Akron.His research interest is early modern Spanish and Italian history.

Amanda Youell was an undergraduate at Clemson University when this workwas performed. She is now pursuing graduate studies in mathematics at the Univer-sity of Maryland.

References

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3. Devos, J. P. 1950. Les Chiffres de Philippe II (1555–1598) et du Despacho UniversalDurant le XVIIe Siecle. Brussels: Palais des Academies.

4. Elliott, J. H. 2002. Imperial Spain, 1469–1714. London: Penguin Books.5. Frigo, Daniela (ed.). 2000. Politics and Diplomacy in Early Modern Italy: The Structure of

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