Decoding Anagrammed Texts Written in an Unknown Language and Script

Bradley Hauer and Grzegorz Kondrak
Department of Computing Science

University of Alberta
Edmonton, Canada

{bmhauer,gkondrak}@ualberta.ca

Abstract

Algorithmic decipherment is a prime exam-
ple of a truly unsupervised problem. The first
step in the decipherment process is the iden-
tification of the encrypted language. We pro-
pose three methods for determining the source
language of a document enciphered with a
monoalphabetic substitution cipher. The best
method achieves 97% accuracy on 380 lan-
guages. We then present an approach to de-
coding anagrammed substitution ciphers, in
which the letters within words have been ar-
bitrarily transposed. It obtains the average de-
cryption word accuracy of 93% on a set of 50
ciphertexts in 5 languages. Finally, we report
the results on the Voynich manuscript, an un-
solved fifteenth century cipher, which suggest
Hebrew as the language of the document.

1 Introduction

The Voynich manuscript is a medieval codex1 con-
sisting of 240 pages written in a unique script, which
has been referred to as the world’s most important
unsolved cipher (Schmeh, 2013). The type of ci-
pher that was used to generate the text is unknown;
a number of theories have been proposed, includ-
ing substitution and transposition ciphers, an abjad
(a writing system in which vowels are not written),
steganography, semi-random schemes, and an elab-
orate hoax. However, the biggest obstacle to deci-

1The manuscript was radiocarbon dated to 1404-1438
AD in the Arizona Accelerator Mass Spectrometry Labo-
ratory (http://www.arizona.edu/crack-voynich-code, accessed
Nov. 20, 2015).

phering the manuscript is the lack of knowledge of
what language it represents.

Identification of the underlying language has been
crucial for the decipherment of ancient scripts, in-
cluding Egyptian hieroglyphics (Coptic), Linear B
(Greek), and Mayan glyphs (Ch’olti’). On the other
hand, the languages of many undeciphered scripts,
such as Linear A, the Indus script, and the Phaistos
Disc, remain unknown (Robinson, 2002). Even the
order of characters within text may be in doubt; in
Egyptian hieroglyphic inscriptions, for instance, the
symbols were sometimes rearranged within a word
in order to create a more elegant inscription (Singh,
2011). Another complicating factor is the omission
of vowels in some writing systems.

Applications of ciphertext language identification
extend beyond secret ciphers and ancient scripts.
Nagy et al. (1987) frame optical character recogni-
tion as a decipherment task. Knight et al. (2006)
note that for some languages, such as Hindi, there
exist many different and incompatible encoding
schemes for digital storage of text; the task of an-
alyzing such an arbitrary encoding scheme can be
viewed as a decipherment of a substitution cipher in
an unknown language. Similarly, the unsupervised
derivation of transliteration mappings between dif-
ferent writing scripts lends itself to a cipher formu-
lation (Ravi and Knight, 2009).

The Voynich manuscript is written in an unknown
script that encodes an unknown language, which is
the most challenging type of a decipherment prob-
lem (Robinson, 2002, p. 46). Inspired by the mys-
tery of both the Voynich manuscript and the un-
deciphered ancient scripts, we develop a series of

75

Transactions of the Association for Computational Linguistics, vol. 4, pp. 75–86, 2016. Action Editor: Regina Barzilay.
Submission batch: 12/2015; Published 4/2016.

c©2016 Association for Computational Linguistics. Distributed under a CC-BY 4.0 license.



algorithms for the purpose of decrypting unknown
alphabetic scripts representing unknown languages.
We assume that symbols in scripts which contain no
more than a few dozen unique characters roughly
correspond to phonemes of a language, and model
them as monoalphabetic substitution ciphers. We
further allow that an unknown transposition scheme
could have been applied to the enciphered text,
resulting in arbitrary scrambling of letters within
words (anagramming). Finally, we consider the pos-
sibility that the underlying script is an abjad, in
which only consonants are explicitly represented.

Our decryption system is composed of three steps.
The first task is to identify the language of a cipher-
text, by comparing it to samples representing known
languages. The second task is to map each symbol
of the ciphertext to the corresponding letter in the
identified language. The third task is to decode the
resulting anagrams into readable text, which may in-
volve the recovery of unwritten vowels.

The paper is structured as follows. We discuss re-
lated work in Section 2. In Section 3, we propose
three methods for the source language identification
of texts enciphered with a monoalphabetic substitu-
tion cipher. In Section 4, we present and evaluate our
approach to the decryption of texts composed of en-
ciphered anagrams. In Section 5, we apply our new
techniques to the Voynich manuscript. Section 6
concludes the paper.

2 Related Work

In this section, we review particularly relevant prior
work on the Voynich manuscript, and on algorithmic
decipherment in general.

2.1 Voynich Manuscript

Since the discovery of the Voynich manuscript
(henceforth referred to as the VMS), there have been
a number of decipherments claims. Newbold and
Kent (1928) proposed an interpretation based on mi-
croscopic details in the text, which was subsequently
refuted by Manly (1931). Other claimed decipher-
ments by Feely (1943) and Strong (1945) have also
been refuted (Tiltman, 1968). A detailed study of
the manuscript by d’Imperio (1978) details various
other proposed solutions and the arguments against
them.

Figure 1: A sample from the Voynich manuscript.

Numerous languages have been proposed to un-
derlie the VMS. The properties and the dating of the
manuscript imply Latin and Italian as potential can-
didates. On the basis of the analysis of the character
frequency distribution, Jaskiewicz (2011) identifies
five most probable languages, which include Mol-
davian and Thai. Reddy and Knight (2011) discover
an excellent match between the VMS and Quranic
Arabic in the distribution of word lengths, as well as
a similarity to Chinese Pinyin in the predictability of
letters given the preceding letter.

It has been suggested previously that some ana-
gramming scheme may alter the sequence order of
characters within words in the VMS. Tiltman (1968)
observes that each symbol behaves as if it had its
own place in an “order of precedence” within words.
Rugg (2004) notes the apparent similarity of the
VMS to a text in which each word has been replaced
by an alphabetically ordered anagram (alphagram).
Reddy and Knight (2011) show that the letter se-
quences are generally more predictable than in nat-
ural languages.

Some researchers have argued that the VMS may
be an elaborate hoax created to only appear as a
meaningful text. Rugg (2004) suggests a tabular
method, similar to the sixteenth century technique
of the Cardan grille, although recent dating of the
manuscript to the fifteenth century provides evi-
dence to the contrary. Schinner (2007) uses analy-
sis of random walk techniques and textual statistics
to support the hoax hypothesis. On the other hand,
Landini (2001) identifies in the VMS language-like
statistical properties, such as Zipf’s law, which were
only discovered in the last century. Similarly, Mon-
temurro and Zanette (2013) use information theo-
retic techniques to find long-range relationships be-
tween words and sections of the manuscript, as well
as between the text and the figures in the VMS.

76



2.2 Algorithmic Decipherment

A monoalphabetic substitution cipher is a well-
known method of enciphering a plaintext by con-
verting it into a ciphertext of the same length using
a 1-to-1 mapping of symbols. Knight et al. (2006)
propose a method for deciphering substitution ci-
phers which is based on Viterbi decoding with map-
ping probabilities computed with the expectation-
maximization (EM) algorithm. The method cor-
rectly deciphers 90% of symbols in a 400-letter ci-
phertext when a trigram character language model
is used. They apply their method to ciphertext
language identification using 80 different language
samples, and report successful outcomes on three ci-
phers that represent English, Spanish, and a Spanish
abjad, respectively.

Ravi and Knight (2008) present a more complex
but slower method for solving substitution ciphers,
which incorporates constraints that model the 1-to-1
property of the key. The objective function is again
the probability of the decipherment relative to an n-
gram character language model. A solution is found
by optimally solving an integer linear program.

Knight et al. (2011) describe a successful deci-
pherment of an eighteenth century text known as
the Copiale Cipher. Language identification was the
first step of the process. The EM-based method of
Knight et al. (2006) identified German as the most
likely candidate among over 40 candidate charac-
ter language models. The more accurate method
of Ravi and Knight (2008) was presumably either
too slow or too brittle for this purpose. The cipher
was eventually broken using a combination of man-
ual and algorithmic techniques.

Hauer et al. (2014) present an approach to solv-
ing monoalphabetic substitution ciphers which is
more accurate than other algorithms proposed for
this task, including Knight et al. (2006), Ravi and
Knight (2008), and Norvig (2009). We provide a
detailed description of the method in Section 4.1.

3 Source Language Identification

In this section, we propose and evaluate three meth-
ods for determining the source language of a docu-
ment enciphered with a monoalphabetic substitution
cipher. We frame it as a classification task, with the
classes corresponding to the candidate languages,

which are represented by short sample texts. The
methods are based on:

1. relative character frequencies,

2. patterns of repeated symbols within words,

3. the outcome of a trial decipherment.

3.1 Character Frequency

An intuitive way of guessing the source language
of a ciphertext is by character frequency analysis.
The key observation is that the relative frequencies
of symbols in the text are unchanged after encipher-
ment with a 1-to-1 substitution cipher. The idea is to
order the ciphertext symbols by frequency, normal-
ize these frequencies to create a probability distri-
bution, and choose the closest matching distribution
from the set of candidate languages.

More formally, let PT be a discrete probability
distribution where PT (i) is the probability of a ran-
domly selected symbol in a text T being the ith most
frequent symbol. We define the distance between
two texts U and V to be the Bhattacharyya (1943)
distance between the probability distributions PU
and PV :

d(U, V ) = − ln
∑

i

√
PU(i) ·PV (i)

The advantages of this distance metric include its
symmetry, and the ability to account for events that
have a zero probability (in this case, due to different
alphabet sizes). The language of the closest sample
text to the ciphertext is considered to be the most
likely source language. This method is not only fast
but also robust against letter reordering and the lack
of word boundaries.

3.2 Decomposition Pattern Frequency

Our second method expands on the character fre-
quency method by incorporating the notion of de-
composition patterns. This method uses multiple oc-
currences of individual symbols within a word as a
clue to the language of the ciphertext. For example,
the word seems contains two instances of ‘s’ and ‘e’,
and one instance of ‘m’. We are interested in captur-
ing the relative frequency of such patterns in texts,
independent of the symbols used.

77



Formally, we define a function f that maps a
word to an ordered n-tuple (t1, t2, . . . tn), where
ti ≥ tj if i < j. Each ti is the number of oc-
currences of the ith most frequent character in the
word. For example, f(seems) = (2, 2, 1), while
f(beams) = (1, 1, 1, 1, 1). We refer to the resulting
tuple as the decomposition pattern of the word. The
decomposition pattern is unaffected by monoalpha-
betic letter substitution or anagramming. As with the
character frequency method, we define the distance
between two texts as the Bhattacharyya distance be-
tween their decomposition pattern distributions, and
classify the language of a ciphertext as the language
of the nearest sample text.

It is worth noting that this method requires word
separators to be preserved in the ciphertext. In fact,
the effectiveness of the method comes partly from
capturing the distribution of word lengths in a text.
On the other hand, the decomposition patterns are
independent of the ordering of characters within
words. We will take advantage of this property in
Section 4.

3.3 Trial Decipherment

The final method that we present involves decipher-
ing the document in question into each candidate
language. The decipherment is performed with a
fast greedy-swap algorithm, which is related to the
algorithms of Ravi and Knight (2008) and Norvig
(2009). It attempts to find the key that maximizes the
probability of the decipherment according to a bi-
gram character language model derived from a sam-
ple document in a given language. The decipher-
ment with the highest probability indicates the most
likely plaintext language of the document.

The greedy-swap algorithm is shown in Figure 2.
The initial key is created by pairing the ciphertext
and plaintext symbols in the order of decreasing fre-
quency, with null symbols appended to the shorter
of the two alphabets. The algorithm repeatedly at-
tempts to improve the current key k by considering
the “best” swaps of ciphertext symbol pairs within
the key (if the key is viewed as a permutation of
the alphabet, such a swap is a transposition). The
best swaps are defined as those that involve a sym-
bol occurring among the 10 least common bigrams
in the decipherment induced by the current key. If
any such swap yields a more probable decipherment,

1: kmax ← InitialKey
2: for m iterations do
3: k ← kmax
4: S ← best swaps for k
5: for each {c1, c2}∈S do
6: k′ ← k(c1↔c2)
7: if p(k′) > p(kmax) then kmax ← k′
8: if kmax = k then return kmax
9: return kmax

Figure 2: Greedy-swap decipherment algorithm.

it is incorporated in the current key; otherwise, the
algorithm terminates. The total number of iterations
is bounded by m, which is set to 5 times the size
of the alphabet. After the initial run, the algorithm
is restarted 20 times with a randomly generated ini-
tial key, which often results in a better decipherment.
All parameters were established on a development
set.

3.4 Evaluation

We now directly evaluate the three methods de-
scribed above by applying them to a set of cipher-
texts from different languages. We adapted the
dataset created by Emerson et al. (2014) from the
text of the Universal Declaration of Human Rights
(UDHR) in 380 languages.2 The average length of
the texts is 1710 words and 11073 characters. We
divided the text in each language into 66% train-
ing, 17% development, and 17% test. The training
part was used to derive character bigram models for
each language. The development and test parts were
separately enciphered with a random substitution ci-
pher.

Table 1 shows the results of the language identifi-
cation methods on both the development and the test
set. We report the average top-1 accuracy on the task
of identifying the source language of 380 enciphered
test samples. The differences between methods are
statistically significant according to McNemar’s test
with p < 0.0001. The random baseline of 0.3% in-
dicates the difficulty of the task. The “oracle” de-
cipherment assumes a perfect decipherment of the
text, which effectively reduces the task to standard

2Eight languages from the original set were excluded be-
cause of formatting issues.

78



Method Dev Test
Random Selection 0.3 0.3
Jaskiewicz (2011) 54.2 47.6
Character Frequency 72.4 67.9
Decomposition Pattern 90.5 85.5
Trial Decipherment 94.2 97.1
Oracle Decipherment 98.2 98.4

Table 1: Language identification accuracy (in % correct)
on ciphers representing 380 languages.

language identification.

All three of our methods perform well, with the
accuracy gains reflecting their increasing complex-
ity. Between the two character frequency methods,
our approach based on Bhattacharyya distance is
significantly more accurate than the method of Jask-
iewicz (2011), which uses a specially-designed dis-
tribution distance function. The decomposition pat-
tern method makes many fewer errors, with the cor-
rect language ranked second in roughly half of those
cases. Trial decipherment yields the best results,
which are close to the upper bound for the character
bigram probability approach to language identifica-
tion. The average decipherment error rate into the
correct language is only 2.5%. In 4 out of 11 identi-
fication errors made on the test set, the error rate is
above the average; the other 7 errors involve closely
related languages, such as Serbian and Bosnian.

The trial decipherment approach is much slower
than the frequency distribution methods, requiring
roughly one hour of CPU time in order to classify
each ciphertext. More complex decipherment algo-
rithms are even slower, which precludes their appli-
cation to this test set. Our re-implementations of
the dynamic programming algorithm of Knight et al.
(2006), and the integer programming solver of Ravi
and Knight (2008) average 53 and 7000 seconds of
CPU time, respectively, to solve a single 256 charac-
ter cipher, compared to 2.6 seconds with our greedy-
swap method. The dynamic programming algorithm
improves decipherment accuracy over our method
by only 4% on a benchmark set of 50 ciphers of 256
characters. We conclude that our greedy-swap al-
gorithm strikes the right balance between accuracy
and speed required for the task of cipher language
identification.

4 Anagram Decryption

In this section, we address the challenging task of
deciphering a text in an unknown language written
using an unknown script, and in which the letters
within words have been randomly scrambled. The
task is designed to emulate the decipherment prob-
lem posed by the VMS, with the assumption that
its unusual ordering of characters within words re-
flects some kind of a transposition cipher. We re-
strict the source language to be one of the candi-
date languages for which we have sample texts; we
model an unknown script with a substitution cipher;
and we impose no constraints on the letter transposi-
tion method. The encipherment process is illustrated
in Figure 3. The goal in this instance is to recover the
plaintext in (a) given the ciphertext in (c) without the
knowledge of the plaintext language. We also con-
sider an additional encipherment step that removes
all vowels from the plaintext.

Our solution is composed of a sequence of three
modules that address the following tasks: language
identification, script decipherment, and anagram de-
coding. For the first task we use the decomposition
pattern frequency method described in Section 3.2,
which is applicable to anagrammed ciphers. After
identifying the plaintext language, we proceed to re-
verse the substitution cipher using a heuristic search
algorithm guided by a combination of word and
character language models. Finally, we unscramble
the anagrammed words into readable text by fram-
ing the decoding as a tagging task, which is effi-
ciently solved with a Viterbi decoder. Our modular
approach makes it easy to perform different levels of
analysis on unsolved ciphers.

4.1 Script Decipherment

For the decipherment step, we adapt the state-of-the-
art solver of Hauer et al. (2014). In this section, we
describe the three main components of the solver:
key scoring, key mutation, and tree search. This is
followed by the summary of modifications that make
the method work on anagrams.

The scoring component evaluates the fitness of
each key by computing the smoothed probability
of the resulting decipherment with both character-
level and word-level language models. The word-
level models promote decipherments that contain

79



(a) organized compositions through improvisational music into genres
(b) fyovicstu dfnrfecpcfie pbyfzob cnryfgcevpcfivm nzecd cipf otiyte
(c) otvfusyci cpifenfercfd bopbfzy fgyiemcpfcvrcnv nczed fpic etotyi
(d) adegiknor ciimnooopsst ghhortu aaiiilmnooprstv cimsu inot eegnrs
(e) adegiknor compositions through aaiiilmnooprstv music into greens

Figure 3: An example of the encryption and decryption process: (a) plaintext; (b) after applying a substitution cipher;
(c) ciphertext after random anagramming; (d) after substitution decipherment (in the alphagram representation); (e)
final decipherment after anagram decoding (errors are underlined).

in-vocabulary words and high-probability word n-
grams, while the character level models allow for
the incorporation of out-of-vocabulary words.

The key mutation component crucially depends
on the notion of pattern equivalence between char-
acter strings. Two strings are pattern-equivalent if
they share the same pattern of repeated letters. For
example, MZXCX is pattern-equivalent with there
and bases. but not with otter. For each word uni-
gram, bigram, and trigram in the ciphertext, a list of
the most frequent pattern equivalent n-grams from
the training corpus is compiled. The solver repeat-
edly attempts to improve the current key through
a series of transpositions, so that a given cipher n-
gram maps to a pattern-equivalent n-gram from the
provided language sample. The number of substi-
tutions for a given n-gram is limited to the k most
promising candidates, where k is a parameter opti-
mized on a development set.

The key mutation procedure generates a tree
structure, which is searched for the best-scoring de-
cipherment using a version of beam search. The root
of the tree contains the initial key, which is gener-
ated according to simple frequency analysis (i.e., by
mapping the n-th most common ciphertext character
to the n-th most common character in the corpus).
New tree leaves are spawned by modifying the keys
of current leaves, while ensuring that each node in
the tree has a unique key. At the end of computa-
tion, the key with the highest score is returned as the
solution.

In our anagram adaptation, we relax the definition
of pattern equivalence to include strings that have
the same decomposition pattern, as defined in Sec-
tion 3.2. Under the new definition, the order of the
letters within a word has no effect on pattern equiv-
alence. For example, MZXCX is equivalent not only
with there and bases, but also with three and otter,

because all these words map to the (2, 1, 1, 1) pat-
tern. Internally, we represent all words as alpha-
grams, in which letters are reshuffled into the alpha-
betical order (Figure 3d). In order to handle the in-
creased ambiguity, we use a letter-frequency heuris-
tic to select the most likely mapping of letters within
an n-gram. The trigram language models over both
words and characters are derived by converting each
word in the training corpus into its alphagram. On
a benchmark set of 50 ciphers of length 256, the av-
erage error rate of the modified solver is 2.6%, with
only a small increase in time and space usage.

4.2 Anagram Decoder

The output of the script decipherment step is gener-
ally unreadable (see Figure 3d). The words might
be composed of the right letters but their order is
unlikely to be correct. We proceed to decode the
sequence of anagrams by framing it as a simple hid-
den Markov model, in which the hidden states corre-
spond to plaintext words, and the observed sequence
is composed of their anagrams. Without loss of gen-
erality, we convert anagrams into alphagrams, so
that the emission probabilities are always equal to
1. Any alphagrams that correspond to unseen words
are replaced with a single ‘unknown’ type. We then
use a modified Viterbi decoder to determine the most
likely word sequence according to a word trigram
language model, which is derived from the train-
ing corpus, and smoothed using deleted interpola-
tion (Jelinek and Mercer, 1980).

4.3 Vowel Recovery

Many writing systems, including Arabic and He-
brew, are abjads that do not explicitly represent vow-
els. Reddy and Knight (2011) provide evidence that
the VMS may encode an abjad. The removal of
vowels represents a substantial loss of information,

80



and appears to dramatically increase the difficulty of
solving a cipher.

In order to apply our system to abjads, we re-
move all vowels in the corpora prior to deriving the
language models used by the script decipherment
step. We assume the ability to partition the plaintext
symbols into disjoint sets of vowels and consonants
for each candidate language. The anagram decoder
is trained to recover complete in-vocabulary words
from sequences of anagrams containing only conso-
nants. At test time, we remove the vowels from the
input to the decipherment step of the pipeline. In
contrast with Knight et al. (2006), our approach is
able not only to attack abjad ciphers, but also to re-
store the vowels, producing fully readable text.

4.4 Evaluation
In order to test our anagram decryption pipeline on
out-of-domain ciphertexts, the corpora for deriving
language models need to be much larger than the
UDHR samples used in the previous section. We
selected five diverse European languages from Eu-
roparl (Koehn, 2005): English, Bulgarian, German,
Greek, and Spanish. The corresponding corpora
contain about 50 million words each, with the excep-
tion of Bulgarian which has only 9 million words.
We remove punctuation and numbers, and lowercase
all text.

We test on texts extracted from Wikipedia articles
on art, Earth, Europe, film, history, language, music,
science, technology, and Wikipedia. The texts are
first enciphered using a substitution cipher, and then
anagrammed (Figure 3a-c). Each of the five lan-
guages is represented by 10 ciphertexts, which are
decrypted independently. In order to keep the run-
ning time reasonable, the length of the ciphertexts is
set to 500 characters.

The first step is language identification. Our de-
composition pattern method, which is resistant to
both anagramming and substitution, correctly iden-
tifies the source language of 49 out of 50 cipher-
texts. The lone exception is the German article on
technology, for which German is the second ranked
language after Greek. This error could be easily de-
tected by noticing that most of the Greek words “de-
ciphered” by the subsequent steps are out of vocab-
ulary. We proceed to evaluate the following steps
assuming that the source language is known.

Step 2 Step 3 Both Ceiling
English 99.5 98.2 97.7 98.7
Bulgarian 97.0 94.7 91.9 95.3
German 97.3 90.6 88.7 91.8
Greek 95.7 96.6 92.7 97.2
Spanish 99.1 98.0 97.1 99.0
Average 97.7 95.7 93.8 96.5

Table 2: Word accuracy on the anagram decryption task.

The results in Table 2 show that our system is able
to effectively break the anagrammed ciphers in all
five languages. For Step 2 (script decipherment), we
count as correct all word tokens that contain the right
characters, disregarding their order. Step 3 (ana-
gram decoding) is evaluated under the assumption
that it has received a perfect decipherment from Step
2. On average, the accuracy of each individual step
exceeds 95%. The values in the column denoted as
Both are the actual results of the pipeline composed
of Steps 2 and 3. Our system correctly recovers
93.8% of word tokens, which corresponds to over
97% of the in-vocabulary words within the test files,
The percentage of the in-vocabulary words, which
are shown in the Ceiling column, constitute the ef-
fective accuracy limits for each language.

The errors fall into three categories, as illustrated
in Figure 3e. Step 2 introduces decipherment errors
(e.g., deciphering ‘s’ as ‘k’ instead of ‘z’ in “orga-
nized”), which typically preclude the word from be-
ing recovered in the next step. A decoding error in
Step 3 may occur when an alphagram corresponds
to multiple words (e.g. “greens” instead of “gen-
res”), although most such ambiguities are resolved
correctly. However, the majority of errors are caused
by out-of-vocabulary (OOV) words in the plaintext
(e.g., “improvisational”). Since the decoder can only
produce words found in the training corpus, an OOV
word almost always results in an error. The German
ciphers stand out as having the largest percentage of
OOV words (8.2%), which may be attributed to fre-
quent compounding.

Table 3 shows the results of the analogous exper-
iments on abjads (Section 4.3). Surprisingly, the
removal of vowels from the plaintext actually im-
proves the average decipherment step accuracy to
99%. This is due not only to the reduced number of

81



Step 2 Step 3 Both Ceiling
English 99.9 84.6 84.5 98.7
Bulgarian 99.1 71.1 70.4 95.0
German 98.5 73.7 72.9 91.8
Greek 97.7 65.4 63.6 97.0
Spanish 99.8 73.7 73.3 99.0
Average 99.0 73.8 73.1 96.4

Table 3: Word accuracy on the abjad anagram decryption
task.

distinct symbols, but also to the fewer possible ana-
gramming permutations in the shortened words. On
the other hand, the loss of vowel information makes
the anagram decoding step much harder. However,
more than three quarters of in-vocabulary tokens are
still correctly recovered, including the original vow-
els.3 In general, this is sufficient for a human reader
to understand the meaning of the document, and de-
duce the remaining words.

5 Voynich Experiments

In this section, we present the results of our experi-
ments on the VMS. We attempt to identify the source
language with the methods described in Section 3;
we quantify the similarity of the Voynich words to
alphagrams; and we apply our anagram decryption
algorithm from Section 4 to the text.

5.1 Data
Unless otherwise noted, the VMS text used in
our experiments corresponds to 43 pages of the
manuscript in the “type B” handwriting (VMS-B),
investigated by Reddy and Knight (2011), which
we obtained directly from the authors. It con-
tains 17,597 words and 95,465 characters, tran-
scribed into 35 characters of the Currier alphabet
(d’Imperio, 1978).

For the comparison experiments, we selected
five languages shown in Table 4, which have
been suggested in the past as the language of the
VMS (Kennedy and Churchill, 2006). Consider-
ing the age of the manuscript, we attempt to use
corpora that correspond to older versions of the
languages, including King James Bible, Bibbia di
Gerusalemme, and Vulgate.

3The differences in the Ceiling numbers between Tables 2
and 3 are due to words that are composed entirely of vowels.

Language Text Words Characters
English Bible 804,875 4,097,508
Italian Bible 758,854 4,246,663
Latin Bible 650,232 4,150,533
Hebrew Tanach 309,934 1,562,591
Arabic Quran 78,245 411,082

Table 4: Language corpora.

5.2 Source Language

In this section, we present the results of our cipher-
text language identification methods from Section 3
on the VMS text.

The closest language according to the letter fre-
quency method is Mazatec, a native American lan-
guage from southern Mexico. Since the VMS was
created before the voyage of Columbus, a New
World language is an unlikely candidate. The top
ten languages also include Mozarabic (3), Italian (8),
and Ladino (10), all of which are plausible guesses.
However, the experiments in Section 3.4 demon-
strate that the frequency analysis is much less reli-
able than the other two methods.

The top-ranking languages according to the de-
composition pattern method are Hebrew, Malay (in
Arabic script), Standard Arabic, and Amharic, in
this order. We note that three of these belong to
the Semitic family. The similarity of decomposition
patterns between Hebrew and the VMS is striking.
The Bhattacharyya distance between the respective
distributions is 0.020, compared to 0.048 for the
second-ranking Malay. The histogram in Figure 4
shows Hebrew as a single outlier in the leftmost bin.
In fact, Hebrew is closer to a sample of the VMS
of a similar length than to any of the remaining 379
UDHR samples.

The ranking produced by the the trial decipher-
ment method is sensitive to parameter changes; how-
ever, the two languages that consistently appear near
the top of the list are Hebrew and Esperanto. The
high rank of Hebrew corroborates the outcome of the
decomposition pattern method. Being a relatively
recent creation, Esperanto itself can be excluded as
the ciphertext language, but its high score is remark-
able in view of the well-known theory that the VMS
text represents a constructed language.4 We hypoth-

4The theory was first presented in the form of an ana-

82



Figure 4: Histogram of distances between the VMS and
samples of 380 other languages, as determined by the de-
composition pattern method. The single outlier on the left
is Hebrew.

esize that the extreme morphological regularity of
Esperanto (e.g., all plural nouns contain the bigram
‘oj’) yields an unusual bigram character language
model which fits the repetitive nature of the VMS
words.

In summary, while there is no complete agree-
ment between the three methods about the most
likely underlying source language, there appears to
be a strong statistical support for Hebrew from the
two most accurate methods, one of which is robust
against anagramming. In addition, the language is
a plausible candidate on historical grounds, being
widely-used for writing in the Middle Ages. In fact,
a number of cipher techniques, including anagram-
ming, can be traced to the Jewish Cabala (Kennedy
and Churchill, 2006).

5.3 Alphagrams

In this section, we quantify the peculiarity of the
VMS lexicon by modeling the words as alphagrams.
We introduce the notion of the alphagram distance,
and compute it for the VMS and for natural language
samples.

We define a word’s alphagram distance with re-
spect to an ordering of the alphabet as the number of
letter pairs that are in the wrong order. For example,
with respect to the QWERTY keyboard order, the
word rye has an alphagram distance of 2 because it
contains two letter pairs that violate the order: (r, e)
and (y, e). A word is an alphagram if and only if its
alphagram distance is zero. The maximum alpha-
gram distance for a word of length n is equal to the
number of its distinct letter pairs.

gram (Friedman and Friedman, 1959). See also a more recent
proposal by Balandin and Averyanov (2014).

In order to quantify how strongly the words in
a language resemble alphagrams, we first need to
identify the order of the alphabet that minimizes
the total alphagram distance of a representative text
sample. The decision version of this problem is NP-
complete, which can be demonstrated by a reduc-
tion from the path variant of the traveling salesman
problem. Instead, we find an approximate solution
with the following greedy search algorithm. Starting
from an initial order in which the letters first occur
in the text, we repeatedly consider all possible new
positions for a letter within the current order, and
choose the one that yields the lowest total alphagram
distance of the text. This process is repeated until no
better order is found for 10 iterations, with 100 ran-
dom restarts.

When applied to a random sample of 10,000 word
tokens from the VMS, our algorithm yields the or-
der 4BZOVPEFSXQYWC28ARUTIJ3*GHK69MDLN5,
which corresponds to the average alphagram dis-
tance of 0.996 (i.e., slightly less than one pair of let-
ters per word). The corresponding result on English
is jzbqwxcpathofvurimslkengdy, with an
average alphagram distance of 2.454. Note that the
letters at the beginning of the sequence tend to have
low frequency, while the ones at the end occur in
popular morphological suffixes, such as −ed and
−ly. For example, the beginning of the first arti-
cle of the UDHR with the letters transposed to fol-
low this order becomes: “All ahumn biseng are born
free and qaule in tiingdy and thrisg.”

To estimate how close the solution produced by
our greedy algorithm is to the actual optimal solu-
tion, we also calculate a lower bound for the total
alphagram distance with any character order. The
lower bound is

∑
x,y min(bxy, byx), where bxy is the

number of times character x occurs before character
y within words in the text.

Figure 5 shows the average alphagram distances
for the VMS and five comparison languages, each
represented by a random sample of 10,000 word to-
kens which exclude single-letter words. The Ex-
pected values correspond to a completely random
intra-word letter order. The Lexicographic values
correspond to the standard alphabetic order in each
language. The actual minimum alphagram distance
is between the Lower Bound and the Computed Min-
imum obtained by our greedy algorithm.

83



Figure 5: Average word alphagram distances.

The results in Figure 5 show that while the ex-
pected alphagram distance for the VMS falls within
the range exhibited by natural languages, its mini-
mum alphagram distance is exceptionally low. In
absolute terms, the VMS minimum is less than half
the corresponding number for Hebrew. In relative
terms, the ratio of the expected distance to the min-
imum distance is below 2 for any of the five lan-
guages, but above 4 for the VMS. These results sug-
gest that, if the VMS encodes a natural language
text, the letters within the words may have been re-
ordered during the encryption process.

5.4 Decipherment Experiments

In this section, we discuss the results of applying our
anagram decryption system described in Section 4 to
the VMS text.

We decipher each of the first 10 pages of the
VMS-B using the five language models derived from
the corpora described in Section 5.1. The pages con-
tain between 292 and 556 words, 3726 in total. Fig-
ure 6 shows the average percentage of in-vocabulary
words in the 10 decipherments. The percentage is
significantly higher for Hebrew than for the other
languages, which suggests a better match with the
VMS. Although the abjad versions of English, Ital-
ian, and Latin yield similar levels of in-vocabulary
words, their distances to the VMS language accord-
ing to the decomposition pattern method are 0.159,
0.176, and 0.245 respectively, well above Hebrew’s
0.020.

None of the decipherments appear to be syntac-

tically correct or semantically consistent. This is
expected because our system is designed for pure
monoalphabetic substitution ciphers. If the VMS
indeed represents one of the five languages, the
amount of noise inherent in the orthography and the
transcription would prevent the system from pro-
ducing a correct decipherment. For example, in a
hypothetical non-standard orthography of Hebrew,
some prepositions or determiners could be written
as separate one-letter words, or a single phoneme
could have two different representations. In addi-
tion, because of the age of the manuscript and the
variety of its hand-writing styles, any transcription
requires a great deal of guesswork regarding the
separation of individual words into distinct symbols
(Figure 1). Finally, the decipherments necessarily
reflect the corpora that underlie the language model,
which may correspond to a different domain and his-
torical period.

Nevertheless, it is interesting to take a closer look
at specific examples of the system output. The first
line of the VMS (VAS92 9FAE AR APAM ZOE
ZOR9 QOR92 9 FOR ZOE89) is deciphered into
Hebrew as אנשיו עלי ו לביחו אליו איש Nהכה לה ועשה
5.המצות According to a native speaker of the lan-
guage, this is not quite a coherent sentence. How-
ever, after making a couple of spelling corrections,
Google Translate is able to convert it into passable
English: “She made recommendations to the priest,
man of the house and me and people.” 6

Even though the input ciphertext is certainly too
noisy to result in a fluent output, the system might
still manage to correctly decrypt individual words
in a longer passage. In order to limit the influence
of context in the decipherment, we restrict the word
language model to unigrams, and apply our sys-
tem to the first 72 words (241 characters)7 from the
“Herbal” section of the VMS, which contains draw-
ings of plants. An inspection of the output reveals
several words that would not be out of place in a me-
dieval herbal, such as הצר ‘narrow’, איכר ‘farmer’,
אור ‘light’, אויר ‘air’, אׁש ‘fire’.

The results presented in this section could be in-
terpreted either as tantalizing clues for Hebrew as

5Hebrew is written from right to left.
6https://translate.google.com/ (accessed Nov. 20, 2015).
7The length of the passage was chosen to match the number

of symbols in the Phaistos Disc inscription.

84



Figure 6: Average percentage of in-vocabulary words in
the decipherments of the first ten pages of the VMS.

the source language of the VMS, or simply as ar-
tifacts of the combinatorial power of anagramming
and language models. We note that the VMS deci-
pherment claims in the past have typically been lim-
ited to short passages, without ever producing a full
solution. In any case, the output of an algorithmic
decipherment of a noisy input can only be a starting
point for scholars that are well-versed in the given
language and historical period.

6 Conclusion

We have presented a multi-stage system for solv-
ing ciphers that combine monoalphabetic letter sub-
stitution and unconstrained intra-word letter trans-
position to encode messages in an unknown lan-
guage.8 We have evaluated three methods of cipher-
text language identification that are based on letter
frequency, decomposition patterns, and trial deci-
pherment, respectively. We have demonstrated that
our language-independent approach can effectively
break anagrammed substitution ciphers, even when
vowels are removed from the input. The application
of our methods to the Voynich manuscript suggests
that it may represent Hebrew, or another abjad script,
with the letters rearranged to follow a fixed order.

There are several possible directions for the future
work. The pipeline approach presented in this pa-
per might be outperformed by a unified generative
model. The techniques could be made more resis-
tant to noise; for example, by softening the emission
model in the anagram decoding phase. It would also
be interesting to jointly identify both the language
and the type of the cipher (Nuhn and Knight, 2014),

8Software at https://www.cs.ualberta.ca/˜kondrak/.

which could lead to the development of methods to
handle more complex ciphers. Finally, the anagram
decoding task could be extended to account for the
transposition of words within lines, in addition to the
transposition of symbols within words.

Acknowledgements

We thank Prof. Moshe Koppel for the assessment of
the Hebrew examples. We thank the reviewers for
their comments and suggestions.

This research was supported by the Natural Sci-
ences and Engineering Research Council of Canada,
and by Alberta Innovates – Technology Futures and
Alberta Innovation & Advanced Education.

References

Arcady Balandin and Sergey Averyanov. 2014. The
Voynich manuscript: New approaches to deciphering
via a constructed logical language.

A. Bhattacharyya. 1943. On a measure of divergence be-
tween two statistical populations defined by their prob-
ability distributions. Bull. Calcutta Math. Soc., 35:99–
109.

Mary E. d’Imperio. 1978. The Voynich manuscript: An
elegant enigma. Technical report, DTIC Document.

Guy Emerson, Liling Tan, Susanne Fertmann, Alexis
Palmer, and Michaela Regneri. 2014. Seedling:
Building and using a seed corpus for the human lan-
guage project. In Workshop on the Use of Computa-
tional Methods in the Study of Endangered Languages,
pages 77–85.

Joseph Martin Feely. 1943. Roger Bacon’s Cypher. The
Right Key Found. Rochester, NY.

William F. Friedman and Elizebeth S. Friedman. 1959.
Acrostics, anagrams, and Chaucer. Philological Quar-
terly, 38(1):1–20.

Bradley Hauer, Ryan Hayward, and Grzegorz Kondrak.
2014. Solving substitution ciphers with combined lan-
guage models. In COLING, pages 2314–2325.

Grzegorz Jaskiewicz. 2011. Analysis of letter frequency
distribution in the Voynich manuscript. In Interna-
tional Workshop on Concurrency, Specification and
Programming (CS&P’11), pages 250–261.

Frederick Jelinek and Robert L. Mercer. 1980. Inter-
polated estimation of Markov source parameters from
sparse data. Pattern recognition in practice.

Gerry Kennedy and Rob Churchill. 2006. The Voynich
manuscript: The mysterious code that has defied inter-
pretation for centuries. Inner Traditions/Bear & Co.

85



Kevin Knight, Anish Nair, Nishit Rathod, and Kenji Ya-
mada. 2006. Unsupervised analysis for decipherment
problems. In COLING/ACL, pages 499–506.

Kevin Knight, Beáta Megyesi, and Christiane Schaefer.
2011. The Copiale cipher. In 4th Workshop on Build-
ing and Using Comparable Corpora: Comparable
Corpora and the Web, pages 2–9.

Philipp Koehn. 2005. Europarl: A parallel corpus for sta-
tistical machine translation. In MT Summit, volume 5,
pages 79–86.

Gabriel Landini. 2001. Evidence of linguistic struc-
ture in the Voynich manuscript using spectral analysis.
Cryptologia, 25(4):275–295.

John Matthews Manly. 1931. Roger Bacon and the
Voynich MS. Speculum, 6(03):345–391.

Marcelo A. Montemurro and Damián H. Zanette. 2013.
Keywords and co-occurrence patterns in the Voynich
manuscript: An information-theoretic analysis. PloS
one, 8(6):e66344.

George Nagy, Sharad Seth, and Kent Einspahr. 1987.
Decoding substitution ciphers by means of word
matching with application to OCR. IEEE Transac-
tions on Pattern Analysis and Machine Intelligence,
9(5):710–715.

William Romaine Newbold and Roland Grubb Kent.
1928. The Cipher of Roger Bacon. University of
Pennsylvania Press.

Peter Norvig. 2009. Natural language corpus data. In
Toby Segaran and Jeff Hammerbacher, editors, Beau-
tiful data: The stories behind elegant data solutions.
O’Reilly.

Malte Nuhn and Kevin Knight. 2014. Cipher type detec-
tion. In EMNLP, pages 1769–1773.

Sujith Ravi and Kevin Knight. 2008. Attacking deci-
pherment problems optimally with low-order n-gram
models. In EMNLP, pages 812–819.

Sujith Ravi and Kevin Knight. 2009. Learning phoneme
mappings for transliteration without parallel data. In
NAACL, pages 37–45.

Sravana Reddy and Kevin Knight. 2011. What we know
about the Voynich manuscript. In 5th ACL-HLT Work-
shop on Language Technology for Cultural Heritage,
Social Sciences, and Humanities, pages 78–86.

Andrew Robinson. 2002. Lost languages: The enigma
of the world’s undeciphered scripts. McGraw-Hill.

Gordon Rugg. 2004. An elegant hoax? A possible
solution to the Voynich manuscript. Cryptologia,
28(1):31–46.

Andreas Schinner. 2007. The Voynich manuscript: Evi-
dence of the hoax hypothesis. Cryptologia, 31(2):95–
107.

Klaus Schmeh. 2013. A milestone in Voyn-
ich manuscript research: Voynich 100 conference in

Monte Porzio Catone, Italy. Cryptologia, 37(3):193–
203.

Simon Singh. 2011. The code book: The science of
secrecy from ancient Egypt to quantum cryptography.
Anchor.

Leonell C Strong. 1945. Anthony Askham, the author
of the Voynich manuscript. Science, 101(2633):608–
609.

John Tiltman. 1968. The Voynich Manuscript, The Most
Mysterious Manuscript in the World. Baltimore Bib-
liophiles.

86