Wednesday, March 23, 2005

The Art of Decryption

A Heuristic Guide to Solving Monoalphabetic Substitution Ciphers

I’ve recently developed a renewed interest in cryptography. I decided that my skills could use some work, and so I set out to get some practice. I would grab chunks of text from documents and web pages and save them to text files. After a suitable period of time had passed, and I wasn’t likely to remember the original contents of the files, I would run them through a program that replaced all the letters with a shuffled alphabet, removed capitalization, and removed all non-alphabetic symbols (punctuation, spacing, numbers, etc.). I would then run the encrypted file through two frequency analysis program that gave me the counts of every 1, 2, and 3 letter sequence in the text, as well as any longer blocks of text that occurred more than once. Finally, with the frequency information in a spreadsheet, I would pull up a substitution program that would help me try out key values, showing me the ciphertext and the candidate plaintext simultaneously.

I started out with texts that were in the 600-1200 letter range, but recently I’ve been tackling much shorter texts in the 200-500 letter range. I’ve been temporarily stumped by some of them, and others, even short ones, sometimes just fall right into place. Actually, a longer body of text doesn’t always factor into easier decoding, although it does increase my confidence in the results of the frequency analysis. In the process of decoding these texts, I’ve developed some techniques that help to crack open the secrets held by the jumbles of letters before me.

This introduction serves to explain what conditions I was working under, and what kind of information I expect the reader to either have or be able to obtain. In summary, the initial information is a text file containing capital letters of ciphertext without spacing or punctuation. Analysis assumes that lists of 1, 2, and 3 letter combinations (letters, digrams, and trigrams respectively) is available and sorted by frequency, and that a similar list for plaintext is available.

Plaintext

For the record, my plaintext sample that I worked from was the complete Hitchhiker trilogy by Douglas Adams, in the original English with only a few spelling errors and some introductory material. While this text does contain a number of unusual letter combinations and some strange uses of letters (Adams would frequently make up words, and in doing so, he would favor the least frequent letters such as Q, Z, X, and J). Thanks to Zaphod Beeblebrox, the letters Z and X appear a bit more often than usual, as do the trigrams ZAP and BEE. It turns out that this has very little bearing on the relative frequencies of the letters. Q, Z, X, and J still appear in the bottom four spots, and E, T, A, O, I, N, H, S, R, D, L, and U top the list in that order. U doesn’t seem to be unfairly biased due to the British use of OU instead of O, and the most common digrams and trigrams appear to be roughly what they should be.

This is much better than a frequency analysis of the 9/11 Commission Report, which has far more of the letter Q than it should, and due to words like Al Qaeda and Iraq, it has a significant number of letters that follow Q instead of U (although it still seems that the letter most likely to appear second after a Q is E).

In my plaintext sample, the letters, in order of frequency, are E, T, A, O, I, N, H, S, R, D, L, U, W, C, G, M, F, Y, P, B, K, V, X, Z, J, and Q. There are a total of 1,152,456 letters in the sample, with E occurring 136,052 times and Q appearing 1,071 times. Total frequencies are listed in Table 1. The middle column contains the number of occurrences of the letter in the Guide, and the third column indicates what percent of the total that is.

E

136052

11.81

T

110940

9.63

A

94865

8.23

O

85077

7.38

I

81190

7.04

N

75116

6.52

H

74789

6.49

S

69698

6.05

R

64330

5.58

D

54228

4.71

L

49171

4.27

U

34741

3.01

W

27612

2.40

C

26937

2.34

G

26462

2.30

M

25103

2.18

F

24427

2.12

Y

24230

2.10

P

21582

1.87

B

17835

1.55

K

10891

0.95

V

10393

0.90

X

2210

0.19

Z

1829

0.16

J

1677

0.15

Q

1071

0.09


The 50 most frequent digrams and trigrams are listed in table 2. No frequency percentages are used. Instead, I have included the total number of instances of the letter combination. Note that these combinations can span words, since all non-alphabetic characters were removed prior to frequency analysis.

TH

38691

THE

22816

HE

33224

ING

10128

IN

22854

AND

8459

ER

17863

HER

5349

AN

16709

HAT

5328

ED

15562

THA

5178

RE

14310

ERE

5031

OU

12917

THI

4887

TO

12801

WAS

4694

NT

12757

DTH

4095

ND

12727

HIS

4032

AT

12708

HES

4006

ST

12629

TTH

3919

HA

12597

ETH

3872

ES

12570

ENT

3742

IT

12186

FOR

3716

NG

11833

YOU

3647

HI

11770

NTH

3559

EA

11193

RTH

3486

ON

11173

INT

3242

EN

11078

AID

3229

AR

10709

ART

3225

AS

10503

SAI

3180

ET

9639

ALL

3162

OR

9146

VER

3160

TI

9107

HIN

3059

TE

8756

EDT

3040

SA

8652

OTH

2804

IS

8626

OUT

2734

OF

8041

ITH

2689

WA

7969

GHT

2653

LE

7860

FTH

2611

SE

7772

EDA

2578

AL

7671

STH

2572

TT

7495

TER

2551

VE

7445

SHE

2533

LL

7162

OFT

2532

TA

7136

REA

2412

RO

6890

OME

2341

ME

6877

ONT

2309

NE

6740

HAD

2298

LY

6606

AST

2260

DT

6604

ONE

2153

RT

6591

TIN

2149

EL

6539

EST

2146

ID

6272

ESA

2139

LI

6245

NGT

2134

AI

6074

ION

2107

RA

6020

ATT

2098

SH

5937

EAR

2078


Some of these are biased by the text, but sometimes it’s merely important that a string appears on the list anywhere. Remember that there is no guarantee that any given digram or trigram will appear in a text. For example, I have decoded one ciphertext that did not contain the trigram THE. We will refer back to these tables.

Frequency Clues

Frequency analysis is the key to breaking a substitution cipher. This section will go over some of the most useful techniques for using the lengthy charts of gibberish that can be obtained through frequency analysis.

Accentuate the Positive:

Whenever you have added a new letter to the key, it is important to go and look for sections of text that can be part of larger words or phrases. Sometimes a lucky guess at some long word will yield several new letters and start an avalanche of new possibilities that lead to finishing up the decryption. Also, the deciphering endgame is entirely made up of looking through the text for spaces and filling in the blanks with appropriate letters. Every other trick in this paper is to help you get to the point where the remaining letters become obvious.

An example of this would be one time when I thought I had found a block that included _ISSI_N. A guess led to me finishing that as MISSION. This filled in a lot of gaps in the text, and soon helped me realize that it didn’t say MISSION, but rather MILLION.

Eliminate the Negative:

After each trial of a new key value, look through the text for strings that don’t make sense. Lots of consonants or vowels in a row, unlikely letter strings, and a general feeling of gibberish are good indications that you’ve made a mistake somewhere. Sometimes it’s a good idea to keep your error for a while to see if any of it reminds you of something else, but often it’s a good idea to get rid of bad key values if you can figure out which ones are likely to be bad.

Also, remember that sometimes strange letter combinations are perfectly legitimate. The Q in Iraq need not be followed by a U, and A can precede E. STS and TST are both legitimate combinations, but TLT is not as likely as LTL. Winnowing out unacceptable combinations is one area where a codebreaker must develop a feel for how the language works.

THE:

The first thing to do when staring at a new block of ciphertext is to find the most common trigram, THE. This is one area where I disagree with most other cryptographers, who recommend finding E first. Fundamentally, they may be about the same task, but my approach looks at more information up front.

THE can often be identified based on its influence on all three major frequency categories. In the list of trigrams, it is often at or near the top. The two digrams, TH and HE, should appear frequently, and usually more often than THE. Also, TH should occur more often than HE, but don’t get hung up on that. In the letter frequencies, both T and E should be near the top of the list (usually in the top two spots), and H should be about 1/4 to 1/2 of the way down the list.

If the most common trigram doesn’t seem to work, then work down the list of trigrams trying to find trigrams that match the right relative letter frequencies. It sometimes helps to limit your search to trigrams ending with the most common letter or two (especially when one letter occurs much more frequently than all of the others).

Another method that can help eliminate unlikely candidates is to look at the candidate TH digram and see how often the HT digram appears. While it is possible to have HT appear often in a text, it is significantly less common than TH in most texts. Also, HT is almost always preceded by G.

A word of warning should be given about other common words. In a specific short body of text, it is common to have a single word or variants of a word to appear many times. When this happens, trigrams from that word may dominate the list of trigrams. If some common trigram is always or almost always found either before or after another letter (or group of letters), then it is probably not THE. One amusing example of this was in a text where HER occurred most often, and it was represented by the ciphertext trigram HIM.

E:

Sometimes THE proves to be more elusive than you’re ready to deal with. When that happens, it is often possible to identify the letter E. It appears far more often than any letter in the English language, and is almost always on the top of the frequency charts. If one letter occurs a couple percent more often than the rest, then it’s probably E.

THAT:

Most bodies of text contain the string THAT. If you see one or more TH_T strings, then try out A in the middle. If this gives AE digrams, then you may want to question it, but remember that TH_T almost always requires a vowel, and that vowel is almost always A.

The ER/RE Effect:

Looking through the list of digrams, one might notice that ER occurs 4th, and RE is 7th on the list. This means that if the same digram appears frequently as both XY and YX, then it probably represents ER/RE (distinguishing which is E and which is R is easy, since E is more than twice as common as R).

Double Letters:

Only so many plaintext letters are likely to occur twice, like the Ts in the word leTTers. The most common doubles are TT, EE, LL, SS, and OO, with DD, FF, HH, MM, NN, PP, and RR being reasonably likely as well. If a letter other than T or E (which are hopefully identified by this point) that is doubled several times is likely to be L or S. If a doubled letter is in the top few spots in terms of frequency, then S and O are likely values. A, I, and U are almost never doubled, although it is not impossible (“spa activity”, “I inched…”, and “gnu udder” are examples).

Double Letters Special Case—IGGIs:

In “The Shadow of the Hegemon” by Orson Scott Card, a character deciphered a code by identifying that a string of four letters in the form XYYX meant IGGI, which was part of another character’s name. The rest of the text fell into place after that. These types of letter combinations are quite uncommon, and therefore of limited use in code breaking, but they can be useful at times. The most common IGGI patterns are ILLI, OTTO, ESSE, ETTE, HTTH, ALLA, OLLO, NOON, ITTI, ELLE, and ISSI. For the record, IGGI occurs twice in the Hitchhiker plaintext, and is 80th on the list of IGGIs. Unless people are writing to you about a Wiggin, then it is unlikely that IGGI will appear in your plaintext.

QU:

It sometimes pays to look through the bottom few letters on the frequency list for possible translations of Q. If a very uncommon letter occurs more than once, and is always followed by the same letter, then the pair could be QU, especially if the third letter after it is E (which you should know by now). The letter U should be about halfway down the frequency list, so candidates for QU should be checked for a match with the appropriate frequencies. If there are letters that only occur once in the ciphertext, look for the letter that follows it and see if it could be Q. If the letter following a single letter isn’t in the top 10 on the frequency chart, then it is probably QU (J, X, and Z are almost always followed by a vowel, and typically that vowel is E).

Pick a Vowel:

If A, I, and O haven’t been found up to this point, then it may make sense to try them out, one at a time, in the top unused spots. As a general rule, when they come together, A comes after E, but I and O are more likely to come before E (I can go either way, but most of the time it doesn’t come after C or sounded like “ay”). This kind of guessing is tricky, and the only way to know if you have it right is to look at what it changes the plaintext to and see if it makes any sense.

Pick a Consonant:

When you’re taking wild stabs at the code, picking a vowel will often create strings of letters that have way too many vowels in a row. When that happens, replace one of the vowels with a consonant, and see what happens. While A, I, and O all occur frequently, and at about the same frequency, the consonants vary from T, which is very common, to Q, which is not at all common. So, when trying consonants, first use the most common ones like T (if you haven’t already found it), S, H (again, if needed), R, D, and L. Anything less common than that shouldn’t have to be found by this kind of haphazard method. Pay some attention to doubled letter frequencies when doing this, although most of the common consonants are likely to appear doubled.

Keep Trying:

If nothing seems to be working, then go back and try again. Look further down the lists for possible candidates. Try to come up with better explanations for strange letter patterns. If nothing else works, go away and come back later when you can look at it with a fresh eye.

Example Problem:

Consider the ciphertext:

UHRTQBJOXUPQOBQUOGKWHQLUXXWPQERLIGQOIROPU
ILDFKVQFUQTQUOGKHQRLIIHRIGKPRDSHIQLUWBJGU
OSHJGQFDOWXJLPWRUPHUWTJUBQVLQRMUOSXJLIHQJ
OFKIUGQUORGUODIQBHRICUIHLQEJLIQLWUYDWIPJO
IMOJCCHQOWJGQIUGQWUIUWRFUIIFQHRLPIJWCRFFJ
CVDIKJDYDWIWCRFFJCUIROPMQQESJUOSVQBRDWQIH
RIWCHRIKJDHRTQIJPJEJFKSLREHWSUTQOIJVJIHHQ
LXRIHQLROPHQLSLROPXRIHQLRLBHUQFDOWXJLPLRU
WQPOJUGGQPURIQBJOBQLOWIJUOTQWIUSRIJLWRDIH
JLUIUQWROOJDOBQPIDQWPRKREJFKSLREHJXYQWWUB
RWSLROPGJIHQLLDIHFDOWXJLPUOBFDPQPICJLQWEJ
OWQWIHRILRUWQPLQPXFRSWVDIBJDFPHRTQVQQOWIL
QWWLQFRIQP

Frequency analysis gives:

C

#

P

#

C

#

P

#

C

#

P

#

C

#

P

#

Q

55

E

136052

IH

11

TH

38691

HQL

6

THE

22816

FF

2

TT

7495

I

46

T

110940

RI

10

HE

33224

HRI

5

ING

10128

II

2

LL

7162

R

40

A

94865

HQ

9

IN

22854

ROP

5

AND

8459

QQ

2

EE

5676

J

36

O

85077

HR

9

ER

17863

IHQ

4

HER

5349

WW

2

SS

4485

U

36

I

81190

QL

9

AN

16709

SLR

4

HAT

5328

CC

1

OO

3730

W

36

N

75116

UO

9

ED

15562

XJL

4

THA

5178

GG

1

DD

1640

L

34

H

74789

JL

8

RE

14310

DOW

3

ERE

5031

HH

1

PP

1571

O

33

S

69698

LR

8

OU

12917

FDO

3

THI

4887

LL

1

RR

1563

H

28

R

64330

QW

8

TO

12801

HRT

3

WAS

4694

OO

1

FF

1277

P

25

D

54228

OW

7

NT

12757

IHR

3

DTH

4095

XX

1

NN

779

D

19

L

49171

QP

7

ND

12727

JLP

3

HIS

4032

AA

0

HH

774

F

18

U

34741

GQ

6

AT

12708

LRO

3

HES

4006

BB

0

MM

612

B

13

W

27612

LQ

6

ST

12629

OBQ

3

TTH

3919

DD

0

GG

570

G

13

C

26937

RO

6

HA

12597

OWX

3

ETH

3872

EE

0

CC

404

S

12

G

26462

TQ

6

ES

12570

QUO

3

ENT

3742

JJ

0

WW

325

X

11

M

25103

UI

6

IT

12186

RTQ

3

FOR

3716

KK

0

BB

285

K

10

F

24427

WI

6

NG

11833

UOS

3

YOU

3647

MM

0

YY

200

C

9

Y

24230

DI

5

HI

11770

WXJ

3

NTH

3559

NN

0

AA

157

E

8

P

21582

IJ

5

EA

11193

BJO

2

RTH

3486

PP

0

KK

139

T

7

B

17835

IQ

5

ON

11173

CRF

2

INT

3242

RR

0

ZZ

102

V

7

K

10891

IU

5

EN

11078

CUI

2

AID

3229

SS

0

UU

52

M

3

V

10393

JO

5

AR

10709

DIH

2

ART

3225

TT

0

II

38

Y

3

X

2210

OP

5

AS

10503

DWI

2

SAI

3180

UU

0

QQ

2

A

0

Z

1829

QO

5

ET

9639

EJF

2

ALL

3162

VV

0

JJ

0

N

0

J

1677

UW

5

OR

9146

FFJ

2

VER

3160

YY

0

VV

0

Z

0

Q

1071

BJ

4

TI

9107

FJC

2

HIN

3059

ZZ

0

XX

0

From this, it seems that Q=e, and IHQ=the. Everything seems to back this up, even with IHQ appearing 4th on the trigram list. Inputting it gives (with lowercase letters indicating plaintext)

UhRTeBJOXUPeOBeUOGKWheLUXXWPeERLtGeOtROPU
tLDFKVeFUeTeUOGKheRLtthRtGKPRDShteLUWBJGU
OShJGeFDOWXJLPWRUPhUWTJUBeVLeRMUOSXJLtheJ
OFKtUGeUORGUODteBhRtCUthLeEJLteLWUYDWtPJO
tMOJCCheOWJGetUGeWUtUWRFUttFehRLPtJWCRFFJ
CVDtKJDYDWtWCRFFJCUtROPMeeESJUOSVeBRDWeth
RtWChRtKJDhRTetJPJEJFKSLREhWSUTeOtJVJthhe
LXRtheLROPheLSLROPXRtheLRLBhUeFDOWXJLPLRU
WePOJUGGePURteBJOBeLOWtJUOTeWtUSRtJLWRDth
JLUtUeWROOJDOBePtDeWPRKREJFKSLREhJXYeWWUB
RWSLROPGJtheLLDthFDOWXJLPUOBFDPePtCJLeWEJ
OWeWthRtLRUWePLePXFRSWVDtBJDFPhRTeVeeOWtL
eWWLeFRteP

Near the middle of the second line, we see “thRt” which means that R=a.

UhaTeBJOXUPeOBeUOGKWheLUXXWPeEaLtGeOtaOPU
tLDFKVeFUeTeUOGKheaLtthatGKPaDShteLUWBJGU
OShJGeFDOWXJLPWaUPhUWTJUBeVLeaMUOSXJLtheJ
OFKtUGeUOaGUODteBhatCUthLeEJLteLWUYDWtPJO
tMOJCCheOWJGetUGeWUtUWaFUttFehaLPtJWCaFFJ
CVDtKJDYDWtWCaFFJCUtaOPMeeESJUOSVeBaDWeth
atWChatKJDhaTetJPJEJFKSLaEhWSUTeOtJVJthhe
LXatheLaOPheLSLaOPXatheLaLBhUeFDOWXJLPLaU
WePOJUGGePUateBJOBeLOWtJUOTeWtUSatJLWaDth
JLUtUeWaOOJDOBePtDeWPaKaEJFKSLaEhJXYeWWUB
aWSLaOPGJtheLLDthFDOWXJLPUOBFDPePtCJLeWEJ
OWeWthatLaUWePLePXFaSWVDtBJDFPhaTeVeeOWtL
eWWLeFateP

Everything’s looking good, but nothing else is sticking out at the moment. So, we move on to something else. Examining the frequency chart shows QL 5th on the list, and LQ 13th. From this, we guess that L=r.

UhaTeBJOXUPeOBeUOGKWherUXXWPeEartGeOtaOPU
trDFKVeFUeTeUOGKheartthatGKPaDShterUWBJGU
OShJGeFDOWXJrPWaUPhUWTJUBeVreaMUOSXJrtheJ
OFKtUGeUOaGUODteBhatCUthreEJrterWUYDWtPJO
tMOJCCheOWJGetUGeWUtUWaFUttFeharPtJWCaFFJ
CVDtKJDYDWtWCaFFJCUtaOPMeeESJUOSVeBaDWeth
atWChatKJDhaTetJPJEJFKSraEhWSUTeOtJVJthhe
rXatheraOPherSraOPXatherarBhUeFDOWXJrPraU
WePOJUGGePUateBJOBerOWtJUOTeWtUSatJrWaDth
JrUtUeWaOOJDOBePtDeWPaKaEJFKSraEhJXYeWWUB
aWSraOPGJtherrDthFDOWXJrPUOBFDPePtCJreWEJ
OWeWthatraUWePrePXFaSWVDtBJDFPhaTeVeeOWtr
eWWreFateP

Near the middle of this, we see “ttherXathera”, which could be “… her father …”. This fits in with the frequency of X, so we try X=f.

UhaTeBJOfUPeOBeUOGKWherUffWPeEartGeOtaOPU
trDFKVeFUeTeUOGKheartthatGKPaDShterUWBJGU
OShJGeFDOWfJrPWaUPhUWTJUBeVreaMUOSfJrtheJ
OFKtUGeUOaGUODteBhatCUthreEJrterWUYDWtPJO
tMOJCCheOWJGetUGeWUtUWaFUttFeharPtJWCaFFJ
CVDtKJDYDWtWCaFFJCUtaOPMeeESJUOSVeBaDWeth
atWChatKJDhaTetJPJEJFKSraEhWSUTeOtJVJthhe
rfatheraOPherSraOPfatherarBhUeFDOWfJrPraU
WePOJUGGePUateBJOBerOWtJUOTeWtUSatJrWaDth
JrUtUeWaOOJDOBePtDeWPaKaEJFKSraEhJfYeWWUB
aWSraOPGJtherrDthFDOWfJrPUOBFDPePtCJreWEJ
OWeWthatraUWePrePfFaSWVDtBJDFPhaTeVeeOWtr
eWWreFateP

At this point, more of it is starting to make sense. Since we have the context of a father, it is reasonable to expect that in the second line we have “PaDShter” meaning “daughter”. This almost looks like too good a match, especially since HT is almost always preceded by a G, so we try it out with P=d, D=u, and S=g.

UhaTeBJOfUdeOBeUOGKWherUffWdeEartGeOtaOdU
truFKVeFUeTeUOGKheartthatGKdaughterUWBJGU
OghJGeFuOWfJrdWaUdhUWTJUBeVreaMUOgfJrtheJ
OFKtUGeUOaGUOuteBhatCUthreEJrterWUYuWtdJO
tMOJCCheOWJGetUGeWUtUWaFUttFehardtJWCaFFJ
CVutKJuYuWtWCaFFJCUtaOdMeeEgJUOgVeBauWeth
atWChatKJuhaTetJdJEJFKgraEhWgUTeOtJVJthhe
rfatheraOdhergraOdfatherarBhUeFuOWfJrdraU
WedOJUGGedUateBJOBerOWtJUOTeWtUgatJrWauth
JrUtUeWaOOJuOBedtueWdaKaEJFKgraEhJfYeWWUB
aWgraOdGJtherruthFuOWfJrdUOBFudedtCJreWEJ
OWeWthatraUWedredfFagWVutBJuFdhaTeVeeOWtr
eWWreFated

At this point, we can see that O=n, and we can guess that F=l. We could also guess that “reEJrter” means “reporter”, but there’s no need to rush things.

UhaTeBJnfUdenBeUnGKWherUffWdeEartGentandU
trulKVelUeTeUnGKheartthatGKdaughterUWBJGU
nghJGelunWfJrdWaUdhUWTJUBeVreaMUngfJrtheJ
nlKtUGeUnaGUnuteBhatCUthreEJrterWUYuWtdJn
tMnJCChenWJGetUGeWUtUWalUttlehardtJWCallJ
CVutKJuYuWtWCallJCUtandMeeEgJUngVeBauWeth
atWChatKJuhaTetJdJEJlKgraEhWgUTentJVJthhe
rfatherandhergrandfatherarBhUelunWfJrdraU
WednJUGGedUateBJnBernWtJUnTeWtUgatJrWauth
JrUtUeWannJunBedtueWdaKaEJlKgraEhJfYeWWUB
aWgrandGJtherruthlunWfJrdUnBludedtCJreWEJ
nWeWthatraUWedredflagWVutBJuldhaTeVeenWtr
eWWrelated

“raUWedredflagW” and the blocks that follow it suggest that U=i, W=s, V=b, B=w, J=o, and T=v. “grandGJther” should be “grandmother”, giving G=m. We try these out:

ihavewonfidenweinmKsheriffsdeEartmentandi
trulKbelieveinmKheartthatmKdaughteriswomi
nghomelunsfordsaidhisvoiwebreaMingfortheo
nlKtimeinaminutewhatCithreEortersiYustdon
tMnoCChensometimesitisalittlehardtosCallo
CbutKouYustsCalloCitandMeeEgoingbewauseth
atsChatKouhavetodoEolKgraEhsgiventobothhe
rfatherandhergrandfatherarwhielunsfordrai
sednoimmediatewonwernstoinvestigatorsauth
oritiesannounwedtuesdaKaEolKgraEhofYessiw
asgrandmotherruthlunsfordinwludedtCoresEo
nsesthatraisedredflagsbutwouldhavebeenstr
essrelated

The first line now reads, “I have wonfidednwe in …” which makes me think that B=c. We also can see that E=p, K=y, M=k, C=w, and Y=j.

ihaveconfidenceinmysheriffsdepartmentandi
trulybelieveinmyheartthatmydaughteriscomi
nghomelunsfordsaidhisvoicebreakingfortheo
nlytimeinaminutechatwithreportersijustdon
tknowwhensometimesitisalittlehardtoswallo
wbutyoujustswallowitandkeepgoingbecauseth
atswhatyouhavetodopolygraphsgiventobothhe
rfatherandhergrandfatherarchielunsfordrai
sednoimmediateconcernstoinvestigatorsauth
oritiesannouncedtuesdayapolygraphofjessic
asgrandmotherruthlunsfordincludedtworespo
nsesthatraisedredflagsbutcouldhavebeenstr
essrelated

At this point, we’re done. The original text read,

“I have confidence in my sheriff's department, and I truly believe in my heart that my daughter is coming home,” Lunsford said, his voice breaking for the only time in a 10-minute chat with reporters. "I just don't know when. Sometimes it is a little hard to swallow, but you just swallow it and keep going because that's what you have to do."

Polygraphs given to both her father and her grandfather, Archie Lunsford, 72, raised no immediate concerns to investigators. Authorities announced Tuesday a polygraph of Jessica's grandmother, Ruth Lunsford, 73, included two responses that "raised red flags," but could have been stress-related.

(From a CNN article about then missing Florida girl Jessica Lunsford. For the record, I’m not morbid, but I typically grab paragraphs from CNN articles for my plaintexts.)

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