caesar.py

#!/usr/bin/env python3

ciphertext = '''
    ymjwj fwj ybt ydujx tk jshwduynts: tsj ymfy bnqq
    uwjajsy dtzw xnxyjw kwtr wjfinsl dtzw infwd fsi tsj ymfy bnqq
    uwjajsy dtzw ltajwsrjsy. ymnx nx f ajwd nrutwyfsy qjxxts yt
    wjrjgjwjxujhnfqqd ktw fyyfhpx zxnsl kwjvzjshd fsfqdxnx bmnhm
    wjvznwj qtsljw ufxxflj tk yjcy ns twijw yt fhmnjaj gjyyjw wjxzqyx.
'''

alphabet = 'abcdefghijklmnopqrstuvwxyz'


def get_letter_counts(text):
    counts = {c: 0 for c in alphabet}
    for letter in text.lower():
        if letter in alphabet:
            counts[letter] += 1
    return counts


assert get_letter_counts('x')['a'] == 0
assert get_letter_counts('aa')['a'] == 2


def get_letter_frequencies(text):
    counts = get_letter_counts(text)
    total = max(counts.values())
    return {letter: count/total for letter, count in counts.items()}


english_frequencies = [0.64297,0.11746,0.21902,0.33483,1.00000,0.17541,
        0.15864,0.47977,0.54842,0.01205,0.06078,0.31688,0.18942,
        0.53133,0.59101,0.15187,0.00748,0.47134,0.49811,0.71296,
        0.21713,0.07700,0.18580,0.01181,0.15541,0.00583]

assert len(english_frequencies) == len(alphabet)
english_frequencies = {letter: freq for letter, freq in zip(alphabet, english_frequencies)}


def rotate_text(text, offset):
    return ''.join(rotate_letter(letter, offset) for letter in text)


def rotate_letter(letter, offset):
    letter = letter.lower()
    if letter in alphabet:
        n = ord(letter) + offset
        if n > ord('z'):
            n -= ord('z') - ord('a') + 1
        return chr(n)
    else:
        return letter

assert rotate_letter('a', 0) == 'a'
assert rotate_letter('a', 1) == 'b'
assert rotate_letter('z', 0) == 'z'
assert rotate_letter('z', 1) == 'a'
assert rotate_letter('z', 2) == 'b'


best_offset = 0
best_offset_distance = None

for offset in range(25):
    print('-' * 80)
    print('Offset:', offset)
    rotated_text = rotate_text(ciphertext, offset)
    print('Text:', rotated_text)
    rotated_freqs = get_letter_frequencies(rotated_text)
    #print(rotated_freqs)
    print('Frequency distance - sum:', sum(abs(english_frequencies[letter] - rotated_freqs[letter]) for letter in alphabet))
    print('Frequency distance - quadratic:', sum((english_frequencies[letter] - rotated_freqs[letter])**2 for letter in alphabet))
    distance = sum((english_frequencies[letter] - rotated_freqs[letter])**2 for letter in alphabet)
    if best_offset_distance is None or distance < best_offset_distance:
        best_offset = offset
        best_offset_distance = distance


plaintext = rotate_text(ciphertext, best_offset)

print()
print('Best plaintext:', plaintext)

output.txt

--------------------------------------------------------------------------------
Offset: 0
Text: 
    ymjwj fwj ybt ydujx tk jshwduynts: tsj ymfy bnqq
    uwjajsy dtzw xnxyjw kwtr wjfinsl dtzw infwd fsi tsj ymfy bnqq
    uwjajsy dtzw ltajwsrjsy. ymnx nx f ajwd nrutwyfsy qjxxts yt
    wjrjgjwjxujhnfqqd ktw fyyfhpx zxnsl kwjvzjshd fsfqdxnx bmnhm
    wjvznwj qtsljw ufxxflj tk yjcy ns twijw yt fhmnjaj gjyyjw wjxzqyx.

Frequency distance - sum: 7.521892857142856
Frequency distance - quadratic: 4.1179784738551035
--------------------------------------------------------------------------------
Offset: 1
Text: 
    znkxk gxk zcu zevky ul ktixevzout: utk zngz corr
    vxkbktz euax yoyzkx lxus xkgjotm euax jogxe gtj utk zngz corr
    vxkbktz euax mubkxtsktz. znoy oy g bkxe osvuxzgtz rkyyut zu
    xkskhkxkyvkiogrre lux gzzgiqy ayotm lxkwaktie gtgreyoy cnoin
    xkwaoxk rutmkx vgyygmk ul zkdz ot uxjkx zu ginokbk hkzzkx xkyarzy.

Frequency distance - sum: 7.825549999999999
Frequency distance - quadratic: 3.7698087595693877
--------------------------------------------------------------------------------
Offset: 2
Text: 
    aolyl hyl adv afwlz vm lujyfwapvu: vul aoha dpss
    wylclua fvby zpzaly myvt ylhkpun fvby kphyf huk vul aoha dpss
    wylclua fvby nvclyutlua. aopz pz h clyf ptwvyahua slzzvu av
    yltlilylzwljphssf mvy haahjrz bzpun mylxblujf huhsfzpz dopjo
    ylxbpyl svunly whzzhnl vm alea pu vykly av hjoplcl ilaaly ylzbsaz.

Frequency distance - sum: 7.269072857142857
Frequency distance - quadratic: 3.594043045283673
--------------------------------------------------------------------------------
Offset: 3
Text: 
    bpmzm izm bew bgxma wn mvkzgxbqwv: wvm bpib eqtt
    xzmdmvb gwcz aqabmz nzwu zmilqvo gwcz lqizg ivl wvm bpib eqtt
    xzmdmvb gwcz owdmzvumvb. bpqa qa i dmzg quxwzbivb tmaawv bw
    zmumjmzmaxmkqittg nwz ibbiksa caqvo nzmycmvkg ivitgaqa epqkp
    zmycqzm twvomz xiaaiom wn bmfb qv wzlmz bw ikpqmdm jmbbmz zmactba.

Frequency distance - sum: 8.430735714285714
Frequency distance - quadratic: 4.222971045283674
--------------------------------------------------------------------------------
Offset: 4
Text: 
    cqnan jan cfx chynb xo nwlahycrxw: xwn cqjc fruu
    yanenwc hxda brbcna oaxv anjmrwp hxda mrjah jwm xwn cqjc fruu
    yanenwc hxda pxenawvnwc. cqrb rb j enah rvyxacjwc unbbxw cx
    anvnknanbynlrjuuh oxa jccjltb dbrwp oanzdnwlh jwjuhbrb fqrlq
    anzdran uxwpna yjbbjpn xo cngc rw xamna cx jlqrnen knccna anbducb.

Frequency distance - sum: 6.820435714285715
Frequency distance - quadratic: 3.207523045283674
--------------------------------------------------------------------------------
Offset: 5
Text: 
    drobo kbo dgy dizoc yp oxmbizdsyx: yxo drkd gsvv
    zbofoxd iyeb cscdob pbyw boknsxq iyeb nskbi kxn yxo drkd gsvv
    zbofoxd iyeb qyfobxwoxd. drsc sc k fobi swzybdkxd voccyx dy
    bowoloboczomskvvi pyb kddkmuc ecsxq pboaeoxmi kxkvicsc grsmr
    boaesbo vyxqob zkcckqo yp dohd sx ybnob dy kmrsofo loddob bocevdc.

Frequency distance - sum: 7.568612857142858
Frequency distance - quadratic: 3.4733264738551024
--------------------------------------------------------------------------------
Offset: 6
Text: 
    espcp lcp ehz ejapd zq pyncjaetzy: zyp esle htww
    acpgpye jzfc dtdepc qczx cplotyr jzfc otlcj lyo zyp esle htww
    acpgpye jzfc rzgpcyxpye. estd td l gpcj txazcelye wpddzy ez
    cpxpmpcpdapntlwwj qzc leelnvd fdtyr qcpbfpynj lylwjdtd hstns
    cpbftcp wzyrpc alddlrp zq epie ty zcopc ez lnstpgp mpeepc cpdfwed.

Frequency distance - sum: 7.005664285714287
Frequency distance - quadratic: 2.9026967595693884
--------------------------------------------------------------------------------
Offset: 7
Text: 
    ftqdq mdq fia fkbqe ar qzodkbfuaz: azq ftmf iuxx
    bdqhqzf kagd euefqd rday dqmpuzs kagd pumdk mzp azq ftmf iuxx
    bdqhqzf kagd sahqdzyqzf. ftue ue m hqdk uybadfmzf xqeeaz fa
    dqyqnqdqebqoumxxk rad mffmowe geuzs rdqcgqzok mzmxkeue ituot
    dqcgudq xazsqd bmeemsq ar fqjf uz adpqd fa motuqhq nqffqd dqegxfe.

Frequency distance - sum: 7.862478571428572
Frequency distance - quadratic: 3.577721330997959
--------------------------------------------------------------------------------
Offset: 8
Text: 
    gurer ner gjb glcrf bs rapelcgvba: bar gung jvyy
    cerirag lbhe fvfgre sebz ernqvat lbhe qvnel naq bar gung jvyy
    cerirag lbhe tbireazrag. guvf vf n irel vzcbegnag yrffba gb
    erzrorerfcrpvnyyl sbe nggnpxf hfvat serdhrapl nanylfvf juvpu
    erdhver ybatre cnffntr bs grkg va beqre gb npuvrir orggre erfhygf.

Frequency distance - sum: 5.984130000000002
Frequency distance - quadratic: 2.2154259024265306
--------------------------------------------------------------------------------
Offset: 9
Text: 
    hvsfs ofs hkc hmdsg ct sbqfmdhwcb: cbs hvoh kwzz
    dfsjsbh mcif gwghsf tfca fsorwbu mcif rwofm obr cbs hvoh kwzz
    dfsjsbh mcif ucjsfbasbh. hvwg wg o jsfm wadcfhobh zsggcb hc
    fsaspsfsgdsqwozzm tcf ohhoqyg igwbu tfseisbqm obozmgwg kvwqv
    fseiwfs zcbusf doggous ct hslh wb cfrsf hc oqvwsjs pshhsf fsgizhg.

Frequency distance - sum: 7.499189999999999
Frequency distance - quadratic: 3.326054473855102
--------------------------------------------------------------------------------
Offset: 10
Text: 
    iwtgt pgt ild ineth du tcrgneixdc: dct iwpi lxaa
    egtktci ndjg hxhitg ugdb gtpsxcv ndjg sxpgn pcs dct iwpi lxaa
    egtktci ndjg vdktgcbtci. iwxh xh p ktgn xbedgipci athhdc id
    gtbtqtgthetrxpaan udg piiprzh jhxcv ugtfjtcrn pcpanhxh lwxrw
    gtfjxgt adcvtg ephhpvt du itmi xc dgstg id prwxtkt qtiitg gthjaih.

Frequency distance - sum: 6.042607142857142
Frequency distance - quadratic: 2.4125927595693875
--------------------------------------------------------------------------------
Offset: 11
Text: 
    jxuhu qhu jme jofui ev udshofjyed: edu jxqj mybb
    fhuludj oekh iyijuh vhec huqtydw oekh tyqho qdt edu jxqj mybb
    fhuludj oekh weluhdcudj. jxyi yi q luho ycfehjqdj buiied je
    hucuruhuifusyqbbo veh qjjqsai kiydw vhugkudso qdqboiyi mxysx
    hugkyhu bedwuh fqiiqwu ev junj yd ehtuh je qsxyulu rujjuh huikbji.

Frequency distance - sum: 7.203041428571428
Frequency distance - quadratic: 3.2265190452836734
--------------------------------------------------------------------------------
Offset: 12
Text: 
    kyviv riv knf kpgvj fw vetipgkzfe: fev kyrk nzcc
    givmvek pfli jzjkvi wifd ivruzex pfli uzrip reu fev kyrk nzcc
    givmvek pfli xfmviedvek. kyzj zj r mvip zdgfikrek cvjjfe kf
    ivdvsvivjgvtzrccp wfi rkkrtbj ljzex wivhlvetp rercpjzj nyzty
    ivhlziv cfexvi grjjrxv fw kvok ze fiuvi kf rtyzvmv svkkvi ivjlckj.

Frequency distance - sum: 7.577392857142856
Frequency distance - quadratic: 3.7596739024265315
--------------------------------------------------------------------------------
Offset: 13
Text: 
    lzwjw sjw log lqhwk gx wfujqhlagf: gfw lzsl oadd
    hjwnwfl qgmj kaklwj xjge jwsvafy qgmj vasjq sfv gfw lzsl oadd
    hjwnwfl qgmj ygnwjfewfl. lzak ak s nwjq aehgjlsfl dwkkgf lg
    jwewtwjwkhwuasddq xgj sllsuck mkafy xjwimwfuq sfsdqkak ozauz
    jwimajw dgfywj hskksyw gx lwpl af gjvwj lg suzawnw twllwj jwkmdlk.

Frequency distance - sum: 8.041958571428571
Frequency distance - quadratic: 4.087395045283674
--------------------------------------------------------------------------------
Offset: 14
Text: 
    maxkx tkx mph mrixl hy xgvkrimbhg: hgx matm pbee
    ikxoxgm rhnk lblmxk ykhf kxtwbgz rhnk wbtkr tgw hgx matm pbee
    ikxoxgm rhnk zhoxkgfxgm. mabl bl t oxkr bfihkmtgm exllhg mh
    kxfxuxkxlixvbteer yhk tmmtvdl nlbgz ykxjnxgvr tgterlbl pabva
    kxjnbkx ehgzxk itlltzx hy mxqm bg hkwxk mh tvabxox uxmmxk kxlneml.

Frequency distance - sum: 7.398490000000001
Frequency distance - quadratic: 3.6256921881408157
--------------------------------------------------------------------------------
Offset: 15
Text: 
    nbyly uly nqi nsjym iz yhwlsjncih: ihy nbun qcff
    jlypyhn siol mcmnyl zlig lyuxcha siol xculs uhx ihy nbun qcff
    jlypyhn siol aipylhgyhn. nbcm cm u pyls cgjilnuhn fymmih ni
    lygyvylymjywcuffs zil unnuwem omcha zlykoyhws uhufsmcm qbcwb
    lykocly fihayl jummuay iz nyrn ch ilxyl ni uwbcypy vynnyl lymofnm.

Frequency distance - sum: 6.594730000000001
Frequency distance - quadratic: 3.4117150452836746
--------------------------------------------------------------------------------
Offset: 16
Text: 
    oczmz vmz orj otkzn ja zixmtkodji: jiz ocvo rdgg
    kmzqzio tjpm ndnozm amjh mzvydib tjpm ydvmt viy jiz ocvo rdgg
    kmzqzio tjpm bjqzmihzio. ocdn dn v qzmt dhkjmovio gznnji oj
    mzhzwzmznkzxdvggt ajm voovxfn pndib amzlpzixt vivgtndn rcdxc
    mzlpdmz gjibzm kvnnvbz ja ozso di jmyzm oj vxcdzqz wzoozm mznpgon.

Frequency distance - sum: 7.350655714285715
Frequency distance - quadratic: 3.876038473855102
--------------------------------------------------------------------------------
Offset: 17
Text: 
    pdana wna psk pulao kb ajynulpekj: kja pdwp sehh
    lnarajp ukqn oeopan bnki nawzejc ukqn zewnu wjz kja pdwp sehh
    lnarajp ukqn ckranjiajp. pdeo eo w ranu eilknpwjp haookj pk
    naiaxanaolayewhhu bkn wppwygo qoejc bnamqajyu wjwhuoeo sdeyd
    namqena hkjcan lwoowca kb patp ej knzan pk wydeara xappan naoqhpo.

Frequency distance - sum: 6.301461428571429
Frequency distance - quadratic: 2.388451045283674
--------------------------------------------------------------------------------
Offset: 18
Text: 
    qebob xob qtl qvmbp lc bkzovmqflk: lkb qexq tfii
    mobsbkq vlro pfpqbo colj obxafkd vlro afxov xka lkb qexq tfii
    mobsbkq vlro dlsbokjbkq. qefp fp x sbov fjmloqxkq ibpplk ql
    objbybobpmbzfxiiv clo xqqxzhp rpfkd cobnrbkzv xkxivpfp tefze
    obnrfob ilkdbo mxppxdb lc qbuq fk loabo ql xzefbsb ybqqbo obpriqp.

Frequency distance - sum: 8.495872857142858
Frequency distance - quadratic: 4.056658473855103
--------------------------------------------------------------------------------
Offset: 19
Text: 
    rfcpc ypc rum rwncq md clapwnrgml: mlc rfyr ugjj
    npctclr wmsp qgqrcp dpmk pcybgle wmsp bgypw ylb mlc rfyr ugjj
    npctclr wmsp emtcplkclr. rfgq gq y tcpw gknmprylr jcqqml rm
    pckczcpcqncagyjjw dmp yrryaiq sqgle dpcosclaw ylyjwqgq ufgaf
    pcosgpc jmlecp nyqqyec md rcvr gl mpbcp rm yafgctc zcrrcp pcqsjrq.

Frequency distance - sum: 8.05287
Frequency distance - quadratic: 3.928586473855103
--------------------------------------------------------------------------------
Offset: 20
Text: 
    sgdqd zqd svn sxodr ne dmbqxoshnm: nmd sgzs vhkk
    oqdudms xntq rhrsdq eqnl qdzchmf xntq chzqx zmc nmd sgzs vhkk
    oqdudms xntq fnudqmldms. sghr hr z udqx hlonqszms kdrrnm sn
    qdldadqdrodbhzkkx enq zsszbjr trhmf eqdptdmbx zmzkxrhr vghbg
    qdpthqd knmfdq ozrrzfd ne sdws hm nqcdq sn zbghdud adssdq qdrtksr.

Frequency distance - sum: 6.754481428571427
Frequency distance - quadratic: 3.3539139024265308
--------------------------------------------------------------------------------
Offset: 21
Text: 
    there are two types of encryption: one that will
    prevent your sister from reading your diary and one that will
    prevent your government. this is a very important lesson to
    remeberespecially for attacks using frequency analysis which
    require longer passage of text in order to achieve better results.

Frequency distance - sum: 1.951481428571429
Frequency distance - quadratic: 0.30071675956938776
--------------------------------------------------------------------------------
Offset: 22
Text: 
    uifsf bsf uxp uzqft pg fodszqujpo: pof uibu xjmm
    qsfwfou zpvs tjtufs gspn sfbejoh zpvs ejbsz boe pof uibu xjmm
    qsfwfou zpvs hpwfsonfou. uijt jt b wfsz jnqpsubou mfttpo up
    sfnfcfsftqfdjbmmz gps buubdlt vtjoh gsfrvfodz bobmztjt xijdi
    sfrvjsf mpohfs qbttbhf pg ufyu jo psefs up bdijfwf cfuufs sftvmut.

Frequency distance - sum: 7.745590000000001
Frequency distance - quadratic: 3.567283616712244
--------------------------------------------------------------------------------
Offset: 23
Text: 
    vjgtg ctg vyq vargu qh gpetarvkqp: qpg vjcv yknn
    rtgxgpv aqwt ukuvgt htqo tgcfkpi aqwt fkcta cpf qpg vjcv yknn
    rtgxgpv aqwt iqxgtpogpv. vjku ku c xgta korqtvcpv nguuqp vq
    tgogdgtgurgekcnna hqt cvvcemu wukpi htgswgpea cpcnauku yjkej
    tgswktg nqpigt rcuucig qh vgzv kp qtfgt vq cejkgxg dgvvgt tguwnvu.

Frequency distance - sum: 7.889132857142859
Frequency distance - quadratic: 3.642691045283673
--------------------------------------------------------------------------------
Offset: 24
Text: 
    wkhuh duh wzr wbshv ri hqfubswlrq: rqh wkdw zloo
    suhyhqw brxu vlvwhu iurp uhdglqj brxu gldub dqg rqh wkdw zloo
    suhyhqw brxu jryhuqphqw. wklv lv d yhub lpsruwdqw ohvvrq wr
    uhphehuhvshfldoob iru dwwdfnv xvlqj iuhtxhqfb dqdobvlv zklfk
    uhtxluh orqjhu sdvvdjh ri whaw lq rughu wr dfklhyh ehwwhu uhvxowv.

Frequency distance - sum: 7.6764100000000015
Frequency distance - quadratic: 3.701904759569388

Best plaintext: 
    there are two types of encryption: one that will
    prevent your sister from reading your diary and one that will
    prevent your government. this is a very important lesson to
    remeberespecially for attacks using frequency analysis which
    require longer passage of text in order to achieve better results.