The encryption use a "Diana" reciprocal tabula recta.
alpha = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' # global
def Diana(s, k):
k = [alpha.index(c) for c in k]
return ''.join([alpha[(25 - alpha.index(s[i]) - k[i%len(k)])%26] for i in range(len(s))])
The "Diana" reciprocal tabula recta:
print(' A B C D E F G H I J K L M N O P Q R S T U V W X Y Z')
print(' ---------------------------------------------------')
for k in alpha:
print(k, '|', ' '.join(list(Diana(alpha, k))))
It's not really a Vigenère cipher, but rather a kind of Beaufort cipher.
Diana('HELLOWORLD', 'DIANA')
Diana('PNOBLADIBW', 'DIANA')
$K \equiv 25 - P - key \mod{26} \Longleftrightarrow P \equiv 25 - K - key \mod{26} $
Diana(Diana('HELLOWORLD', 'DIANA'), 'MINERVA')
DIANA MINERVA
EJBOB NJOFSWB +1
FKCPC OKPGTXC +2
... etcDiana(Diana('HELLOWORLD', 'EJBOB'), 'NJOFSWB')
Diana(Diana('HELLOWORLD', 'FKCPC'), 'OKPGTXC')
For double encryption (and decryption) the pairs of keywords DIANA-MINERVA, EJBOB-NJOFSWB, FKCPC-OKPGTXC...etc are equivalent.
def index_coincidence( s ):
effectif = {} # effectif de chaque caractère
n = 0 # effectif total
ic = 0 # indice de coïncidence (résultat)
for c in s:
if c in effectif:
effectif[c] += 1
else:
effectif[c] = 1
n += 1
for c in effectif:
ic += effectif[c]*(effectif[c]-1)
ic /= n*(n-1)
return ic
def Kullback(t, n):
c = {}
for i in range(len(t)):
if i%n in c:
c[i%n] += t[i]
else:
c[i%n] = t[i]
ic = 0
for i in c:
ic += index_coincidence(c[i])
return ic/n
The original example of Kullback (S. Kullback - Statistical Methods in Cryptanalysis, p. 41-47):
The following cryptogram is known to be enciphered polyalphabetically with a number of alphabets between 40 and 50
txt = '\
HSKUS PMFHD UJJIX MSPTP OIPCI WKZVU \
YPPNE USAIG BOOGA OPGPR HBOUC SHPVG \
HQXZS ACKRK VBGHM VSFRY YTKHK VWZXV \
LIJHW ARLKF IJSLT MHKAH QTUVT XSMEC \
FCSKT GOOYB XZVLI JRYAC DWEJM SCAFP \
IEAXO KAQDW EXPYP QHDNO JIXNZ JGNUD \
OARFU ERJOY BDOKE IKDUV TDVEV LETDO \
AFROU NYNBD VQOBE GGSHQ HXOPU ZCOCU \
KKZLT PHKRT CCOAS BZUGB UBBUN OVTPO \
VMIZD EPQFV KZ'.replace(' ', '')
for n in range(40, 50, 1):
print(n, Kullback(txt, n))
The period is 43.
k = 'jlykydrxjwurqbyoofpkzctbdvveldcepufciylpgnjxvmrtfeymaouehyughrtinjoypsacqyfwlvq\
mmbsponbwfcpqrkxdxihvuaepjnajoivprbdszhvrkdoghspvbylcpbjvrevlxxwjducayrgwwsnlrwm\
cyrgweezpgfugtftucfjovmjxrdycnbhsncudutruhiwyofhtqsctzcldltuajdxxowamwbvlezyaodm\
ngjjfkgydaibdfvuziuaulicseoxwrwqpgrnzobwdzfcgjzrnhckmnnmmjxqrqqyemrlshxwdfzwtfjs\
rxxpbwofmjhjvxecxysdpcbcbnlndblirmusnwwqrkuelkoxeenimqkoyocctlyfccbczhocurwfkwfp\
ibgtfjvtkjmlypvrpbumvpehxjwpdvvaawaekrvrmfyjfgehkjjeuibrztnofgevrmlbedlvbmogxmsb\
ywspxxcyektzenausxhdinnnervvtnegqkldjimvctgalviswdkizcfzfttadostxnykrcmdtbflbbje\
sfjpbtokxxihihmwefxzogiblaavcztrzubxzdztxihvrokorxebpdumfthavvbpvaqzithpvovkuzpu\
dnjmxymdzsuqeyqtckqbpltigwpegsqsncxvuntydkjvdsbodhknfkowcwqkfjzkqyugenqfoherjxjh\
icebidyguxilymljgyiatfnkwymvwopcfulinuxxthzcapujmmdvobpekyidzwywszgfuoceeilhqpzx\
tstrckerakdhkupwmymuaihehwnmwqwdevpgknooicedsyitdotbvftltgumxccyucuhdpkwbuhatvzn\
prjcglfrmtlajoxjkhtuahllodwbkjfhcbsotiiqvchpnifvnzjbxvvfozzxaymcefwkathwhhlrsrtz\
wkohjihqzhnkdebkiupenpexjbnferwozpztzhbymrrixkwzyufbiozavmfizcbkwsyfvfmxmojrggvw\
qwmpkwfwzafozcrkgbgqovjmamehtkuhmutejfjyuncbnvhcwlolleubcyzcxjdrvycygnoalxxkkhhd\
mgnbmhkdqotairihimckizfofsulzgkwjayluapelpesaanbgrgybsolfzeunzzdtpjjxghawdmgmblf\
ndesoomeythuxrymwwpkvyadfivjyuyqhxgghbvpkppjgtltsqepertluycvnauzrtnsfdiklycdiqob\
iyzxnnovetjvahcrsozslacywgiaeikzdgmvgpdxtwbstfeglqmpjnkoksdootjnaotneibawkqqnvlr\
uwblphljetmhtzznolcgvmmzusrbmgmvgletifydfkiqexydnvqargqhbglxpxvxgeugkgwnujdpvxvi\
xfvditivyzdimlvobhrojjtxfanqmtjizmcqnggnzlngprhcgbizimzkayugacezynzghwcyubcknydb\
vvdpmoimxlpaosknkccgacbbktpuhixqfhvsrdgycivrfbckchfdcwpvqsrlvneyplvpddbpwnoidpiz\
fnyxzblfrxvpxicrqdtobhsrepiimjkybtwopvqxzngpllofsnrgvqjcsytiugesdjeuevdxcaeiatjh\
zfuhcourzureimopolqzwknpusbkesahzcdatujxvxfheodinukjkmwnksuoanuxljweeymytcgjtlss\
pfhyeifkiacncwwxjickpndipsczcjujsdsovzdhmsvvnnckysomwyuyjheljsgkdwyvnwpxgrbudbiq\
fqptdtyeedhjnsbcsnhqelihkgjdfbsfngfthoyegwndmmmopcruetgdqjucjsorvwswkhcrurgpjbvv\
kcrbexsnzsjtywgpqayrokilwaurqqfqxkbkiajkxevrshzttbicmtqsenwxvnohpwznzdyrkfsraxma\
ityvcowwhztdrrtqbemdzzdqrvincqrirappvqiymsaygjsfoqzgtvvrcmvwuwlohgmafxfwopjxmcww\
qtznlxupnlkdaaczkgzcwrehyxrjneyfxssxsprxagvszclquuviddyblzhwkeyhtahyzemnidibqrit\
ittgxttuieccotyztianhcopxkeayufslmqtvbvidhuwzaewivtlduyqbntifpzowpuablpaekjbczwq\
enxcoukjksopdsrjcopchkietsdvykadlfmsedgyiexqqxrsfwwrvuivhorhiiggccbkzlgwhifuwyyu\
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len(k), len(set(k))
from __future__ import division
import numpy as np
import pyopencl as cl
import pyopencl.array
from ccrypto import *
import time
PyOpenCL comes with IPython integration, which lets you seamlessly integrate PyOpenCL kernels into your IPython notebooks. Simply load the PyOpenCL IPython extension using:
%load_ext pyopencl.ipython_ext
Create an OpenCL context and a command queue:
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
This kernel translates all the characters of the buffer.
%%cl_kernel -o "-cl-fast-relaxed-math"
__kernel void translate(__global char *txt, int offset)
{
int gid = get_global_id(0);
txt[gid] = txt[gid] + offset;
}
translate.set_scalar_arg_dtypes( [None, np.int32] )
This kernel searches by brute force the trigram of the key at the position pos which gives the maximum IC.
%%cl_kernel -o "-cl-fast-relaxed-math"
__kernel void best_trig_max_ic(__global char *k,
int sizek,
__global char *pw,
int sizepw,
int period,
int pos,
__global float *clic)
{
int gid0 = get_global_id(0);
int gid1 = get_global_id(1);
int gid2 = get_global_id(2);
char mypw[100]; // local copy of pw
for(int i=0; i<sizepw; i++) {
mypw[i] = pw[i];
}
mypw[pos%sizepw] = gid0;
mypw[(pos+1)%sizepw] = gid1;
mypw[(pos+2)%sizepw] = gid2; // pw for this thread
unsigned short eff[1600][26];
for(int i=0; i<period; i++) { // initialization
for(int j=0; j<26; j++) {
eff[i][j] = 0;
}
}
int ipw = 0;
for(int i = 0; i<sizek; i++) {
char t = (25 - k[i] - mypw[ipw] + 26)%26; // Diana
eff[i%period][t]++;
ipw = (ipw + 1)%sizepw;
}
float mean_ic = 0;
for(int i=0; i<period; i++) { // Kullback
float ic = 0.0;
float n = 0;
for(int j=0; j<26; j++) {
float tmp = eff[i][j];
tmp *= eff[i][j]-1;
ic += tmp;
n += eff[i][j];
}
mean_ic += ic/n/(n-1);
}
clic[(gid0*26+gid1)*26+gid2] = mean_ic/period;
}
best_trig_max_ic.set_scalar_arg_dtypes( [None, np.int32, None, np.int32, np.int32, np.int32, None] )
def triconv(n):
g2 = n%26
n = (n-g2)//26
g1 = n%26
g0 = (n-g1)//26
return g0, g1, g2
def Find_best_ic(ktxt, p, q):
start = time.time()
assert(p < 100)
k = np.array(list(ktxt), dtype=np.character)
clk = cl.array.to_device(queue, k)
translate(queue, (len(clk),), None, clk.data, -65)
# Key
pw = np.array(['E' for i in range(p)], dtype=np.character)
clpw = cl.array.to_device(queue, pw)
translate(queue, (len(clpw),), None, clpw.data, -65)
# array of ic
ic = np.full(26*26*26, 0.0, dtype=np.float32) # table des ic
clic = cl.array.to_device(queue, ic)
# traitement
for i in range(0, 2*len(pw), 3): # two rounds
best_trig_max_ic(queue, (26, 26, 26), None, clk.data, len(clk),
clpw.data, p, q, i, clic.data)
ic = clic.get()
max_ic = max(ic)
print(max_ic)
idmax = np.where(ic==max(ic))[0][0]
pw = clpw.get()
pw[i%len(pw)], pw[(i+1)%len(pw)], pw[(i+2)%len(pw)] = map(chr, triconv(idmax))
clpw = cl.array.to_device(queue, pw)
translate(queue, (len(clpw),), None, clpw.data, 65)
pw = clpw.get()
pw = b''.join(pw.tolist())
pw = pw.decode("utf-8")
delta = int(time.time()-start)
print('----- Elapsed time ',delta//60, 'min', delta%60, 'sec')
return max_ic, pw
Find_best_ic(k, 41, 37*43)
kk = Diana(k, 'NECESSARYFORONEPEOPLETODISSOLVETHEPOLITIC')
Stroke of luck, the key is in clear. Period verification:
for i in range(1585, 1595, 1):
print(i, Kullback(kk, i))
Find_best_ic(kk, 43, 37)
kkk = Diana(kk, 'XIYXKAPTEFZEEXSBZLKKBZQBAQEBJTFQEXKLQEBOXKA')
Period verification:
for i in range(35, 45, 1):
print(i, Kullback(kkk, i))
Table of logarithms of quadrigram frequencies for the English language.
def quadidx(q):
"""Returns the index corresponding to a quadrigram
"""
idx = ord(q[0])-ord('A')
idx = idx*26+ord(q[1])-ord('A')
idx = idx*26+ord(q[2])-ord('A')
idx = idx*26+ord(q[3])-ord('A')
return idx
quadf = np.full(26*26*26*26, 100, dtype=np.float32)
file = open('logf4g_en.txt', 'r')
for w in file:
q, f = w.split()
quadf[quadidx(q)] = f
file.close()
clquadf = cl.array.to_device(queue, quadf)
This kernel searches by brute force the trigram of the key at the position pos which gives the minimum logscore.
%%cl_kernel -o "-cl-fast-relaxed-math"
__kernel void best_trig_score(__global float *clquadf,
__global char *k,
int sizek,
__global char *pw,
int sizepw,
int pos,
__global float *clscore)
{
int gid0 = get_global_id(0);
int gid1 = get_global_id(1);
int gid2 = get_global_id(2);
char mypw[100]; // local copy of pw
for(int i=0; i<sizepw; i++) {
mypw[i] = pw[i];
}
mypw[pos%sizepw] = gid0;
mypw[(pos+1)%sizepw] = gid1;
mypw[(pos+2)%sizepw] = gid2; // pw for this thread
float myscore = 0.0;
char t0 = (25 - k[0] - mypw[0] + 26)%26;
char t1 = (25 - k[1] - mypw[1] + 26)%26;
char t2 = (25 - k[2] - mypw[2] + 26)%26;
int ipw = 3;
for(int i = 3; i<sizek; i++) {
char t3 = (25 - k[i] - mypw[ipw] + 26)%26; // Diana
ipw = (ipw + 1)%sizepw;
int idx = ((t0*26+t1)*26+t2)*26+t3;
if ((idx >= 0) && (idx <= 456975)) { // 26^4 = 456976
myscore += clquadf[idx];
}
else {
myscore = -1; // In case of error (never happens!)
break;
}
t0 = t1;
t1 = t2;
t2 = t3;
}
clscore[(gid0*26+gid1)*26+gid2] = myscore;
}
best_trig_score.set_scalar_arg_dtypes( [None, None, np.int32, None, np.int32, np.int32, None] )
def Solve_Diana(ktxt, p):
start = time.time()
assert(p < 100)
# crypto
k = np.array(list(ktxt), dtype=np.character)
clk = cl.array.to_device(queue, k)
translate(queue, (len(clk),), None, clk.data, -65)
# key:
pw = np.array(['E' for i in range(p)], dtype=np.character)
clpw = cl.array.to_device(queue, pw)
translate(queue, (len(clpw),), None, clpw.data, -65)
# scores array:
score = np.full(26*26*26, 0.0, dtype=np.float32) # flat array of scores
clscore = cl.array.to_device(queue, score)
# processing:
for i in range(0, 2*len(pw), 3): # two rounds
best_trig_score(queue, (26,26,26), None, clquadf.data, clk.data, len(clk),
clpw.data, p, i, clscore.data)
score = clscore.get()
min_score = min(score)
print(min(score))
idmin = np.where(score==min(score))[0][0]
pw = clpw.get()
pw[i%len(pw)], pw[(i+1)%len(pw)], pw[(i+2)%len(pw)] = map(chr, triconv(idmin))
clpw = cl.array.to_device(queue, pw)
translate(queue, (len(clpw),), None, clpw.data, 65)
pw = clpw.get()
pw = b''.join(pw.tolist())
pw = pw.decode("utf-8")
delta = int(time.time()-start)
print('----- Elapsed time ',delta//60, 'min', delta%60, 'sec')
return min_score, pw
Solve_Diana(kkk, 37)
Diana(kkk, 'TEBKFKQEBZLROPBLCERJXKBSBKQPFQYBZLJBP')
We can search for keys in any order:
Find_best_ic(k, 43, 37*41)
kk = Diana(k, 'LAKLYITPEDJEELQHJXYYHJSHISEHZPDSELYXSEHULYI')
Find_best_ic(kk, 41, 37)
kkk = Diana(kk, 'VEGEQQIRKDURUVETEUTXEPUFAQQUXNEPBETUXAPAG')
Solve_Diana(kkk, 37)
Diana(kkk, 'TEBKFKQEBZLROPBLCERJXKBSBKQPFQYBZLJBP')
Le 19/09/2018 - Contact : Rossignol@bribes.org