So I have to decrypt a .txt file that is crypted with XOR code and with a repeated password that is unknown, and the goal is to discover the message.
Here are the things that I already know because of the professor:
First I need to find the length of the unknown password
The message has been altered and it doesn't have spaces (this may add a bit more difficulty because the space character has the highest frequency in a message)
Any ideas on how to solve this?
thx in advanced :)
First you need to find out the length of the password. You do this by assessing the Index of Coincidence or Kappa-test. XOR the ciphertext with itself shifted 1 step and count the number of characters that are the same (value 0). You get the Kappa value by dividing the result with the total number of characters minus 1. Shift one more time and again calculate the Kappa value. Shift the ciphertext as many times as needed until you discover the password length. If the length is 4 you should see something similar to this:
Offset Hits
-------------------------
1 2.68695%
2 2.36399%
3 3.79009%
4 6.74012%
5 3.6953%
6 1.81582%
7 3.82744%
8 6.03504%
9 3.60273%
10 1.98052%
11 3.83241%
12 6.5627%
As you see the Kappa value is significantly higher on multiples of 4 (4, 8 and 12) than the others. This suggests that the length of the password is 4.
Now that you have the password length you should again XOR the cipher text with itself but now you shift by multiples of the length. Why? Since the ciphertext looks like this:
THISISTHEPLAINTEXT <- Plaintext
PASSPASSPASSPASSPA <- Password
------------------
EJKELDOSOSKDOWQLAG <- Ciphertext
When two values which are the same are XOR:ed the result is 0:
EJKELDOSOSKDOWQLAG <- Ciphertext
EJKELDOSOSKDOWQLAG <- Ciphertext shifted 4.
Is in reality:
THISISTHEPLAINTEXT <- Plaintext
PASSPASSPASSPASSPA <- Password
THISISTHEPLAINTEXT <- Plaintext
PASSPASSPASSPASSPA <- Password
Which is:
THISISTHEPLAINTEXT <- Plaintext
THISISTHEPLAINTEXT <- Plaintext
As you see the password "disappears" and the plaintext is XOR:ed with itself.
So what can we do now then? You wrote that the spaces are removed. This makes it a bit harder to get the plaintext or password. But not at all impossible.
The following table shows the ciphertext values for all english characters:
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
A 0
B 3 0
C 2 1 0
D 5 6 7 0
E 4 7 6 1 0
F 7 4 5 2 3 0
G 6 5 4 3 2 1 0
H 9 10 11 12 13 14 15 0
I 8 11 10 13 12 15 14 1 0
J 11 8 9 14 15 12 13 2 3 0
K 10 9 8 15 14 13 12 3 2 1 0
L 13 14 15 8 9 10 11 4 5 6 7 0
M 12 15 14 9 8 11 10 5 4 7 6 1 0
N 15 12 13 10 11 8 9 6 7 4 5 2 3 0
O 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
P 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0
Q 16 19 18 21 20 23 22 25 24 27 26 29 28 31 30 1 0
R 19 16 17 22 23 20 21 26 27 24 25 30 31 28 29 2 3 0
S 18 17 16 23 22 21 20 27 26 25 24 31 30 29 28 3 2 1 0
T 21 22 23 16 17 18 19 28 29 30 31 24 25 26 27 4 5 6 7 0
U 20 23 22 17 16 19 18 29 28 31 30 25 24 27 26 5 4 7 6 1 0
V 23 20 21 18 19 16 17 30 31 28 29 26 27 24 25 6 7 4 5 2 3 0
W 22 21 20 19 18 17 16 31 30 29 28 27 26 25 24 7 6 5 4 3 2 1 0
X 25 26 27 28 29 30 31 16 17 18 19 20 21 22 23 8 9 10 11 12 13 14 15 0
Y 24 27 26 29 28 31 30 17 16 19 18 21 20 23 22 9 8 11 10 13 12 15 14 1 0
Z 27 24 25 30 31 28 29 18 19 16 17 22 23 20 21 10 11 8 9 14 15 12 13 2 3 0
What does this mean then? If an A and a B is XOR:ed then the resulting value is 3. E and P will result in 21. Etc. OK but how will this help you?
Remember that the plaintext is XOR:ed with itself shifted by multiples of the password length. For each value you can check the above table and determine what combinations that position could have. Lets say the value is 25 then the two characters that resulted in the value 25 could be one of the following combinations:(I-P), (H-Q), (K-R), (J-S), (M-T), (L-U), (O-V), (N-W), (A-X) or (C-Z). But which one? Now you do more shifts and look up the corresponding values in the table again for each position. Next time the value might be 7 and since you already have a list of possible character combinations you only check against them. At the next two shifts the values are 3 and 1. Now you can determine that the character is W since that is the only common character in each shift, (N-W), (P-W), (T-W), (V-W). You can do this for most positions.
You will not get all the plaintext but you will get enough characters to discover the password. Take the known characters and XOR them in the correct position in the ciphertext. This will yield the password. The number of known characters you need atleast is the number of characters in the password if they are at the "correct" positions in regards to the password.
Good luck!
you should look at cracking a vigenere chiffre, especially at auto-correlation. The latter will help you finding out the length of the password and the rest is usually just bruteforcing on the normal distribution of letters (where the most common one is the letter e in the english language).
Although spaces are the most common characters and make decryptions like this easy, the other character also have different frequencies. For example, see this Wikipedia article. If you've got enough encrypted text and the password length isn't too large, it might just be enough to find out the most common bytes in the encrypted text. They will most likely be the encrypted versions of e that has the highest frequency in english texts.
This alone won't give you the decrypted text, but it's very likely you can find out the password length and (part of) the password itself with it. For example, let's assume the most frequent encrypted bytes are
w x m z y
with almost the same frequency and there's a significant drop in frequency after the last one. This will tell you two things:
The password length most likely is 5, because statistically, all encrypted e will be equally likely. EDIT: OK, this isn't correct, it will be 5 or above because the password can contain the same character multiple times.
The password will be some permutation of (w x m z y XOR e e e e e) - you can use the byte offsets modulo the password length to get the correct permutation.
EDIT: The same character occuring in the password multiple times makes things a bit harder, but you'll most likely be able to identify those because as I said, encrypted versions of e will cluster around frequency f - now if the character occurs n times, it will have a frequency near n*f.
The most common three letter trigram in English (assuming the language is probably English) is "the". Place "the" at all possible points on your cyphertext to derive a possible 3 characters of the key. Try each possible key fragment at all other possible positions on the cyphertext and see what you get. For example, "qzg" is unlikely to be correct, but "fen" could be. Look at the spacing between possible positions to derive the key length. With a key length and a key fragment you can place a lot more of the key.
As Lars said, look at ways of decrypting Vigenère, which is effectively what you have here.
Related
Suppose I have an array:
30 20 29 19 28 18 27 17 26 16 25 15 24 14 23 13 22 12 21 11
I am not understanding how to do the shell sort using sequence 3:
Would I simply do this:
30 20 29 19 28 18 27 17 | 26 16 25 15 24 14 |23 13 22 12 21 11
Where I split it into 3 parts and sort the respective parts? And then do the same with 2 sorting after, except split into halves? What is the right way to do this? Can someone please explain?
If you look at your array and number the locations
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
30 20 29 19 28 18 27 17 26 16 25 15 24 14 23 13 22 12 21 11
In a shell sort, what you do is start with a skip number (in your case 3) so to make the first "list" you take a number and skip. With 3 this would be 1st, 4th, 7th etc.
So you would have a list of
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
30 19 27 16 24 13 21
and a second list of
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
20 28 17 25 14 22 11
The 3rd list is the remaining items.
For the next round you do it with one less... so items at odd number locations and items at even number locations.
In response to comment below
A Shell sort is an in-place sort — that means you don't remove the items to new lists or create any new data structures. You are using the array to "treat" items which are "far apart" in terms of array locations as next to each other. You don't actually make new lists or new arrays (that is why I showed my diagrams as I did); you just look at these locations.
Why?
Because it means that when you start (for example with 3) you are moving stuff farther) -- eg the 13 that starts at location 16 gets moved to location 1 in the first pass. Then as you reduce the number you start doing more local changes. This means you gain an advantage over a typical bubble sort. Still not good — but MUCH better than a bubble sort.
Given a 5 x 5 Grid comprising of tiles numbered from 1 to 25 and a set of 5 start-end point pairs.
For each pair,find a path from the start point to the end point.
The paths should meet the below conditions:
a) Only Horizontal and Vertical moves allowed.
b) No two paths should overlap.
c) Paths should cover the entire grid
Input consist of 5 lines.
Each line contains two space-separated integers,Starting and Ending point.
Output: Print 5 lines. Each line consisting of space-separated integers,the path for the corresponding start-end pair. Assume that such a path Always exists. In case of Multiple Solution,print any one of them.
Sample Input
1 22
4 17
5 18
9 13
20 23
Sample Output
1 6 11 16 21 22
4 3 2 7 12 17
5 10 15 14 19 18
9 8 13
20 25 24 23
i think there should be restriction or it lacks some more information about the input ( start point and endpoint)
because if we take following input then covering whole grid is not possible
1 22,
6 7,
11 12,
16 17,
8 9
I need to loop through coloumn 1 of a matrix and return (i) when I have come across ALL of the elements of another vector which i can predefine.
check_vector = [1:43] %% I dont actually need to predefine this - i know I am looking for the numbers 1 to 43.
matrix_a coloumn 1 (which is the only coloumn i am interested in looks like this for example
1
4
3
5
6
7
8
9
10
11
12
13
14
16
15
18
17
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
1
3
4
2
6
7
8
We want to loop through matrix_a and return the value of (i) when we have hit all of the numbers in the range 1 to 43.
In the above example we are looking for all the numbers from 1 to 43 and the iteration will end round about position 47 in matrix_a because it is at this point that we hit number '2' which is the last number to complete all numbers in the sequence 1 to 43.
It doesnt matter if we hit several of one number on the way, we count all those - we just want to know when we have reached all the numbers from the check vector or in this example in the sequence 1 to 43.
Ive tried something like:
completed = []
for i = 1:43
complete(i) = find(matrix_a(:,1) == i,1,'first')
end
but not working.
Assuming A as the input column vector, two approaches could be suggested here.
Approach #1
With arrayfun -
check_vector = [1:43]
idx = find(arrayfun(#(n) all(ismember(check_vector,A(1:n))),1:numel(A)),1)+1
gives -
idx =
47
Approach #2
With customary bsxfun -
check_vector = [1:43]
idx = find(all(cumsum(bsxfun(#eq,A(:),check_vector),1)~=0,2),1)+1
To find the first entry at which all unique values of matrix_a have already appeared (that is, if check_vector consists of all unique values of matrix_a): the unique function almost gives the answer:
[~, ind] = unique(matrix_a, 'first');
result = max(ind);
Someone might have a more compact answer but is this what your after?
maxIndex = 0;
for ii=1:length(a)
[f,index] = ismember(ii,a);
maxIndex=max(maxIndex,max(index));
end
maxIndex
Here is one solution without a loop and without any conditions on the vectors to be compared. Given two vectors a and b, this code will find the smallest index idx where a(1:idx) contains all elements of b. idx will be 0 when b is not contained in a.
a = [ 1 4 3 5 6 7 8 9 10 11 12 13 14 16 15 18 17 19 20 21 22 23 24 25 26 ...
27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 1 3 4 2 6 7 8 50];
b = 1:43;
[~, Loca] = ismember(b,a);
idx = max(Loca) * all(Loca);
Some details:
ismember(b,a) checks if all elements of b can be found in a and the output Loca lists the indices of these elements within a. The index will be 0, if the element cannot be found in a.
idx = max(Loca) then is the highest index in this list of indices, so the smallest one where all elements of b are found within a(1:idx).
all(Loca) finally checks if all indices in Loca are nonzero, i.e. if all elements of b have been found in a.
I have the following example dataset which consists of the # of fish caught per check of a net. The nets are not checked at uniform intervals. The day of the check is denoted in julian days as well as the number of days the net had been fishing since last checked (or since it's deployment in the case of the first check)
http://textuploader.com/9ybp
Site_Number Check_Day_Julian Set_Duration_Days Fish_Caught
2 5 3 100
2 10 5 70
2 12 2 65
2 15 3 22
100 4 3 45
100 10 6 20
100 18 8 8
450 10 10 10
450 14 4 4
In any case, I would like to turn the raw data above into the following format:
http://textuploader.com/9y3t
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2 0 0 100 100 100 70 70 70 70 70 65 65 22 22 22 0 0 0
100 0 45 45 45 20 20 20 20 20 20 8 8 8 8 8 8 8 8
450 10 10 10 10 10 10 10 10 10 10 4 4 4 4 0 0 0 0
This is a matrix which assigns the # of fish caught during the period to EACH of the days that were within that period. The columns of the matrix are Julian days, the rows are site numbers.
I have tried to do this with some matrix functions but I have had much difficulty trying to populate all the fields that are within the time period, but I do not necessarily have a row of data for?
I had posted my small bit of code here, but upon reflection, my approach is quite archaic and a bit off point. Can anyone suggest a method to convert the data into the matrix provided? I've been scratching my head and googling all day but now I am stumped.
Cheers,
C
Two answers, the second one is faster but a bit low level.
Solution #1:
library(IRanges)
with(d, {
ir <- IRanges(end=Check_Day_Julian, width=Set_Duration_Days)
cov <- coverage(split(ir, Site_Number),
weight=split(Fish_Caught, Site_Number),
width=max(end(ir)))
do.call(rbind, lapply(cov, as.vector))
})
Solution #2:
with(d, {
ir <- IRanges(end=Check_Day_Julian, width=Set_Duration_Days)
site <- factor(Site_Number, unique(Site_Number))
m <- matrix(0, length(levels(site)), max(end(ir)))
ind <- cbind(rep(site, width(ir)), as.integer(ir))
m[ind] <- rep(Fish_Caught, width(ir))
m
})
I don't see a super obvious matrix transformation here. This is all i've got assuming the raw data is in a data.frame called dd
dd$Site_Number<-factor(dd$Site_Number)
mm<-matrix(0, nrow=nlevels(dd$Site_Number), ncol=18)
for(i in 1:nrow(dd)) {
mm[as.numeric(dd[i,1]), (dd[i,2]-dd[i,3]):dd[i,2] ] <- dd[i,4]
}
mm
Ok I need to make this program to display "cal" 3 month(one month before and one month after) side by side, rather than just one single month it displays in any Linux/UNIX. I got it working to display 3 calendar by using "system(customCommand)" three times; but then it's not side by side.
I got some hint to use the following system calls:
close(..) pipe(..) dup2(..) read(..) and write(..)
my question is what should I start with? Do I need to create child process and than catch it in pipe(..)?
How can I display three calendar side by side.
ex.
February 2009 March 2009 April 2009
S M Tu W Th F S S M Tu W Th F S S M Tu W Th F S
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4
8 9 10 11 12 13 14 8 9 10 11 12 13 14 5 6 7 8 9 10 11
15 16 17 18 19 20 21 15 16 17 18 19 20 21 12 13 14 15 16 17 18
22 23 24 25 26 27 28 22 23 24 25 26 27 28 19 20 21 22 23 24 25
29 30 31 26 27 28 29 30
Assuming you want to write it yourself instead of using "cal -3", what I'd do (in psuedo code):
popen three calls to "cal" with the appropriate args
while (at least one of the three pipes hasn't hit EOF yet)
{
read a line from the first if it isn't at EOF
pad the results out to a width W, print it
read a line from the second if it isn't at EOF
pad the results out to a width W, print it
read a line from the third if it isn't at EOF
print it
print "\n"
}
pclose all three.
if "cal -3" doesn't work, just use paste :)
$ TERM=linux setterm -regtabs 24
$ paste <(cal 2 2009) <(cal 3 2009) <(cal 4 2009)
febbraio 2009 marzo 2009 aprile 2009
do lu ma me gi ve sa do lu ma me gi ve sa do lu ma me gi ve sa
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4
8 9 10 11 12 13 14 8 9 10 11 12 13 14 5 6 7 8 9 10 11
15 16 17 18 19 20 21 15 16 17 18 19 20 21 12 13 14 15 16 17 18
22 23 24 25 26 27 28 22 23 24 25 26 27 28 19 20 21 22 23 24 25
29 30 31 26 27 28 29 30
$
(setterm ignores -regtabs unless TERM=linux or TERM=con.)
just do
cal -3
Does this not work?
cal -3
Ok, how about cal -3?
cal -3 12 2120 to make it a special month and year, with one before and one after.
The approach I would use for this would be to capture the output, split it into lines, and printf the lines out next to each other. I'd probably do it in Perl, though, rather than C.
Or just use cal -3, if your cal has it.