关于算法:分析COMP122-The-Caesar-Cipher

COMP122 Assessment 1 Due 2021-03-05 at 5pm
The Caesar Cipher
The Caesar cipher is an ancient method of encrypting text, i.e. to transform text into a format that is
unreadable for anyone without a secret key. It is believed that Julius Caesar actually used such a cipher
for his correspondence. Unfortunately for him, This type of cipher is easily broken using a frequency
analysis method outlined below. Your assignment is to implement this in Java.
Part 1: Encrypting and Decrypting
The Caesar cipher is a“rotation cipher”and operates by translating each letter into the one that is
shied along the alphabet by a fixed distance. This distance is called the shi. It is the same for all
letters in the alphabet and therefore can be seen as the secret key to encrypt and decrypt: To encrypt
your text using a given shi, you translate letters by that many places later in the alphabet. A Caesar
cipher with shi 3 can be illustrated as follows.
For example, if your text to encrypt is“Meet me at midnight under the bridge”and your shi is 3, the
encrypted text is“Phhw ph dw plgqljkw xqghu wkh eulgjh”, as the letter“b”gets translated into an“e”,
and“e”gets translated into“h”and so on. We“wrap around”at the end of the alphabet, so that“z”
gets changed to a“c”given a shi of 3. We can interpret a negative value for the shi as translating
letters backwards (e.g. an“f”gets encrypted as the letter“b”if the shi is −4).
Requirements
In a file called Caesar.java, implement the following (public static) methods.
• a method called rotate that rotates a single character. It should have two arguments: an integer
(int) shi and a char to rotate, and return the character rotated by the given shi, as a char.
Lower-case characters should be translated into lower-case characters, capitalised ones into
capitalised ones, and all other characters should remain untouched.
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COMP122 Assessment 1 Due 2021-03-05 at 5pm
• another method called rotate that rotates a whole string. It should have two arguments: an
integer (int) shi and a String to rotate and return the string rotated by the given shi, as a
String.
• a main method, that allows to encode/decode text, as follows. This should interpret the first two
The first argument is interpreted as an integer shi and the second one as a (string) message to
be rotated. The only output printed by the program should be the rotated string output.
Moreover, the main method should check if it was called with exactly two arguments and complain
otherwise. See below for example outputs. Your program needs to print the exact same
output to be considered correct.
$> java Caesar 3 “The ships hung in the sky in much the same way that bricks don’t.”
Wkh vklsv kxqj lq wkh vnb lq pxfk wkh vdph zdb wkdw eulfnv grq’w.
$> java Caesar -13 “The ships hung in the sky in much the same way that bricks don’t.”
Gur fuvcf uhat va gur fxl va zhpu gur fnzr jnl gung oevpxf qba’g
$> java Caesar 13 The ships hung in the sky in much the same way that bricks don’t.
Too many parameters!
Usage: java Caesar n “cipher text”
$> java Caesar 13
Too few parameters!
Usage: java Caesar n “cipher text”
Part 2: Cracking the Caesar cipher.
Suppose we are given a cipher text, i.e. text that has already been encrypted with some (unknown)
shi, and we want to determine the original unencrypted text (typically referred to as the plaintext).
To reconstruct the original text we could decode with each of the 26 possible shis, and take the result
that looks“closest”to an English sentence.
How do we measure“closeness”? This is where letter frequencies and a small statistical trick comes in.
First of all, we know how oen each letter occurs on average in English text. For instance,“e”is the
most common letter, then“t”, and so on. To decode our cipher text, we can compute the frequencies
of each letter as they appear in the text. To measure how“close”these are to the known English letter
frequencies, we use the χ
2
-score (that is the Greek letter“chi”, so it’s the“chi-squared score”). This
score is defined as
χ
2 =
Xz
α=a
(freqα − Englishα
)
2
Englishα
where freqα denotes the frequency of a letter α (the number of occurrences divided by the total number
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COMP122 Assessment 1 Due 2021-03-05 at 5pm
of letters in the text), and Englishα
is the corresponding English letter frequency. In other words, we
sum the fraction over all 26 possible letters to determine this score, which is a single number.
The χ
2
score will be lower when the frequencies are closer to English. Note that when we do this, we
are ignoring the case of letters (we want to treat upper and lower case equally for our purposes).
You are provided with a file called Brutus.java, which already defines letter frequencies in English
texts. This is given as array of doubles, in alphabetical order:
1 public static final double[] english = {
2 0.0855, 0.0160, 0.0316, 0.0387, 0.1210, 0.0218, 0.0209, 0.0496, 0.0733,
3 0.0022, 0.0081, 0.0421, 0.0253, 0.0717, 0.0747, 0.0207, 0.0010, 0.0633,
4 0.0673, 0.0894, 0.0268, 0.0106, 0.0183, 0.0019, 0.0172, 0.0011
5 };
Accordingly, the frequency of the letter“a”, the probability that a randomly chosen letter in an English
text is an“a”, is Englisha = 0.0855 and can be accessed as english[0]. Similarly, Englishb = 0.0160
and so on.
Requirements
In Brutus.java, write
• a method called count that takes a single String parameter and returns a length-26 integer
array whose values reflect how oen each character occurred. You should not make a dierence
between upper and lower case letters and the returned array should be in alphabetical order.
This way, if letterCounts is an array resulting from your method then letterCounts[25] is
the number of times the letter“z”or“Z”occurs.
• a method called frequency that takes a single String and returns a length-26 array of double
s whose values correspond, in alphabetical order, to the frequency of the letter. This way, if
letterFreq is an array resulting from this method then letterFreq[24] is the number of
times the letter“x”or“X”occurs, divided by the length of the string input.
• a method called chiSquared, which returns the χ
2
-score (a double) for two given sets of
frequencies. That is, it should take two parameters, both of type double[], and return a single
double value that tells us how close these two arrays are. You may assume that the two inputs
are always of length 26.
• a main method that can be used to decipher Caesar-encoded English cryptotext without the
key. Of course, you should be using your chiSquared method as well as the given English letter
frequencies.
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COMP122 Assessment 1 Due 2021-03-05 at 5pm
The string that is to be deciphered should be read from the first command line argument and
your program should ensure that it gets exactly this one argument and complain otherwise.
Sample output below.
$> java Brutus “Vg vf n zvfgnxr gb guvax lbh pna fbyir nal znwbe ceboyrzf whfg jvgu
cbgngbrf.”
It is a mistake to think you can solve any major problems just with potatoes.
$> java Brutus
Too few parameters!
Usage: java Brutus “cipher text”
$> java Brutus Too Many Parameters
Too many parameters!
Usage: java Brutus “cipher text”
Hints and Comments

1. In Java, char and int variables are (more or less) interchangeable. A Java statement like
2. int diff = ‘e’ – ‘b’;
   is perfectly legal, i.e. Java can interpret the“dierence of two letters”with no problem, and
   this will give an integer value. If the two letters are of the same case, then this will give a value
   between −25 and 25. In particular, if ch is a lower case (char) letter, then
3. int diff = ch – ‘a’;
   tells you how many places aer‘a’that letter is in the alphabet. (The value of diff will be
   between 0 and 25 inclusive).
4. When translating letters, notice that if ch-‘a’ is between 0 and 25 (inclusive), then ch is a lower
   case letter, and we encrypt as above. Alternatively, if ch-‘A’ is between 0 and 25 (inclusive), we
   encrypt ch similarly to get a new upper case letter. You may also use helper methods isLetter,
   isLowerCase etc from the Character class.
5. In order to translate whole strings, recall that you can access the individual characters in a string
   using the charAt method: if str is a String then str.charAt(i) gives you the char at index
   i in str.
6. When counting letter frequencies remember that for this exercise, we consider upper and lower
   case to be the same and do not consider spaces and punctuation characters. For example, in the
   string “Mississippi moon!”, the frequency of the letter“m”is 2/15, while the frequency of
   the letter“s”is 4/15.
7. Make sure you that your code is readable and appropriately documented. There will be points for
   javadoc comments that explain what each method does and how its parameters are interpreted.
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   COMP122 Assessment 1 Due 2021-03-05 at 5pm
8. You can run a (partial) automarker to check that your submission is in the correct format.
   $> check50 liv-ac-uk/comp122/2021/problems/caesar
   Submission
   Submit you solution using submit50 just like the lab exercises.
   $> submit50 liv-ac-uk/comp122/2021/problems/caesar
   You can submit multiple times and only the latest version (and it’s submission time) will be considered
   for grading.
   Submissions are subject to UoL’s Code of Practice on Assessment and the usual late penalties (-5% per
   for each 24 hour period immediately following the deadline) apply. If you require an extension due to
   extenuating circumstances please get in touch with the CS student oice (csstudy@liv.ac.uk) before
   the submission deadline. We will not grant any extensions aerwards.