Problem 59: XOR decryption

(see projecteuler.net/problem=59)

Each character on a computer is assigned a unique code and the preferred standard is ASCII (American Standard Code for Information Interchange).
For example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107.

A modern encryption method is to take a text file, convert the bytes to ASCII, then XOR each byte with a given value, taken from a secret key.
The advantage with the XOR function is that using the same encryption key on the cipher text, restores the plain text; for example, 65 XOR 42 = 107, then 107 XOR 42 = 65.

For unbreakable encryption, the key is the same length as the plain text message, and the key is made up of random bytes.
The user would keep the encrypted message and the encryption key in different locations, and without both "halves", it is impossible to decrypt the message.

Unfortunately, this method is impractical for most users, so the modified method is to use a password as a key.
If the password is shorter than the message, which is likely, the key is repeated cyclically throughout the message.
The balance for this method is using a sufficiently long password key for security, but short enough to be memorable.

Your task has been made easy, as the encryption key consists of three lower case characters.
Using cipher.txt (right click and 'Save Link/Target As...'), a file containing the encrypted ASCII codes, and the knowledge that the plain text must contain common English words,
decrypt the message and find the sum of the ASCII values in the original text.

Algorithm

Three nested loops try all possible keys "aaa" to "zzz" until a match is found.
The only valid characters are 0-9 a-z A-Z ;:,.'?-!() and space.
I don't analyze the contents and just got lucky that the key which produces only valid characters is indeed correct.

Alternative Approaches

I expected to write some clever AI code to figure out whether the text "sounds" English.
But my simple logic was already successful. Somehow I feel disappointed ...

My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, as well as the input data, too.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

#include <vector>
#include <iostream>
 
int main()
{
// read encrypted message from STDIN
std::vector<unsigned char> encrypted;
 
//#define ORIGINAL
#ifdef ORIGINAL
// read numbers in CSV format, e.g. 74,2,999,1,...
while (true)
{
unsigned int current;
std::cin >> current;
 
// no more data
if (!std::cin)
break;
 
encrypted.push_back(current);
 
// skip comma
std::cin.get();
}
 
#else
 
// text length
unsigned int size;
std::cin >> size;
encrypted.clear();
// read text from STDIN
while (size--)
{
unsigned int current;
std::cin >> current;
encrypted.push_back(current);
}
#endif
 
// try all possible keys
for (unsigned char i = 'a'; i <= 'z'; i++)
for (unsigned char j = 'a'; j <= 'z'; j++)
for (unsigned char k = 'a'; k <= 'z'; k++)
{
// current key
const unsigned char key[] = { i, j, k };
 
// apply XOR to all bytes
std::vector<unsigned char> decoded;
for (size_t pos = 0; pos < encrypted.size(); pos++)
decoded.push_back(encrypted[pos] ^ key[pos % 3]);
 
// classify result
bool valid = true;
for (auto d : decoded)
{
// only allow:
// 0-9 a-z A-Z ;:,.'?-!() and space
valid = (d >= '0' && d <= '9');
valid |= (d >= 'a' && d <= 'z');
valid |= (d >= 'A' && d <= 'Z');
valid |= (d == ' ' || d == ',' || d == '.' || d == '?' || d == '!');
valid |= (d == ';' || d == '-' || d == '\'');
valid |= (d == '(' || d == ')');
 
// reject any invalid character
if (!valid)
break;
}
 
// try next key
if (!valid)
continue;
 
// bonus feature: show decoded text
//#define SHOW_DECODED
#ifdef SHOW_DECODED
for (auto d : decoded)
std::cout << d;
std::cout << std::endl;
#endif
 
#ifdef ORIGINAL
// we found the key, now add all ASCII codes of the decrypted text
// add ASCII codes
unsigned int asciiSum = 0;
for (auto d : decoded)
asciiSum += d;
std::cout << asciiSum << std::endl;
return 0;
#else
// print key
std::cout << i << j << k << std::endl;
#endif
}
 
return 0;
}

This solution contains 15 empty lines, 20 comments and 10 preprocessor commands.

Interactive test

You can submit your own input to my program and it will be instantly processed at my server:

This live test is based on the Hackerrank problem.

Input data (separated by spaces or newlines):
Note: Bonus feature: my live test prints the decoded text, too

This is equivalent to
echo "82 32 66 50 20 11 0 42 66 33 19 13 20 47 66 37 14 58 67 43 23 14 17 49 67 46 20 6 \
51 66 55 9 39 67 45 3 25 56 66 39 14 37 34 65 51 22 8 1 40 65 32 17 14 21 \
45 65 36 12 57 66 41 20 15 19 50 66 44 23 7 49 65 54 11 36 66 47 0 24 58 \
65 38 12 38
" | ./59

Output:

(please click 'Go !')

(this interactive test is still under development, computations will be aborted after one second)

Benchmark

The correct solution to the original Project Euler problem was found in 0.03 seconds on a Intel® Core™ i7-2600K CPU @ 3.40GHz.
(compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=c++11 -DORIGINAL)

See here for a comparison of all solutions.

Note: interactive tests run on a weaker (=slower) computer. Some interactive tests are compiled without -DORIGINAL.

Changelog

March 1, 2017 submitted solution
April 21, 2017 added comments
May 9, 2017 read numbers from STDIN

Hackerrank

see https://www.hackerrank.com/contests/projecteuler/challenges/euler059

My code solves 4 out of 4 test cases (score: 100%)

Difficulty

Project Euler ranks this problem at 5% (out of 100%).

Hackerrank describes this problem as easy.

Note:
Hackerrank has strict execution time limits (typically 2 seconds for C++ code) and often a much wider input range than the original problem.
In my opinion, Hackerrank's modified problems are usually a lot harder to solve. As a rule thumb: brute-force is never an option.

Links

projecteuler.net/thread=59 - the best forum on the subject (note: you have to submit the correct solution first)

Code in various languages:

Python: www.mathblog.dk/project-euler-59-xor-encryption/ (written by Kristian Edlund)
Java: github.com/nayuki/Project-Euler-solutions/blob/master/java/p059.java (written by Nayuki)
Go: github.com/frrad/project-euler/blob/master/golang/Problem059.go (written by Frederick Robinson)
Scala: github.com/samskivert/euler-scala/blob/master/Euler059.scala (written by Michael Bayne)

Heatmap

green problems solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too.
yellow problems score less than 100% at Hackerrank (but still solve the original problem).
gray problems are already solved but I haven't published my solution yet.
blue problems are solved and there wasn't a Hackerrank version of it at the time I solved it or I didn't care about it because it differed too much.

Please click on a problem's number to open my solution to that problem:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 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 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
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201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225
226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250
The 160 solved problems had an average difficulty of 21.8% at Project Euler and I scored 11,807 points (out of 13100) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
more about me can be found on my homepage.
some names mentioned on this site may be trademarks of their respective owners.
thanks to the KaTeX team for their great typesetting library !