<< problem 58 - Spiral primes Prime pair sets - problem 60 >>

# Problem 59: XOR decryption

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.

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.

# My 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 ...

# 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:

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

# 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. Or just jump to my GitHub repository.

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();
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
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.

# Benchmark

The correct solution to the original Project Euler problem was found in 0.03 seconds on an Intel® Core™ i7-2600K CPU @ 3.40GHz.
(compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++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
May 9, 2017 read numbers from STDIN

# Hackerrank

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 rarely an option.

# Heatmap

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

 green solutions solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too yellow solutions score less than 100% at Hackerrank (but still solve the original problem easily) gray problems are already solved but I haven't published my solution yet blue solutions are relevant for Project Euler only: there wasn't a Hackerrank version of it (at the time I solved it) or it differed too much orange problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte red problems are not solved yet but I wrote a simulation to approximate the result or verified at least the given example - usually I sketched a few ideas, too black problems are solved but access to the solution is blocked for a few days until the next problem is published [new] the flashing problem is the one I solved most recently

I stopped working on Project Euler problems around the time they released 617.
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The 310 solved problems (that's level 12) had an average difficulty of 32.6% at Project Euler and
I scored 13526 points (out of 15700 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+.

My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.

Look at my progress and performance pages to get more details.

 << problem 58 - Spiral primes Prime pair sets - problem 60 >>
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