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

# 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 `#ifdef`

s 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.

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)*

# 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 solved **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 already 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:*

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