Create an implementation of the affine cipher, an ancient encryption system created in the Middle East.
The affine cipher is a type of monoalphabetic substitution cipher. Each character is mapped to its numeric equivalent, encrypted with a mathematical function and then converted to the letter relating to its new numeric value. Although all monoalphabetic ciphers are weak, the affine cypher is much stronger than the atbash cipher, because it has many more keys.
the encryption function is:
E(x) = (ax + b) mod m
x
is the letter's index from 0 - length of alphabet - 1m
is the length of the alphabet. For the roman alphabet m == 26
.a
and b
make the keythe decryption function is:
D(y) = a^-1(y - b) mod m
y
is the numeric value of an encrypted letter, ie. y = E(x)
a^-1
is the modular multiplicative inverse
of a mod m
a
only exists if a
and m
are
coprime.To find the MMI of a
:
an mod m = 1
n
is the modular multiplicative inverse of a mod m
More information regarding how to find a Modular Multiplicative Inverse and what it means can be found here.
Because automatic decryption fails if a
is not coprime to m
your
program should return status 1 and "Error: a and m must be coprime."
if they are not. Otherwise it should encode or decode with the
provided key.
The Caesar (shift) cipher is a simple affine cipher where a
is 1 and
b
as the magnitude results in a static displacement of the letters.
This is much less secure than a full implementation of the affine cipher.
Ciphertext is written out in groups of fixed length, the traditional group size being 5 letters, and punctuation is excluded. This is to make it harder to guess things based on word boundaries.
test
gives ybty
with the key a=5 b=7ybty
gives test
with the key a=5 b=7ybty
gives lqul
with the wrong key a=11 b=7kqlfd jzvgy tpaet icdhm rtwly kqlon ubstx
thequickbrownfoxjumpsoverthelazydog
with the key a=19 b=13test
with the key a=18 b=13
Error: a and m must be coprime.
9 mod 26 = 9
9 * 3 mod 26 = 27 mod 26 = 1
3
is the MMI of 9 mod 26
15 mod 26 = 15
15 * 7 mod 26 = 105 mod 26 = 1
7
is the MMI of 15 mod 26
<?php
require_once 'affine-cipher.php';
/**
* The test are divided into two groups:
*
* * Encoding from English to affine cipher,
* * Decoding from affine cipher to all-lowercase-mashed-together English
*/
class AffineCipherTest extends PHPUnit\Framework\TestCase
{
/**
* Tests for encoding English to ciphertext with keys.
*/
public function testEncodeYes()
{
$this->assertEquals('xbt', encode('yes', 5, 7));
}
public function testEncodeNo()
{
$this->assertEquals('fu', encode('no', 15, 18));
}
public function testEncodeOMG()
{
$this->assertEquals('lvz', encode('OMG', 21, 3));
}
public function testEncodeOMGWithSpaces()
{
$this->assertEquals('hjp', encode('O M G', 25, 47));
}
public function testEncodemindblowingly()
{
$this->assertEquals('rzcwa gnxzc dgt', encode('mindblowingly', 11, 15));
}
public function testEncodenumbers()
{
$this->assertEquals(
'jqgjc rw123 jqgjc rw',
encode('Testing,1 2 3, testing.', 3, 4)
);
}
public function testEncodeDeepThought()
{
$this->assertEquals('iynia fdqfb ifje', encode('Truth is fiction.', 5, 17));
}
public function testEncodeAllTheLetters()
{
$this->assertEquals(
'swxtj npvyk lruol iejdc blaxk swxmh qzglf',
encode('The quick brown fox jumps over the lazy dog.', 17, 33)
);
}
public function testEncodeWithANotCoprimeToM()
{
$this->expectException(Exception::class);
encode('This is a test', 6, 17);
}
/**
* Test decoding from ciphertext to English with keys
*/
public function testDecodeExercism()
{
$this->assertEquals('exercism', decode('tytgn fjr', 3, 7));
}
public function testDecodeASentence()
{
$this->assertEquals(
decode("qdwju nqcro muwhn odqun oppmd aunwd o", 19, 16),
"anobstacleisoftenasteppingstone"
);
}
public function testDecodeNumbers()
{
$this->assertEquals(
decode("odpoz ub123 odpoz ub", 25, 7),
"testing123testing"
);
}
public function testDecodeAllTheLetters()
{
$this->assertEquals(
decode("swxtj npvyk lruol iejdc blaxk swxmh qzglf", 17, 33),
"thequickbrownfoxjumpsoverthelazydog"
);
}
public function testDecodeWithNoSpacesInInput()
{
$this->assertEquals(
decode("swxtjnpvyklruoliejdcblaxkswxmhqzglf", 17, 33),
"thequickbrownfoxjumpsoverthelazydog"
);
}
public function testDecodeWithTooManySpaces()
{
$this->assertEquals(
decode("vszzm cly yd cg qdp", 15, 16),
"jollygreengiant"
);
}
public function testDecodeWithANotCoprimeToM()
{
$this->expectException(Exception::class);
decode("Test", 13, 5);
}
}
<?php
function encode(string $message, int $a, int $b): string
{
$fn = function(int $a, int $x, int $b, int $m) {
return ($a * $x + $b) % $m;
};
$encoded = convert($message, $a, $b, $fn);
return trim(preg_replace('/(.{5})/', '$1 ', $encoded));
}
function decode(string $message, int $a, int $b): string
{
$fn = function(int $a, int $x, int $b, int $m) {
return (gmp_intval(gmp_invert($a, $m)) * ($x - $b)) % $m;
};
return convert($message, $a, $b, $fn);
}
function convert(string $message, int $a, int $b, callable $fn): string
{
$alphabet = join(range('a', 'z'));
$m = strlen($alphabet);
if (gmp_intval(gmp_gcd($a, $m)) !== 1) {
throw new Exception("Error: a and m must be coprime.");
}
$message = preg_replace('/[^a-z0-9]/', '', strtolower($message));
$message_length = strlen($message);
$transformed = '';
for ($i = 0; $i < $message_length; $i++) {
$x = strpos($alphabet, $message[$i]);
if ($x === false) {
$transformed .= $message[$i];
}
else {
$idx = $fn($a, $x, $b, $m);
$transformed .= $alphabet[$idx];
}
}
return $transformed;
}
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