[New Exercise]: Affine Cipher (#322)

config.json

@@ -880,6 +880,14 @@
         "prerequisites": [],
         "difficulty": 4
       },
+      {
+        "slug": "affine-cipher",
+        "name": "Affine Cipher",
+        "uuid": "0db7efd5-2ece-481a-b706-0e011aad52aa",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "markdown",
         "name": "Markdown",

exercises/practice/affine-cipher/.docs/instructions.md

@@ -0,0 +1,74 @@
+# Instructions
+
+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 cipher is much stronger than the atbash cipher, because it has many more keys.
+
+[//]: # ( monoalphabetic as spelled by Merriam-Webster, compare to polyalphabetic )
+
+## Encryption
+
+The encryption function is:
+
+```text
+E(x) = (ai + b) mod m
+```
+
+Where:
+
+- `i` is the letter's index from `0` to the length of the alphabet - 1
+- `m` is the length of the alphabet.
+  For the Roman alphabet `m` is `26`.
+- `a` and `b` are integers which make the encryption key
+
+Values `a` and `m` must be *coprime* (or, *relatively prime*) for automatic decryption to succeed, i.e., they have number `1` as their only common factor (more information can be found in the [Wikipedia article about coprime integers][coprime-integers]).
+In case `a` is not coprime to `m`, your program should indicate that this is an error.
+Otherwise it should encrypt or decrypt with the provided key.
+
+For the purpose of this exercise, digits are valid input but they are not encrypted.
+Spaces and punctuation characters are excluded.
+Ciphertext is written out in groups of fixed length separated by space, the traditional group size being `5` letters.
+This is to make it harder to guess encrypted text based on word boundaries.
+
+## Decryption
+
+The decryption function is:
+
+```text
+D(y) = (a^-1)(y - b) mod m
+```
+
+Where:
+
+- `y` is the numeric value of an encrypted letter, i.e., `y = E(x)`
+- it is important to note that `a^-1` is the modular multiplicative inverse (MMI) of `a mod m`
+- the modular multiplicative inverse only exists if `a` and `m` are coprime.
+
+The MMI of `a` is `x` such that the remainder after dividing `ax` by `m` is `1`:
+
+```text
+ax mod m = 1
+```
+
+More information regarding how to find a Modular Multiplicative Inverse and what it means can be found in the [related Wikipedia article][mmi].
+
+## General Examples
+
+- Encrypting `"test"` gives `"ybty"` with the key `a = 5`, `b = 7`
+- Decrypting `"ybty"` gives `"test"` with the key `a = 5`, `b = 7`
+- Decrypting `"ybty"` gives `"lqul"` with the wrong key `a = 11`, `b = 7`
+- Decrypting `"kqlfd jzvgy tpaet icdhm rtwly kqlon ubstx"` gives `"thequickbrownfoxjumpsoverthelazydog"` with the key `a = 19`, `b = 13`
+- Encrypting `"test"` with the key `a = 18`, `b = 13` is an error because `18` and `26` are not coprime
+
+## Example of finding a Modular Multiplicative Inverse (MMI)
+
+Finding MMI for `a = 15`:
+
+- `(15 * x) mod 26 = 1`
+- `(15 * 7) mod 26 = 1`, ie. `105 mod 26 = 1`
+- `7` is the MMI of `15 mod 26`
+
+[mmi]: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse
+[coprime-integers]: https://en.wikipedia.org/wiki/Coprime_integers

exercises/practice/affine-cipher/.meta/AffineCipher.example.ps1

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+Function Invoke-Encode() {
+    <#
+    .SYNOPSIS
+    Use the affine cipher, an ancient encryption system created in the Middle East to encrypt text.
+
+    .DESCRIPTION
+    The encryption function is: E(x) = (ai + b) mod m
+    
+    i is the letter's index from 0 to the length of the alphabet - 1
+    m is the length of the alphabet. For the Roman alphabet m is 26.
+    a and b are integers which make the encryption key
+    Values a and m must be coprime, if not you should throw error.
+
+    .PARAMETER Plaintext
+    The text to be encrypted.
+
+    .PARAMETER Keys
+    A hashtable contain the pair of keys `a` and `b`.
+
+    .EXAMPLE
+    Invoke-Encode -Plaintext "test" -Keys @{a = 5; b = 7}
+    Returns: "ybty"
+    #>
+    [CmdletBinding()]
+    Param(
+        [string]$Plaintext,
+        [hashtable]$Keys
+    )
+    $alphabets = 'a'..'z'
+    $m = $alphabets.Length
+    $gcd , $ex, $_ =  ExtendedEuclidean $Keys.a $m
+
+    if ($gcd -ne 1) {
+        Throw "a and m must be coprime"
+    }
+
+    $charsArray = $Plaintext.ToCharArray() | Where-Object {$_ -match "\w"} | ForEach-Object {
+        if ($_ -match "[a-z]") {
+            $i = $alphabets.IndexOf([char]::ToLower($_))
+            $x = ($Keys.a * $i + $Keys.b) % $m
+            $alphabets[$x]
+        }else {
+            $_
+        } 
+    }
+
+    (-join $charsArray -split '(\w{5})' | Where-Object {$_}) -join " "
+}
+
+Function Invoke-Decode() {
+    <#
+    .SYNOPSIS
+    Use the affine cipher, an ancient encryption system created in the Middle East to decrypt ciphertext.
+
+    .DESCRIPTION
+    The decryption function is: D(y) = (a^-1)(y - b) mod m
+    
+    y is the numeric value of an encrypted letter, i.e., y = E(x)
+    it is important to note that a^-1 is the modular multiplicative inverse (MMI) of a mod m
+    the modular multiplicative inverse only exists if a and m are coprime, if they are not you should throw error.
+    The MMI of a is x such that the remainder after dividing ax by m is 1: ax mod m = 1
+
+    .PARAMETER Ciphertext
+    The text to be decrypted.
+
+    .PARAMETER Keys
+    A hashtable contain the pair of keys `a` and `b`.
+
+    .EXAMPLE
+    Invoke-Decode -Ciphertext "ybty" -Keys @{a = 5; b = 7}
+    Returns: "test"
+     #>
+    [CmdletBinding()]
+    Param(
+        [string]$Ciphertext,
+        [hashtable]$Keys
+    )
+    $alphabets = 'a'..'z'
+    $m = $alphabets.Length
+
+    $gcd , $ex, $_ =  ExtendedEuclidean $Keys.a $m
+
+    if ($gcd -ne 1) {
+        Throw "a and m must be coprime"
+    }else {
+        $MMI = ($ex % $m + $m) % $m
+    }
+
+    $charsArray = $Ciphertext.ToCharArray() | ForEach-Object {
+        if ($_ -match "[a-z]") {
+            $y = $alphabets.IndexOf($_)
+            $x = ($MMI * ($y - $Keys.b)) % $m
+            $alphabets[$x]
+        } elseif ($_ -match "\d") {
+            $_
+        }
+    }
+
+    -join $charsArray
+}
+
+function ExtendedEuclidean($a, $b) {
+    if ($a -eq 0) {
+        return $b, 0, 1
+    }
+
+    $gcd , $x, $y = ExtendedEuclidean ($b % $a) $a 
+    $x1, $y1 = $x, $y
+
+    $x = $y1 - [math]::Floor($b / $a) * $x1
+    $y = $x1
+    return $gcd , $x, $y
+}

exercises/practice/affine-cipher/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "glaxxie"
+  ],
+  "files": {
+    "solution": [
+      "AffineCipher.ps1"
+    ],
+    "test": [
+      "AffineCipher.tests.ps1"
+    ],
+    "example": [
+      ".meta/AffineCipher.example.ps1"
+    ]
+  },
+  "blurb": "Create an implementation of the Affine cipher, an ancient encryption algorithm from the Middle East.",
+  "source": "Wikipedia",
+  "source_url": "https://en.wikipedia.org/wiki/Affine_cipher"
+}

exercises/practice/affine-cipher/.meta/tests.toml

@@ -0,0 +1,58 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[2ee1d9af-1c43-416c-b41b-cefd7d4d2b2a]
+description = "encode -> encode yes"
+
+[785bade9-e98b-4d4f-a5b0-087ba3d7de4b]
+description = "encode -> encode no"
+
+[2854851c-48fb-40d8-9bf6-8f192ed25054]
+description = "encode -> encode OMG"
+
+[bc0c1244-b544-49dd-9777-13a770be1bad]
+description = "encode -> encode O M G"
+
+[381a1a20-b74a-46ce-9277-3778625c9e27]
+description = "encode -> encode mindblowingly"
+
+[6686f4e2-753b-47d4-9715-876fdc59029d]
+description = "encode -> encode numbers"
+
+[ae23d5bd-30a8-44b6-afbe-23c8c0c7faa3]
+description = "encode -> encode deep thought"
+
+[c93a8a4d-426c-42ef-9610-76ded6f7ef57]
+description = "encode -> encode all the letters"
+
+[0673638a-4375-40bd-871c-fb6a2c28effb]
+description = "encode -> encode with a not coprime to m"
+
+[3f0ac7e2-ec0e-4a79-949e-95e414953438]
+description = "decode -> decode exercism"
+
+[241ee64d-5a47-4092-a5d7-7939d259e077]
+description = "decode -> decode a sentence"
+
+[33fb16a1-765a-496f-907f-12e644837f5e]
+description = "decode -> decode numbers"
+
+[20bc9dce-c5ec-4db6-a3f1-845c776bcbf7]
+description = "decode -> decode all the letters"
+
+[623e78c0-922d-49c5-8702-227a3e8eaf81]
+description = "decode -> decode with no spaces in input"
+
+[58fd5c2a-1fd9-4563-a80a-71cff200f26f]
+description = "decode -> decode with too many spaces"
+
+[b004626f-c186-4af9-a3f4-58f74cdb86d5]
+description = "decode -> decode with a not coprime to m"

exercises/practice/affine-cipher/AffineCipher.ps1

@@ -0,0 +1,61 @@
+Function Invoke-Encode() {
+    <#
+    .SYNOPSIS
+    Use the affine cipher, an ancient encryption system created in the Middle East to encrypt text.
+
+    .DESCRIPTION
+    The encryption function is: E(x) = (ai + b) mod m
+    
+    i is the letter's index from 0 to the length of the alphabet - 1
+    m is the length of the alphabet. For the Roman alphabet m is 26.
+    a and b are integers which make the encryption key
+    Values a and m must be coprime, if not you should throw error.
+
+    .PARAMETER Plaintext
+    The text to be encrypted.
+
+    .PARAMETER Keys
+    A hashtable contain the pair of keys `a` and `b`.
+
+    .EXAMPLE
+    Invoke-Encode -Plaintext "test" -Keys @{a = 5; b = 7}
+    Returns: "ybty"
+    #>
+    [CmdletBinding()]
+    Param(
+        [string]$Plaintext,
+        [hashtable]$Keys
+    )
+    Throw "Please implement this function"
+}
+
+Function Invoke-Decode() {
+    <#
+    .SYNOPSIS
+    Use the affine cipher, an ancient encryption system created in the Middle East to decrypt ciphertext.
+
+    .DESCRIPTION
+    The decryption function is: D(y) = (a^-1)(y - b) mod m
+    
+    y is the numeric value of an encrypted letter, i.e., y = E(x)
+    it is important to note that a^-1 is the modular multiplicative inverse (MMI) of a mod m
+    the modular multiplicative inverse only exists if a and m are coprime, if they are not you should throw error.
+    The MMI of a is x such that the remainder after dividing ax by m is 1: ax mod m = 1
+
+    .PARAMETER Ciphertext
+    The text to be decrypted.
+
+    .PARAMETER Keys
+    A hashtable contain the pair of keys `a` and `b`.
+
+    .EXAMPLE
+    Invoke-Decode -Ciphertext "ybty" -Keys @{a = 5; b = 7}
+    Returns: "test"
+     #>
+    [CmdletBinding()]
+    Param(
+        [string]$Ciphertext,
+        [hashtable]$Keys
+    )
+    Throw "Please implement this function"
+}