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Caesar's Cipher

Julius Caesar had many secrets. He used a simple form of encryption to hide his secrets from his enemies. The cipher was easy: shift the alphabet over by a number of letters and replace each letter with the shifted version.

For instance, if you shift the alphabet by two, you get:

a b c d e f g h i j k l m n o p q r s t u v w x y z
c d e f g h i j k l m n o p q r s t u v w x y z a b

When encrypting a string, we replace instances of the top letter with the lower letter. m becomes o. And notice that the alphabet wraps around.

This was cutting edge technology back in those times! You can get this as a prize in a Cracker Jack box :)

Anyway, write a function that will encrypt a string. It should take the shift number and the string. Leave non-letters alone and keep caps in place. You only have to deal with regular ASCII letters for simplicity.

Bonus: make it so to decrypt it you can pass in a negative number.

Thanks to this site for the idea.

(ns tst.demo.core
(:use tupelo.core tupelo.test)
[schema.core :as s]
[tupelo.chars :as chars]
[clojure.string :as str])
(:import [java.lang Character]))
(def alphabet-lower (vec chars/lowercase))
(def alphabet-len (count alphabet-lower))
(def char->index (zipmap alphabet-lower (range)))
(s/defn encipher-char :- Character
"Implements a Ceasar cipher with shift N (N=0 => noop)"
[shift :- s/Int
char-in :- Character]
(if-not (chars/alpha? char-in)
(let [idx-plain (char->index (chars/->lowercase char-in))
idx-cipher (mod (+ idx-plain shift) alphabet-len)
char-out (cond-it-> (nth alphabet-lower idx-cipher)
(chars/uppercase? char-in) (chars/->uppercase it))]
(s/defn encipher :- s/Str
"Implements a Ceasar cipher with shift N (N=0 => noop)"
[shift :- s/Int
msg :- s/Str]
(let [chars-plain (str->chars msg)
chars-cipher (forv [char-plain chars-plain]
(encipher-char shift char-plain))
msg-out (str/join chars-cipher)]
(s/defn decipher :- s/Str
"Deciphers a Ceasar cipher with shift N (N=0 => noop)"
[shift :- s/Int
msg :- s/Str]
(encipher (- shift) msg))
(let [vv (vec (range 6))]
; like Python indexing:
(is= (idx vv 1) 1)
(is= (idx vv -1) 5)))
(is= (encipher-char 0 \a) \a)
(is= (encipher-char 1 \a) \b)
(is= (encipher-char -1 \a) \z)
(is= (encipher-char 0 \A) \A)
(is= (encipher-char 1 \A) \B)
(is= (encipher-char -1 \A) \Z)
(is= (encipher 1 "Hello") "Ifmmp")
(is= (encipher 0 "Hello") "Hello")
(is= (encipher 1 "Hello") "Ifmmp")
(is= "Hello" (it-> "Hello"
(encipher 1 it)
(encipher -1 it)))
(is= "Hello" (it-> "Hello"
(encipher 1 it)
(decipher 1 it)))
(let [msg-plain "James Bond will attack SPECTRE at dawn!"
cipher-expected "Wnzrf Obaq jvyy nggnpx FCRPGER ng qnja!"
msg-cipher (encipher 13 msg-plain)]
(is= msg-cipher cipher-expected)
(is= msg-plain (it-> msg-plain
(encipher 17 it)
(decipher 17 it)))))
(def lower (clojure.string/lower-case "abcdefghijklmnopqrstuvwxyz"))
(def upper (clojure.string/upper-case "abcdefghijklmnopqrstuvwxyz"))
(defn rotate [n letters]
(->> letters
(drop (mod n (count letters)))
(zipmap letters)))
(defn ->ring [n]
(merge (rotate n lower) (rotate n upper)))
(defn encrypt [n s]
(let [ring (->ring n)]
(->> s
(map #(get ring % %))
(ns caesar-cipher
(:require [clojure.test :refer :all]))
(def capital-floor 65)
(def capital-ceiling 90)
(def lowercase-floor 97)
(def lowercase-ceiling 122)
(defmulti wrap :letter-type)
(defmethod wrap :upper [{:keys [value]}]
(if (> value capital-ceiling)
(+ capital-floor (dec (mod value capital-ceiling)))
(defmethod wrap :lower [{:keys [value]}]
(if (> value lowercase-ceiling)
(+ lowercase-floor (dec (mod value lowercase-ceiling)))
(defn- ascii-letter-type [c]
(and (>= c capital-floor) (<= c capital-ceiling)) :upper
(and (>= c lowercase-floor) (<= c lowercase-ceiling)) :lower))
(defn- shift-char [c n]
(if-let [letter-type (ascii-letter-type (int c))]
(char (wrap {:value (+ (int c) n)
:letter-type letter-type}))
(char c)))
(defn shuffle-message
"Accepts a message and shift value and produces a shuffled version of the message.
:message string to shuffle
:shift integer indicating the number of letters to shift"
[message shift]
(if (empty? message)
(let [reduced-shift (mod shift 26)
chars (seq message)]
(apply str (map #(shift-char % reduced-shift) chars)))))
(deftest shuffle-test
(is (= "Khoor" (shuffle-message "Hello" 3)))
(is (= "Hello" (shuffle-message "Khoor" -3)))
(is (= "Uryyb" (shuffle-message "Hello" -13)))
(is (= "Hello" (shuffle-message "Hello" 104)))
(is (= "Hello" (shuffle-message "Gdkkn" -51)))
(is (= "Kh110#Z0u1g!" (shuffle-message "He110#W0r1d!" 3)))
(is (= "" (shuffle-message "" 0)))
(is (nil? (shuffle-message nil 0))))
;; O(n) complexity
;; 400-600ms execution time for 1,000,000 chars
(time (shuffle-message (take 1000000 (repeatedly #(char (+ 65 (rand-int 26))))) 3))
(defn encode [x step]
"Encode string x with step size step"
(letfn [(encode [i step]
(+ (mod (+ (- i (int \a)) step) 26) (int \a)))]
(apply str (map (comp char #(encode % step) int) x))))
(defn encrypt [n s]
(let [offset (mod n 26)
alphabet1 (map char (range 97 123))
alphabet2 (concat (drop offset alphabet1) (take offset alphabet1))
encryptor (zipmap alphabet1 alphabet2)]
(apply str (map #(get encryptor % %) s))))
(ns jvw.caesar-cipher
(:require [clojure.string :refer [upper-case]]
[clojure.test :refer [deftest testing is]]))
(defn shift
"Returns an cycle of `coll`, shifted by `n`.
`n` can be negative."
[n coll]
(cond->> (cycle coll)
(seq coll) (drop (mod n (count coll)))))
(defn cipher [n coll]
(zipmap coll (shift n coll)))
(defn encrypt
"Returns an encryption of the string `s` by applying a Caesar cipher of `n` rotations.
`n` can be negative: (encrypt -n s) is the inverse of (encrypt n s)."
[n s]
(let [az "abcdefghijklmnopqrstuvwxyz"
ciph (merge (cipher n az)
(cipher n (upper-case az)))]
(apply str (map #(if-let [c (ciph %)]
(deftest shift-test
(testing "empty collection"
(is (empty? (shift 0 [])))
(is (empty? (shift 1 [])))
(is (empty? (shift -1 []))))
(testing "non-empty collection"
(is (= [1 2 3 4] (take 4 (shift 0 [1 2 3 4]))))
(is (= [3 4 1 2] (take 4 (shift 2 [1 2 3 4]))))
(is (= [4 5 1 2 3] (take 5 (shift -2 [1 2 3 4 5]))))))
(deftest cipher-test
(testing "empty collection"
(is (= {} (cipher 0 []))))
(testing "non-empty collection"
(is (= {1 2
2 3
3 1}
(cipher 1 [1 2 3])))
(is (= {1 2
2 3
3 1}
(cipher -2 [1 2 3])))))
(deftest encrypt-test
(testing "empty string"
(is (= "" (encrypt 1 ""))))
(testing "no shift"
(is (= "abc" (encrypt 0 "abc"))))
(testing "some shift"
(is (= "ya" (encrypt 24 "ac")))
(is (= "ya" (encrypt -2 "ac"))))
(testing "capital preservation"
(is (= "aBc" (encrypt 0 "aBc")))
(is (= "bCd" (encrypt 1 "aBc"))))
(testing "non-letters"
(is (= "a-b-c" (encrypt 0 "a-b-c")))
(is (= "b-c-d" (encrypt 1 "a-b-c")))
(let [non-letters "!@#$%^&*()_+"]
(is (= non-letters (encrypt 123 non-letters))))))
(defn caesar-encrypt
[k s]
(letfn [(ctoi [c] (- (int c) (int \a))) ; char to int
(itoc [i] (char (+ i (int \a)))) ; int to char
(shift [i c] (itoc (mod (+ i (ctoi c)) 26) ))] ; shift char c by i
(apply str (mapv (partial shift k) s))))
;; standard caeasr (offset 3)
(def caesar (partial caesar-encrypt 3))
(def uncaesar (partial caesar-encrypt -3))
(uncaesar (caesar "thisisatest"))
;; "thisisatest"
(defn encode
[cleartext shift]
{:pre [(<= (Math/abs shift) 26)]}
(let [abc "abcdefghijklmnopqrstuvwxyz"
ABC (clojure.string/upper-case abc)
rshift (if (< shift 0)
(+ shift (count abc))
coder (apply merge
(for [run [abc ABC]]
(drop rshift run)
(take rshift run)))))]
(apply str (map #(get coder %1 %1) cleartext))))
;; `rfstr` is a "reducing step function" for transduce, no arg for init, expects
;; chars, returns final result string
(defn rfstr
([] (StringBuilder.))
([sb] (.toString ^StringBuilder sb))
([sb ch] (.append ^StringBuilder sb ^char ch)))
(defn caesar
([message] (caesar message 13))
([message offset]
(let [rotch (fn [ch]
(let [ic (long ch)
ia (long \a)
iz (long \z)
iA (long \A)
iZ (long \Z)]
(cond (<= ia ic iz) (char (+ ia (mod (+ (- ic ia) offset) 26)))
(<= iA ic iZ) (char (+ iA (mod (+ (- ic iA) offset) 26)))
:else ch)))]
(transduce (map rotch) rfstr message))))
(ns purelyfunctional-newsletters.issue-367
(:require [clojure.string :as str]
[clojure.test :refer :all]))
(def lower-ascii-letters
(vec (for [ch (range (int \a) (inc (int \z)))]
(char ch))))
(defn caesar-map [alphabet shift ch]
(let [char-idx (.indexOf alphabet ch)]
(if (= -1 char-idx)
(let [new-char-idx (+ char-idx shift)
new-char-idx (mod new-char-idx (count alphabet))]
(get alphabet new-char-idx)))))
(defn caesar-crypt [shift msg]
(map #(caesar-map lower-ascii-letters shift %) msg)))
(deftest caesar-cipher
(is (= "" (caesar-crypt 2 nil)))
(is (= "" (caesar-crypt 2 "")))
(is (= "a" (caesar-crypt 0 "a")))
(is (= "z" (caesar-crypt 25 "a")))
(is (= "z" (caesar-crypt -1 "a")))
(is (= "a" (caesar-crypt 1 "z")))
;; from the newsletter test
(is (= "c d e f g h i j k l m n o p q r s t u v w x y z a b"
(caesar-crypt 2 "a b c d e f g h i j k l m n o p q r s t u v w x y z")))
;; encrypt-decrypt test
(is (= "Hello World!" (->> "Hello World!"
(caesar-crypt 2)
(caesar-crypt -2)))))
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