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1+++
2title = "1.7.1 Walkthrough: Caesar Cipher"
3weight = 16
4template = "doc.html"
5+++
7A Caesar cipher is a very simple way to obfuscate a message. The technique
8takes a string and swaps out each component letter with another letter that is
9a specified number of positions up or down in the alphabet. For example, with a
10"right-shift" of 1, `a` would become `b`, `j` would become `k`, and `z` would
11wrap around back to `a`.
13Consider the message below, and the cipher that results when we Caesar-shift the
14message to the right by 1.
16```
17Plaintext message: "do not give way to anger"
18Right-shifted cipher: "ep opu hjwf xbz up bohfs"
19```
21Note that the Caesar cipher is completely unsuitable for actually securing
22information. Implementing it in a program is just a fun exercise.
24## A Caesar Cipher In Hoon
26Below is a generator that performs a Caesar cipher on a tape. This example
27isn't the most compact implementation of such a cipher in Hoon, but it
28demonstrates important principles that more laconic code would not. Save it as
29`caesar.hoon` in your `/gen` directory.
31```hoon
32!:
33|= [msg=tape key=@ud]
34=<
35=. msg (cass msg)
36:- (shift msg key)
37(unshift msg key)
38|%
39++ alpha "abcdefghijklmnopqrstuvwxyz"
40++ shift
41 |= [message=tape key=@ud]
42 (operate message key (encoder key))
43++ unshift
44 |= [message=tape key=@ud]
45 (operate message key (decoder key))
46++ operate
47 |= [message=tape key=@ud encoder=(map @t @t)]
48 ^- tape
49 %+ turn message
50 |= a=@t
51 (~(got by encoder) a)
52++ encoder
53 |= [key=@ud]
54 =/ keytape=tape (rott alpha key)
55 (coder alpha keytape)
56++ decoder
57 |= [key=@ud]
58 =/ keytape=tape (rott alpha key)
59 (coder keytape alpha)
60++ coder
61 |= [a=tape b=tape]
62 (~(put by (zipper a b)) ' ' ' ')
63++ zipper
64 |= [a=tape b=tape]
65 ^- (map @t @t)
66 =| chart=(map @t @t)
67 ?. =((lent a) (lent b))
68 ~| %uneven-lengths !!
69 |-
70 ?: |(?=(~ a) ?=(~ b))
71 chart
72 $(chart (~(put by chart) i.a i.b), a t.a, b t.b)
73++ rott
74 |= [m=tape n=@ud]
75 =/ length=@ud (lent m)
76 =+ s=(trim (mod n length) m)
77 (weld q.s p.s)
78--
79```
81This generator takes two arguments: a `tape`, which is your plaintext message,
82and an unsigned integer, which is the shift-value of the cipher. It produces
83a cell of two `tapes`: one that has been shifted right by the value, and another
84that has been shifted left. It also converts any uppercase input into lowercase.
86Try it out in the Dojo:
88```
89> +caesar ["test" 2]
90["vguv" "rcqr"]
92> +caesar ["test" 26]
93["test" "test"]
95> +caesar ["test" 28]
96["vguv" "rcqr"]
98> +caesar ["test" 104]
99["test" "test"]
101> +caesar ["tESt" 2]
102["vguv" "rcqr"]
104> +caesar ["test!" 2]
105nest-fail
106```
108### Examining Our Code
110Let's examine our `caesar.hoon` code piece by piece. We won't necessarily go
111in written order; instead, we'll cover code in the intuitive order of the
112program. For each chunk that we cover, try to read and understand the code
113itself before reading the explanation.
115```hoon
116!:
117|= [msg=tape key=@ud]
118=+ ^= caesar
119 |%
120```
122The `!:` in the first line of the above code enables a full stack trace in the
123event of an error.
125`|= [msg=tape key=@ud]` creates a gate that takes a cell. The head of this cell
126is a `tape`, which is a string type that's a list of `cord`s. Tapes are represented
127as text surrounded by double-quotes, such as this: `"a tape"`. We give this input
128tape the face `msg`. The tail of our cell is a `@ud` -- an unsigned decimal atom
129-- that we give the face `key`.
131`=<` is the rune that evaluates its first child expression with respect to its
132second child expression as the subject. In this case, we evaluate the
133expressions in the code chunk below against the core declared later, which
134allows us reference the core's contained arms before they are defined. Without
135`=<`, we would need to put the code chunk below at the bottom of our program.
137```hoon
138=. msg (cass msg)
139:- (shift msg key)
140(unshift msg key)
141```
143`=. msg (cass msg)` changes the input string `msg` to lowercases. `=.` changes
144the leg of the subject to something else. In our case, the leg to be changed is
145`msg`, and the thing to replace it is `(cass msg)`. `cass` is a standard-library
146gate that converts uppercase letters to lowercase.
148`:- (shift msg key)` and `(unshift msg key)` simply composes a
149cell of a right-shifted cipher and a left-shifted cell. This is the final output
150of our generator.
152```hoon
153 ++ rott
154 |= [m=tape n=@ud]
155 =/ length=@ud (lent m)
156 =+ s=(trim (mod n length) m)
157 (weld q.s p.s)
158```
160The `rott` arm takes takes a specified number of characters off of a tape and
161puts them on the end of the tape.
163`|= [m=tape n=@ud]` creates a gate that takes two arguments: `m`, a `tape`,
164and `n`, a `@ud`.
166`=/ length=@ud (lent m)` stores the length of `m` to make the following
167code a little clearer.
169`trim` is a a gate from the standard library that splits a tape at into two
170parts at a specified position. So `=+ s=(trim (mod n length) m)` splits the
171tape `m` into two parts, `p` and `q`, and stores it in `s`. We call the modulus
172operation `mod` to make sure that we split our `tape` at the correct place, even
173if `n` is larger than `length`.
175`(weld q.s p.s)` uses `weld`, which combines two strings into one. In this
176instance, we are switching the two parts: the second part `q.s` is welded to the
177front, and the first part `p.s` is welded to the back.
179```hoon
180 ++ zipper
181 |= [a=tape b=tape]
182 ^- (map @t @t)
183 =| chart=(map @t @t)
184 ?. =((lent a) (lent b))
185 ~| %uneven-lengths !!
186 |-
187 ?: |(?=(~ a) ?=(~ b))
188 chart
189 $(chart (~(put by chart) i.a i.b), a t.a, b t.b)
190```
192The `zipper` arm takes two tapes and creates a `map` out of them -- an
193an association between their elements.
195So then if `tapes` are easier to manipulate, why then are we producing `cords`?
196In this case what we are going to to be doing is mapping a single element of a `
197tape` to another element of a `tape`, which as we have established as being a
198`cord`. This will simplify our use of this method and we don't need to
199manipulate the keys or values, simply look them up.
201`|= [a=tape b=tape]` builds a gate that takes two tapes, `a` and `b`, as its
202sample.
204`^- (map @t @t)` casts the gate to a `map` with a `cord` key and a `cord`
205value. A `map` is a type equivalent to a dictionary in other languages: it's a
206data structure that associates a key with a value. If, for example, we wanted
207to have an association between `a` and 1 and `b` and 2, we could use a `map`.
209`=| chart=(map @t @t)` adds a noun to the subject with the default value of
210the `(map @t @t)` type, and gives that noun the face `chart`.
212`?. =((lent a) (lent b))` checks if the two tapes are the same length. If not,
213the program crashes.
215`|-` creates a trap, a gate that is called immediately.
217`?: |(?=(~ a) ?=(~ b))` checks if either tape is empty. If this is true, we
218the program is finished and can return `chart`, the the `map` that we have been
219creating.
221If the above test finds that its condition to be false, we trigger a recursion
222that constructs our `map`: `$(chart (~(put by chart) i.a i.b), a t.a, b t.b)`.
223This code recursively adds an entry in our `map` where the head of the tape `a`
224maps to the value of the head of tape `b` with `~(put by chart)`, our calling
225of the `put` arm of the `by` map-engine core. The recursion also "consumes"
226those heads with every iteration by changing `a` and `b` to their tails.
228Perhaps now you can understand why this arm is named `zipper`. It's putting two
229tapes together by matching pieces from each side, something akin to a jacket zipper.
231We have three related arms to look at next, `coder`, `encoder`, and
232`decoder`. `coder` is the foundation of the other two, so we'll look at it
233first.
235```hoon
236 ++ coder
237 |= [a=tape b=tape]
238 (~(put by (zipper a b)) ' ' ' ')
239```
241`|= [a=tape b=tape]` creates a gate that takes two `tapes`.
243We use `put by` on the next line, giving it a `map` produced by the `zipper`
244arm that we created before. This adds an entry to the map where the space
245character (called `ace`) simply maps to itself. This is done to simplify
246the handling of spaces in `tapes` we want to encode, since we don't want to
247shift them.
249```hoon
250 ++ encoder
251 |= [key=@ud]
252 =/ keytape=tape (rott alpha key)
253 (coder alpha keytape)
254 ++ decoder
255 |= [key=@ud]
256 =/ keytape=tape (rott alpha key)
257 (coder keytape alpha)
258```
260`encoder` and `decoder` are implemented in terms of the `coder` arm. These gates
261are essentially identical, with the arguments reversed. They simplify the two
262common transactions you want to do in this program: producing `maps` that we can
263use to encode and decode messages.
265In both cases, we create a gate that accepts a `@ud` named `key`.
267`=/ keytape=tape (rott alpha key)` creates a `keytape` noun by calling `rott`
268on `alpha` our `key` input. `alpha` is our arm which contains a `tape` of the
269entire alphabet.
271`(coder alpha keytape)`, for `encoder`, and `(coder keytape alpha)`, for
272`decoder`, produce a `map` that has the first argument as the keys and the
273second as the values.
275If our two inputs to `coder` were `"abcdefghijklmnopqrstuvwxyz"` and
276`"bcdefghijklmnopqrstuvwxyza"` We would get a `map` where `'a'` maps to `'b'`,
277`'b'` to `'c'` and so on. By doing this we can produce a `map` that gives us a
278translation between the alphabet and our shifted alphabet, or vice versa.
280Still with us? Good. We are finally about to use all the stuff that we've
281walked through.
283```hoon
284 ++ shift
285 |= [message=tape key=@ud]
286 (operate message key (encoder key))
287 ++ unshift
288 |= [message=tape key=@ud]
289 (operate message key (decoder key))
290```
292Both `shift` and `unshift` take two arguments: our `message`, the `tape` that we
293want to manipulate; and our `key`, the value that we want to shift our message
294by.
296`shift` is for encoding, and `unshift` is for decoding. Thus, `shift` calls the
297`operate` arm with `(operate message key (encoder key))`, and `unshift` makes
298that call with `(operate message key (decoder key))`. These both produce the
299final output of the core, to be called in the form of `(shift msg key)`
300and `(unshift msg key)` at the bottom of the program.
302```hoon
303++ operate
304 |= [message=tape key=@ud encoder=(map @t @t)]
305 ^- tape
306 %+ turn message
307 |= a=@t
308 (~(got by encoder) a)
309```
311`operate` produces a `tape`. The `%+` rune allows us to pull an arm
312with a pair sample. The arm we are going to pull is `turn`. This arm
313takes two arguments, a `list` and a `gate` to apply to each element of the
314`list`.
316If we then give our arm Caesar's famous statement, and get our left- and
317right-ciphers.
319```
320> +caesar ["i came i saw i conquered" 4]
321["m geqi m wea m gsruyivih" "e ywia e ows e ykjmqanaz"]
322```
324Now, to decode, we can put either of our ciphers in with the appropriate key and
325look for the legible result.
327```
328> +caesar ["m geqi m wea m gsruyivih" 4]
329["q kium q aie q kwvycmzml" "i came i saw i conquered"]
331> +caesar ["e ywia e ows e ykjmqanaz" 4]
332["i came i saw i conquered" "a usew a kso a ugfimwjwv"]
333```
335### Exercises
3371. Take the example generator and modify it to add a second layer of shifts.
3392. Extend the example generator to allow for use of characters other than a-z.
3413. Build a gate that can take a Caesar shifted `tape` and produce
342possible unshifted `tapes`.
3444. Modify the example generator into a `%say` generator.
346### [Next Up: Reading -- Doors](../doors)