1.7.1 Walkthrough: Caesar Cipher
A Caesar cipher is a very simple way to obfuscate a message. The technique
takes a string and swaps out each component letter with another letter that is
a specified number of positions up or down in the alphabet. For example, with a
"right-shift" of 1,
a would become
j would become
wrap around back to
Consider the message below, and the cipher that results when we Caesar-shift the message to the right by 1.
Plaintext message: "do not give way to anger" Right-shifted cipher: "ep opu hjwf xbz up bohfs"
Note that the Caesar cipher is completely unsuitable for actually securing information. Implementing it in a program is just a fun exercise.
A Caesar Cipher In Hoon
Below is a generator that performs a Caesar cipher on a tape. This example
isn't the most compact implementation of such a cipher in Hoon, but it
demonstrates important principles that more laconic code would not. Save it as
caesar.hoon in your
!: |= [msg=tape steps=@ud] =< =. msg (cass msg) :- (shift msg steps) (unshift msg steps) |% ++ alpha "abcdefghijklmnopqrstuvwxyz" ++ shift |= [message=tape shift-steps=@ud] ^- tape (operate message (encoder shift-steps)) ++ unshift |= [message=tape shift-steps=@ud] ^- tape (operate message (decoder shift-steps)) ++ encoder |= [steps=@ud] ^- (map @t @t) =/ value-tape=tape (rotation alpha steps) (space-adder alpha value-tape) ++ decoder |= [steps=@ud] ^- (map @t @t) =/ value-tape=tape (rotation alpha steps) (space-adder value-tape alpha) ++ operate |= [message=tape shift-map=(map @t @t)] ^- tape %+ turn message |= a=@t (~(got by shift-map) a) ++ space-adder |= [key-position=tape value-result=tape] ^- (map @t @t) (~(put by (map-maker key-position value-result)) ' ' ' ') ++ map-maker |= [key-position=tape value-result=tape] ^- (map @t @t) =| chart=(map @t @t) ?. =((lent key-position) (lent value-result)) ~| %uneven-lengths !! |- ?: |(?=(~ key-position) ?=(~ value-result)) chart $(chart (~(put by chart) i.key-position i.value-result), key-position t.key-position, value-result t.value-result) ++ rotation |= [my-alphabet=tape my-steps=@ud] =/ length=@ud (lent my-alphabet) =+ (trim (mod my-steps length) my-alphabet) (weld q p) --
This generator takes two arguments: a
tape, which is your plaintext message,
and an unsigned integer, which is the shift-value of the cipher. It produces
a cell of two
tapes: one that has been shifted right by the value, and another
that has been shifted left. It also converts any uppercase input into lowercase.
Try it out in the Dojo:
> +caesar ["abcdef" 1] ["bcdefg" "zabcde"] > +caesar ["test" 2] ["vguv" "rcqr"] > +caesar ["test" 26] ["test" "test"] > +caesar ["test" 28] ["vguv" "rcqr"] > +caesar ["test" 104] ["test" "test"] > +caesar ["tESt" 2] ["vguv" "rcqr"] > +caesar ["test!" 2] nest-fail
Examining Our Code
Let's examine our
caesar.hoon code piece by piece. We won't necessarily go
in written order; instead, we'll cover code in the intuitive order of the
program. For each chunk that we cover, try to read and understand the code
itself before reading the explanation.
!: |= [msg=tape steps=@ud] =<
!: in the first line of the above code enables a full stack trace in the
event of an error.
|= [msg=tape steps=@ud] creates a gate that takes a cell. The head of this cell
tape, which is a string type that's a list of
cords. Tapes are represented
as text surrounded by double-quotes, such as this:
"a tape". We give this input
tape the face
msg. The tail of our cell is a
@ud -- an unsigned decimal atom
-- that we give the face
=< is the rune that evaluates its first child expression with respect to its
second child expression as the subject. In this case, we evaluate the
expressions in the code chunk below against the core declared later, which
allows us reference the core's contained arms before they are defined. Without
=<, we would need to put the code chunk below at the bottom of our program. In Hoon, as previously
stated, we always want to keep the longer code towards the bottom of our programs -
=< helps us do that.
=. msg (cass msg) :- (shift msg steps) (unshift msg steps)
=. msg (cass msg) changes the input string
msg to lowercases.
the leg of the subject to something else. In our case, the leg to be changed is
msg, and the thing to replace it is
cass is a standard-library
gate that converts uppercase letters to lowercase.
:- (shift msg steps) and
(unshift msg steps) simply composes a
cell of a right-shifted cipher and a left-shifted cipher of our original message.
We will see how this is done using the core described below, but this is the final
output of our generator.
|% creates a
core, the second child of
=<. Everything after
|% is part of that
core, and will be used as the subject of the first child of
above. The various parts, or
arms, of the
core are denoted by
++ beneath it, for
++ rotation |= [my-alphabet=tape my-steps=@ud] =/ length=@ud (lent my-alphabet) =+ (trim (mod my-steps length) my-alphabet) (weld q p)
rotation arm takes takes a specified number of characters off of a tape and
puts them on the end of the tape. We're going to use this to create our shifted alphabet,
based on the number of
steps given as an argument to our gate.
|= [my-alphabet=tape my-steps=@ud] creates a gate that takes two arguments:
=/ length=@ud (lent my-alphabet) stores the length of
my-alphabet to make the following
code a little clearer.
trim is a a gate from the standard library that splits a tape at into two
parts at a specified position. So
=+ (trim (mod my-steps length) my-alphabet) splits the
my-alphabet into two parts,
q, which are now directly available in the subject.
We call the modulus operation
mod to make sure that the point at which we split our
a valid point inside of
my-alphabet even if
my-steps is greater than
length, the length of
my-alphabet. Try trim in the dojo:
> (trim 2 "abcdefg") [p="ab" q="cdefg"] > (trim 4 "yourbeard") [p="your" q="beard"]
(weld q p) uses
weld, which combines two strings into one. Remember that
trim has given us
a split version of
p being the front half that was split off of
q being the back half. Here we are welding the two parts back together, but in reverse order:
the second part
q is welded to the front, and the first part
p is welded to the back.
++ map-maker |= [key-position=tape value-result=tape] ^- (map @t @t) =| chart=(map @t @t) ?. =((lent key-position) (lent value-result)) ~| %uneven-lengths !! |- ?: |(?=(~ key-position) ?=(~ value-result)) chart $(chart (~(put by chart) i.key-position i.value-result), key-position t.key-position, value-result t.value-result)
map-maker arm, as the name implies, takes two tapes and creates a
map out of them.
map is a type equivalent to a dictionary in other languages: it's a data structure that
associates a key with a value. If, for example, we wanted to have an association
a and 1 and
b and 2, we could use a
|= [a=tape b=tape] builds a gate that takes two tapes,
b, as its
^- (map @t @t) casts the gate to a
map with a
@t) key and a
You might wonder, if our gate in this arm takes
tapes, why then are we producing
a map of
cord keys and values?
As we discussed earlier, a
tape is a list of
cords. In this case what we are going to do
is map a single element of a
tape (either our alphabet or shifted-alphabet) to an element of
tape (either our shifted-alphabet or our alphabet). This pair will therefore be
a pair of
cords. When we go to use this
map to convert our incoming
msg, we will take
each element (
cord) of our
tape, use it as a
key when accessing our
map and get
value from that position in the
map. This is how we're going to encode
or decode our
=| chart=(map @t @t) adds a noun to the subject with the default value of
(map @t @t) type, and gives that noun the face
?. =((lent key-position) (lent value-result)) checks if the two
tapes are the same length. If not,
the program crashes with an error message of
|~ %uneven-lengths !!.
If the two
tapes are of the same length, we continue on to create a trap.
|- creates a trap, a gate that is called immediately.
?: |(?=(~ key-position) ?=(~ value-result)) checks if either
tape is empty. If this is true, the
map-maker arm is finished and can return
chart, the the
map that we have been
If the above test finds that the
tapes are not empty, we trigger a recursion
that constructs our
$(chart (~(put by chart) i.a i.b), a t.a, b t.b).
This code recursively adds an entry in our
map where the head of the
maps to the value of the head of
~(put by chart), our calling
put arm of the
by map-engine core (note that
~(<wing> <door> <sample>) is
a shorthand for
%~ <wing> <door> <sample> (see the Calls % ('cen')
documentation for more information). The recursion also "consumes"
those heads with every iteration by changing
b to their tails using
a t.a, b t.b.
We have three related arms to look at next,
space-adder is required for the other two, so we'll look at it
++ space-adder |= [key-position=tape value-result=tape] ^- (map @t @t) (~(put by (map-maker key-position value-result)) ' ' ' ')
|= [key-position=tape value-result=tape] creates a gate that takes two
We use the
put arm of the
by core on the next line, giving it a
map-maker arm that we created before as its sample. This adds an entry to the
map where the space character (called
ace) simply maps to itself. This is done to
simplify the handling of spaces in
tapes we want to encode, since we don't want to
++ encoder |= [steps=@ud] ^- (map @t @t) =/ value-tape=tape (rotation alpha steps) (space-adder alpha value-tape) ++ decoder |= [steps=@ud] ^- (map @t @t) =/ key-tape=tape (rotation alpha steps) (space-adder key-tape alpha)
decoder utilize the
space-adder arms. These gates
are essentially identical, with the arguments passed to
rotation reversed. They
simplify the two common transactions you want to do in this program: producing
that we can use to encode and decode messages.
In both cases, we create a gate that accepts a
=/ value-tape=tape (rotation alpha steps) creates a
value-tape noun by calling
alpha is our arm which contains a
tape of the entire alphabet. The
value-tape will be the list of
values in our
=/ key-tape (rotation alpha steps) does the same work, but when passed to
it will be the list of
keys in our
(space-adder alpha value-tape), for
(space-adder key-tape alpha), for
decoder, produce a
map that has the first argument as the keys and the
second as the values.
If our two inputs to
"bcdefghijklmnopqrstuvwxyza", we would get a
'a' maps to
'c' and so on. By doing this we can produce a
map that gives us a
translation between the alphabet and our shifted alphabet, or vice versa.
Still with us? Good. We are finally about to use all the stuff that we've walked through.
++ shift |= [message=tape shift-steps=@ud] ^- tape (operate message (encoder shift-steps)) ++ unshift |= [message=tape shift-steps=@ud] ^- tape (operate message (decoder shift-steps))
unshift take two arguments: our
tape that we
want to manipulate; and our
shift-steps, the number of positions of the alphabet
by which we want to shift our message.
shift is for encoding, and
unshift is for decoding. Thus,
shift calls the
operate arm with
(operate message (encoder shift-steps)), and
that call with
(operate message (decoder shift-steps)). These both produce the
final output of the core, to be called in the form of
(shift msg steps)
(unshift msg steps) in the cell being created at the beginning of our code.
++ operate |= [message=tape shift-map=(map @t @t)] ^- tape %+ turn message |= a=@t (~(got by shift-map) a)
operate produces a
%+ rune allows us to pull an arm
with a pair sample. The arm we are going to pull is
turn. This arm
takes two arguments, a
list and a
gate to apply to each element of the
In this case, the
gate we are applying to our
message uses the
by door with our
shift-map as the sample (which is either the standard alphabet
for keys, and the shifted alphabet for values, or the other way, depending on
whether we are encoding or decoding) to look up each
cord in our
message, one by one
and replace it with the
value from our
map (either the encoded or decoded version).
If we then give our arm Caesar's famous statement, and get our left- and right-ciphers.
> +caesar ["i came i saw i conquered" 4] ["m geqi m wea m gsruyivih" "e ywia e ows e ykjmqanaz"]
Now, to decode, we can put either of our ciphers in with the appropriate key and look for the legible result.
> +caesar ["m geqi m wea m gsruyivih" 4] ["q kium q aie q kwvycmzml" "i came i saw i conquered"] > +caesar ["e ywia e ows e ykjmqanaz" 4] ["i came i saw i conquered" "a usew a kso a ugfimwjwv"]
Take the example generator and modify it to add a second layer of shifts.
Extend the example generator to allow for use of characters other than a-z. Make it shift the new characters independently of the alpha characters, such that punctuation is only encoded as other punctuation marks.
Build a gate that can take a Caesar shifted
tapeand produce all possible unshifted
Modify the example generator into a