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;; hill.lisp - A very bad implementation of a hill cipher along with some
;; unnessesary, insecure PRNG key stuff.
;;
;; This file is free software under the terms of the GPL3 license. You can find
;; a copy of the license at: https://www.gnu.org/licenses/gpl-3.0.en.html
;; PRNG subroutines
(defparameter *system-rng-stream*
(open "/dev/random" :element-type '(unsigned-byte 8)))
(defun number-bits (num)
"Return the number of bits in NUM."
(ceiling (log num 2)))
(defun get-random (&key (size 8) (rng-stream *system-rng-stream*))
"Read SIZE random bytes from the systems high-quality random source."
(let ((read-buf (make-array size)))
(read-sequence read-buf rng-stream)
(loop with out-val = 0
for part across read-buf do
(setq out-val (+ (ash out-val 8) part))
finally (return out-val))))
(defun xorshift*64 (seed)
"Generate the next number in the xorshift* sequence starting or continuing
from SEED. That is, SEED should either be an initial, non-zero seed or the last
number generated in the sequence."
(setq seed (logxor seed (ash seed -12))
seed (logxor seed (ash seed 25))
seed (logxor seed (ash seed -27)))
;; #x2545F4914F6CDD1DULL
(logand (* seed 2685821657736338717)
#xFFFFFFFFFFFFFFFF))
(defun rand-clamp (num &key (bits 64) (min 0 has-min-p)
(max (1- (expt 2 bits)) has-max-p))
"Clamp the randomly generated number NUM to between [MIN, MAX]. The random
numbers is assumed to be between 0 and 2^BITS - 1."
(if (or has-min-p has-max-p)
(+ (* (- max min) (/ num (1- (expt 2 bits)))) min)
num))
(defclass xorshift*64-stream ()
((state :initarg :seed
:initform 1
:documentation "The last generated number. If no number has yet been
generated, this is the seed."))
(:documentation "A stream of random numbers generated and xorshift*64
algorithm."))
(defun make-xorshift* (&key (seed (get-random)) (bits 64))
(case bits
(64 (make-instance 'xorshift*64-stream :seed seed))
(t (error "Invalid prandom number size: ~d" bits))))
(defmethod next-int ((stream xorshift*64-stream) &key (max #xFFFFFFFFFFFFFFFF)
(min 0))
"Get the next random integer between MIN and MAX from STREAM."
(with-slots (state) stream
(setf state (xorshift*64 state))
(floor (rand-clamp state :bits 64 :max max :min min))))
(defparameter *default-rng* (make-xorshift*)
"The default RNG source to use when generating matrices.")
;; Matrix subroutines
(defun mat-minor (transpose-mat i j)
"Find the minor of MAT for I and J."
(destructuring-bind (height width)
(array-dimensions transpose-mat)
(let ((minor (make-array (list (1- height)
(1- width)))))
(dotimes (row height minor)
(dotimes (col width)
(unless (or (= row i)
(= col j))
(let ((out-row (if (> row i)
(1- row)
row))
(out-col (if (> col j)
(1- col)
col)))
(setf (aref minor out-row out-col) (aref transpose-mat row col)))))))))
(defun cofactor-sgn (i j)
"Return the sign of the cofactor at I and J."
(expt -1 (+ i j)))
(defun cofactor (mat i j)
"Find the cofactor for I and J in MAT."
(* (cofactor-sgn i j) (det (mat-minor mat i j))))
(defun first-column-cofactors (mat)
"Find the cofactors for the first column of MAT."
(let* ((height (array-dimension mat 0))
(out-arr (make-array height)))
(dotimes (i height out-arr)
(setf (aref out-arr i) (cofactor mat i 0)))))
(defun det2x2 (mat)
"Find the determinate of a 2x2 matrix MAT."
(let ((a (aref mat 0 0))
(b (aref mat 0 1))
(c (aref mat 1 0))
(d (aref mat 1 1)))
(- (* a d) (* b c))))
(defun det (mat &key first-column-cofactors)
"Find the determinant of MAT. If the cofactors for the first column have
already been calculated, they can be supplied in FIRST-COLUMN-COFACTORS."
(destructuring-bind (height width)
(array-dimensions mat)
(if (and (= height 2)
(= width 2))
(det2x2 mat)
(loop for i below height
when first-column-cofactors
summing (* (aref mat i 0) (aref first-column-cofactors i))
else
summing (* (aref mat i 0) (cofactor mat i 0))))))
(defun map-mat (function mat)
"Return a new matrix of the same dimensions as MAT, with each element being
the result of applying FUNCTION to each index of MAT. FUNCTION is passed two
values, (i j), where i and j are the row and column of the element."
(destructuring-bind (height width)
(array-dimensions mat)
(let ((out-mat (make-array (list height width))))
(dotimes (row height out-mat)
(dotimes (col width)
(setf (aref out-mat row col)
(funcall function row col)))))))
(defun extended-gcd (n1 n2)
"Return the greatest common denominator of N1 and N2. As a second value,
return a cons of (x . y) such char x * N1 + y * N2 = GCD."
(if (zerop n1)
(values n2 (cons 0 1))
(multiple-value-bind (div rem) (floor n2 n1)
(destructuring-bind (gcd (x . y))
(multiple-value-list (extended-gcd rem n1))
(values gcd (cons (- y (* div x)) x))))))
(defun modular-multiplicative-inverse (n m)
"Find the modular multiplicative inverse of N with respect to M. That is, some
integer i such that (N * i) mod M = 1."
(destructuring-bind (gcd (x . y))
(multiple-value-list (extended-gcd n m))
(declare (ignorable y))
(unless (= 1 gcd)
(error "N and M must be coprime. N: ~d, M: ~d" n m))
(+ x m)))
(defun modular-inverse-det (mat modulo &key first-column-cofactors)
"Calculate the inverse determinant of MAT under MODULO. If MODULO is nil, this
is just 1/det."
(let ((det (det mat :first-column-cofactors first-column-cofactors)))
(if modulo
(modular-multiplicative-inverse det modulo)
(/ det))))
(defun invert-2x2-mat (mat &key modulo)
"Invert the 2x2 matrix MAT."
(let ((a (aref mat 0 0))
(b (aref mat 0 1))
(c (aref mat 1 0))
(d (aref mat 1 1))
(ood (modular-inverse-det mat modulo)))
(make-array '(2 2)
:initial-contents (list (list (* ood d) (* ood (- b)))
(list (* ood (- c)) (* ood a))))))
(defun invert-mat (mat &key modulo)
"Invert MAT. This naively assumes that MAT is not singular."
(destructuring-bind (height width)
(array-dimensions mat)
(if (and (= width 2)
(= height 2))
(invert-2x2-mat mat :modulo modulo)
(let* ((first-column-cofactors (first-column-cofactors mat))
(one-over-det (modular-inverse-det mat modulo
:first-column-cofactors
first-column-cofactors)))
(map-mat (lambda (i j)
;; this calculates 1/det * adjugate[i][j]
(* one-over-det
(if (and first-column-cofactors (zerop i))
(aref first-column-cofactors j)
(cofactor mat j i))))
mat)))))
(defun transpose-mat (mat)
"Transpose MAT."
(map-mat (lambda (i j)
(aref mat j i))
mat))
(defun dot-row-col (mat1 mat2 row col)
"Take the dot (scalar) product of ROW of MAT1 and COL of MAT2."
(let ((sum 0))
(dotimes (n (array-dimension mat2 0) sum)
(setq sum (+ sum (* (aref mat1 row n)
(aref mat2 n col)))))))
(defun *mm (mat1 mat2 &key modulo)
"Multiply MAT1 by MAT2. This naively assumes that these matrices can be
multiplied without issue. The result will be taken under MODULO, if it is
non-nil."
(let* ((width (array-dimension mat1 0))
(height (array-dimension mat2 1))
(out-mat (make-array (list height width))))
(dotimes (i height out-mat)
(dotimes (j width)
(let ((dot (dot-row-col mat1 mat2 i j)))
(setf (aref out-mat i j)
(if modulo
(mod dot modulo)
dot)))))))
(defun *mv (mat vec &key modulo)
"Multiply MAT by VEC. This naively assumes that these can be multiplied
without issue. The result will be taken under MODULO, if it is non-nil."
(let* ((width (array-dimension mat 1))
(height (array-dimension mat 0))
(out-vec (make-array height)))
(dotimes (row height out-vec)
(setf (aref out-vec row)
(loop for col below width
summing (* (aref vec col) (aref mat row col)) into sum
finally (return (if modulo
(mod sum modulo)
sum)))))))
(defun generate-matrix (width height &key (rng *default-rng*) max)
"Generate a random matrix of size WIDTH x HEIGHT. Use RNG to get the random
data for this matrix."
(map-mat (lambda (i j)
(declare (ignorable i j))
(if max
(next-int rng :max max)
(next-int rng)))
(make-array (list height width))))
(defun generate-invertible-matrix (width height &key (rng *default-rng*) max)
"Generate a random invertible matrix of size WIDTH x HEIGHT. Use RNG to get
the random data for this matrix. This generates a strictly diagonally dominant
matrix."
(let ((rand-mat (generate-matrix width height :rng rng :max max)))
(dotimes (row height rand-mat)
(let ((sum 0))
(dotimes (col width)
(setq sum (+ sum (abs (aref rand-mat row col)))))
(setf (aref rand-mat row row) sum)))))
;; Base64 subroutines
(defparameter +base64-alphabet+
"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"
"Lookup table for base64 encode.")
(defparameter +inverse-base64-alphabet+
(loop with alph = (make-array 123 :initial-element 0)
for i below (length +base64-alphabet+)
for char = (aref +base64-alphabet+ i)
do (setf (aref alph (char-code char)) i)
finally (return alph))
"Inverse lookup table for base64 decode.")
(defun base64-encode-block (b1 &optional b2 b3)
"Base64 encode B1, B2, and B3, each of which should be a single byte. The
result of this function is a list of the 4 encoded characters."
;; allow B2 and B3 to be nil, so we can't just check if they where passed, we
;; need to know if they where nil when the function was called
(let ((has-b2-p b2)
(has-b3-p b3))
(unless b2
(setq b2 0))
(unless b3
(setq b3 0))
(let ((e1 (ash (logand b1 #b11111100) -2))
(e2 (logior (ash (logand b1 #b11) 4)
(ash (logand b2 #b11110000) -4)))
(e3 (logior (ash (logand b2 #b1111) 2)
(ash (logand b3 #b11000000) -6)))
(e4 (logand b3 #b111111)))
(cond
((and has-b2-p has-b3-p)
(list (aref +base64-alphabet+ e1)
(aref +base64-alphabet+ e2)
(aref +base64-alphabet+ e3)
(aref +base64-alphabet+ e4)))
(has-b2-p
(list (aref +base64-alphabet+ e1)
(aref +base64-alphabet+ e2)
(aref +base64-alphabet+ e3)
#\=))
(t
(list (aref +base64-alphabet+ e1)
(aref +base64-alphabet+ e2)
#\= #\=))))))
(defun base64-encode (data)
"Encode DATA, a vector of numbers, as base64."
(loop with output = ()
for i upfrom 0 by 3 below (- (length data) 2)
do (setf output (nconc (nreverse (base64-encode-block
(aref data i)
(aref data (+ i 1))
(aref data (+ i 2))))
output))
finally
(return
(coerce (if (< i (length data))
(let ((b1 (aref data i))
(b2 (when (< (1+ i) (length data))
(aref data (1+ i)))))
(nreverse (nconc (nreverse
(base64-encode-block b1 b2))
output)))
(nreverse output))
'string))))
(defun base64-decode-block (e1 e2 e3 e4)
"Base64 decode E1, E2, E3, and E4, each of which is a single character. The
result of this function is a list of 3 bytes."
(let ((i1 (aref +inverse-base64-alphabet+ (char-code e1)))
(i2 (aref +inverse-base64-alphabet+ (char-code e2)))
(i3 (aref +inverse-base64-alphabet+ (char-code e3)))
(i4 (aref +inverse-base64-alphabet+ (char-code e4))))
(list (logior (ash i1 2)
(ash (logand i2 #b110000) -4))
(unless (eq e3 #\=)
(logior (ash (logand i2 #b1111) 4)
(ash (logand i3 #b111100) -2)))
(unless (eq e4 #\=)
(logior (ash (logand i3 #b11) 6)
i4)))))
(defun base64-decode (data)
"Decode DATA, a string, as base64."
(coerce (loop for i upfrom 0 by 4 below (length data)
append (delete-if 'null
(base64-decode-block (aref data i)
(aref data (+ i 1))
(aref data (+ i 2))
(aref data (+ i 3)))))
'vector))
;; Hill subroutines
(defun nth-hill-block (plain n &key (size 4))
"Get the Nth hill block in PLAIN. If there are not enough characters in PLAIN,
pad the block with zeros. Each block is SIZE characters."
(let* ((start (* size n))
(end (+ start size)))
(when (< (length plain) end)
(setq end (+ start (- (length plain) start))))
(cond
((> start (length plain))
(make-array size :initial-element 0))
((>= end (length plain))
(loop with out-vec = (make-array size :initial-element 0 :fill-pointer 0)
for elem across (subseq plain start (length plain)) do
(vector-push elem out-vec)
finally
(setf (fill-pointer out-vec) size)
(return out-vec)))
(t
(subseq plain start end)))))
(defun hill-block-count (plain &key (size 4))
"Return the number of hill blocks in PLAIN."
(ceiling (length plain) size))
(defmacro do-hill-blocks ((var plain &optional retval) (&key (size 4))
&body body)
"Evaluate BODY once for each hill cipher block in PLAIN, with VAR bound to
that block."
(let ((i-var (gensym))
(plain-var (gensym)))
`(let ((,plain-var ,plain))
(dotimes (,i-var (hill-block-count ,plain-var :size ,size) ,retval)
(let ((,var (nth-hill-block ,plain-var ,i-var :size ,size)))
,@body)))))
(defun make-hill-matrix (key &key (size 4))
"Get the hill cipher matrix for KEY and block size SIZE."
(let ((rng (make-xorshift* :seed key)))
(generate-invertible-matrix size size :rng rng :max 128)))
(defun hill-process (data mat size dict-size)
"Perform hill encryption or decryption on DATA. Each block is SIZE bytes. MAT
is taken to be the key matrix (or its inverse). DICT-SIZE is the modulus."
(let ((processed (make-array 0)))
(do-hill-blocks (bl data (map 'vector (lambda (elem)
(mod elem dict-size))
processed))
(:size size)
(setq processed (concatenate 'vector processed
(*mv mat bl))))))
(defun hill-encrypt (plain key &key (size 4) (dict-size 251))
"Encrypt PLAIN using a hill cipher, using KEY as the secret and SIZE as the
block size. DICT-SIZE is the largest character code in PLAIN."
(hill-process (map 'vector 'char-code plain)
(make-hill-matrix key :size size)
size dict-size))
(defun make-inverse-hill-matrix (key &key (size 4) (dict-size 251))
"Create an inverse hill matrix for KEY. SIZE and DICT-SIZE are as they are to
`hill-decrypt'."
(invert-mat (make-hill-matrix key :size size) :modulo dict-size))
(defun hill-remove-padding (plain-vec)
"Remove trailing null bytes from PLAIN-VEC."
(loop for i downfrom (1- (length plain-vec))
while (and (>= i 0) (eq (aref plain-vec i) #\Nul))
finally (return (subseq plain-vec 0 (1+ i)))))
(defun hill-decrypt (cipher key &key (size 4) (dict-size 251))
"Perform the inverse operation of `hill-encrypt', restoring the plaintext
of CIPHER that was encrypted using KEY with a block size of SIZE. DICT-SIZE must
be the same value originally used to encrypt the text."
(coerce (hill-remove-padding
(map 'vector 'code-char
(hill-process cipher
(make-inverse-hill-matrix key :size size
:dict-size dict-size)
size dict-size)))
'string))
;; Local Variables:
;; jinx-local-words: "adjugate cofactor cofactors det plaintext prandom unnessesary xorshift"
;; End:

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;; shift-affine.lisp - Some simple subroutines for working with affine and shift
;; ciphers.
;;
;; This file is free software under the terms of the GPL3 license. You can find
;; a copy of the license at: https://www.gnu.org/licenses/gpl-3.0.en.html
(defpackage shift-affine
(:use :cl)
(:export
:char-letter :letter-char :affine-encrypt :extended-gcd
:modular-multiplicative-inverse :affine-encrypt :affine-decrypt
:shift-encrypt :shift-decrypt :*english-letter-frequencies*
:relative-frequencies :chi-squared :count-letters :shift-guess-key
:shift-try-break))
(in-package shift-affine)
(defun char-letter (char)
"Return the index of CHAR in the alphabet. The returned number is 0 for A, 1
for B, 2 for C, etc. Note that this will return the save value for upper and
lower case letters."
(- (char-code char)
(if (upper-case-p char)
(char-code #\A)
(char-code #\a))))
(defun letter-char (letter)
"Return the Lisp character object for LETTER. Letter should be the index of a
letter in the alphabet. For example, 0 for A, 1 for B, 2 for C, etc."
(code-char (+ letter (char-code #\A))))
(defun affine-encrypt (plain coef offset)
"Encrypt PLAIN using an affine encryption algorithm. COEF cannot be coprime
with 26. That is, it cannot be a multiple of 2 or 13. The algorithm used is:
f(p) = (COEF * p + OFFSET) mod 26
where this function is used to transform every letter of PLAIN."
(when (or (zerop (mod coef 2))
(zerop (mod coef 13)))
(error
"COEF must be coprime with 26 (not divisible by 2 or 13), but it was ~d"
coef))
(map 'string (lambda (char)
(if (alpha-char-p char)
(let ((letter (char-letter char)))
(letter-char
(mod (+ (* coef letter) offset) 26)))
char))
plain))
(defun extended-gcd (n1 n2)
"Return the greatest common denominator of N1 and N2. As a second value,
return a cons of (x . y) such char x * N1 + y * N2 = GCD."
(if (zerop n1)
(values n2 (cons 0 1))
(multiple-value-bind (div rem) (floor n2 n1)
(destructuring-bind (gcd (x . y))
(multiple-value-list (extended-gcd rem n1))
(values gcd (cons (- y (* div x)) x))))))
(defun modular-multiplicative-inverse (n m)
"Find the modular multiplicative inverse of N with respect to M. That is, some
integer i such that (N * i) mod M = 1."
(destructuring-bind (gcd (x . y))
(multiple-value-list (extended-gcd n m))
(declare (ignorable y))
(unless (= 1 gcd)
(error "N and M must be coprime. N: ~d, M: ~d" n m))
(+ x m)))
(defun affine-decrypt (cipher coef offset)
"Decrypt CIPHER, which should be a string encrypted by `affine-encrypt'. COEF
and OFFSET should be the same as the values passed when encrypting CIPHER."
(let ((ic (modular-multiplicative-inverse coef 26)))
(affine-encrypt cipher ic (- (* offset ic)))))
(defun shift-encrypt (plain offset)
"Encrypt PLAIN by shifting each letter by OFFSET."
(affine-encrypt plain 1 offset))
(defun shift-decrypt (cipher offset)
"Decrypt CIPHER by shifting each letter by -1 * OFFSET."
(affine-encrypt cipher 1 (- offset)))
(defparameter *english-letter-frequencies*
#(8.2 1.5 2.8 4.3 12.7 2.2 2.0 6.1 7.0 0.15 0.77 4.0 2.4 6.7 7.5 1.9 0.095 6.0
6.3 9.1 2.8 0.98 2.4 0.15 2.0 0.074)
"Percent frequency of each letter of the English alphabet in standard writing.
Source: https://en.wikipedia.org/wiki/Letter_frequency")
(defun relative-frequencies (seq)
"Find the relative percent frequency of the sample data in SEQ."
(let ((sample-count (reduce '+ seq)))
(map 'vector (lambda (elem)
(/ elem sample-count))
seq)))
(defun chi-squared (data ref-data &key (offset 0))
"Return the sum of the square of the error between each index of DATA and
REF-DATA. Before performing the calculation, shift each element in DATA by
OFFSET indexes, wrapping. That is, with OFFSET 1, index 0 becomes index 1, and
the last index becomes index 0."
(loop for ref across ref-data
for i upfrom offset
for sample = (aref data (mod i (length data)))
summing (/ (expt (- sample ref) 2) ref)))
(defun count-letters (str)
"Count the number of times each letter appears in STR. Return a vector with
each index being the number of times that letter appeared."
(loop with freq-data = (make-array '(26) :initial-element 0)
for char across str
for letter = (char-letter char)
when (alpha-char-p char)
do (incf (aref freq-data letter))
finally (return freq-data)))
(defun shift-guess-key (cipher &key (reference *english-letter-frequencies*))
"Try to guess the shift offset for CIPHER. This is done by analyzing the
frequencies of letters in CIPHER and finding the shift offset that most closely
matches those listed in REFERENCE, which defaults to `*english-letter-frequencies*'."
;; We also try CIPHER as is, just in case
(let ((best-chi-squared most-positive-fixnum)
(best-offset 0)
(freq-data (relative-frequencies (count-letters cipher))))
(dotimes (i (length reference) best-offset)
(let ((chi-squared (chi-squared freq-data reference
:offset i)))
(when (< chi-squared best-chi-squared)
(setq best-chi-squared chi-squared
best-offset i))))))
(defun shift-try-break (cipher &key (reference *english-letter-frequencies*))
"Attempt to decrypt CIPHER by guessing the shift offset. This uses
`shift-guess-key' (which see) internally. REFERENCE is passed verbatim to
`shift-guess-key'. As a second value, return the key used for decryption."
(let ((key (shift-guess-key cipher :reference reference)))
(values (shift-decrypt cipher key)
key)))
;; Local Variables:
;; jinx-local-words: "coprime"
;; End:

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;; vigenere.lisp - Simple implementation of a Vigenere cipher.
;;
;; This file is free software under the terms of the GPL3 license. You can find
;; a copy of the license at: https://www.gnu.org/licenses/gpl-3.0.en.html
(defpackage vigenere
(:use :cl)
(:export
:+vigenere-alphabet+ :+vigenere-inverse-alphabet+ :vigenere-letter-char
:vigenere-char-letter :vigenere-add :vigenere-encrypt :vigenere-invert-char
:vigenere-decrypt))
(in-package vigenere)
(defparameter +vigenere-alphabet+
" abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789."
"Alphabet for use in `vigenere-encrypt'.")
(defparameter +vigenere-inverse-alphabet+
(loop with alph = (make-array 123 :initial-element 0)
for i below (length +vigenere-alphabet+)
for char = (aref +vigenere-alphabet+ i)
do (setf (aref alph (char-code char)) i)
finally (return alph))
"Inverse lookup table for `vigenere-encrypt'.")
(defun vigenere-letter-char (letter)
"Convert LETTER to a Lisp char object."
(aref +vigenere-alphabet+ letter))
(defun vigenere-char-letter (char)
"Convert a Lisp char object CHAR to a letter."
(aref +vigenere-inverse-alphabet+ (char-code char)))
(defun vigenere-add (elem by)
"Add ELEM and BY under the modulo (length `+vigenere-alphabet+')"
(mod (+ elem by) (length +vigenere-alphabet+)))
(defun vigenere-encrypt (plain key)
"Encrypt PLAIN using a vigenere cipher. This works by shifting each element of
PLAIN by each consecutive elements of KEY, wrapping around if there are no more
elements left in KEY."
(let ((done (make-array (length plain))))
(dotimes (i (length plain) (map 'string 'vigenere-letter-char
done))
(setf (aref done i)
(vigenere-add (vigenere-char-letter (aref plain i))
(vigenere-char-letter
(aref key (mod i (length key)))))))))
(defun vigenere-invert-char (char)
"Invert CHAR. That is, return the character that will invert the effect that
CHAR had during encryption."
(let ((letter (vigenere-char-letter char)))
(vigenere-letter-char (- (length +vigenere-alphabet+) letter))))
(defun vigenere-decrypt (cipher key)
"Decrypt CIPHER using a vigenere cipher, with the key KEY."
(vigenere-encrypt cipher (map 'string 'vigenere-invert-char key)))
;; Local Variables:
;; jinx-local-words: "vigenere"
;; End: