elisp-snippets/diffie-hellman.el

;; author: phga
;; date: 2020-06-27
;; description: I was bored while preparing for exams so I procrastinated
;; and implemented a shitty DH-Algorithm-Example in Elisp which cannot handle
;; large numbers because I don't know anything about Elisp-Integers

;; Notes:
;; (with-current-buffer buffer-or-name)
;; (defvar buffer-local-var nil "DOC")
;; (set (make-local-variable 'buffer-local-var) value)
;; (insert "FOO" "BAR")
(defun phga/dh-example (&optional n)
  "Prints out a Diffie-Hellman Example.
   N is the Cap for the initial random number used to get the primitive root
   for the Galois Field"
  (interactive)
  ;; Random prime number for Galois Field (Finite Field)
  (let* (
         (buf-a "*Alice*")
         (buf-b "*Bob*")
         (buf-p "*Public*")
         (n (or n 200))
         ;; get p
         (p (phga/dh-get-generator-p (phga/dh-get-random-prime-number n)))
         ;; get primitive root in p
         (g (phga/dh-get-generator-elem p))
         ;; generate secret in in GF(p) for Alice
         (a (+ 1 (random (- p 2))))
         ;; generate secret in in GF(p) for Bob
         (b (+ 1 (random (- p 2))))
         ;; generate public alpha for Alice (gets transmitted to Bob)
         (aa (mod (expt g a) p))
         ;; generate public beta for Bob (gets transmitted to Alice)
         (bb (mod (expt g b) p))
         ;; generate secret key for further symmetric encrytion for Alice and Bob
         (ka (mod (expt bb a) p))
         (kb (mod (expt aa b) p))
         )
    ;; Alice
    (when (get-buffer buf-a) (kill-buffer buf-a))
    (generate-new-buffer buf-a)
    (with-current-buffer buf-a
      (insert (phga/dh-pretty-name "Alice"))
      (insert (concat "P for GF(P) = " (number-to-string p) "\n"))
      (insert (concat "G = " (number-to-string g) "\n"))
      (insert (concat "A = " (number-to-string a) " (only known by Alice!)\n"))
      (insert (concat "Alpha = " (number-to-string aa) "\n"))
      (insert (concat "Beta = " (number-to-string bb) " (sent by Bob to Alice)\n"))
      (insert (concat "Secret Key = " (number-to-string ka) " (Beta^A mod P == (G^B)^A mod P\n"))
      )
    ;; Bob
    (when (get-buffer buf-b) (kill-buffer buf-b))
    (generate-new-buffer buf-b)
    (with-current-buffer buf-b
      (insert (phga/dh-pretty-name "Bob"))
      (insert (concat "P for GF(P) = " (number-to-string p) "\n"))
      (insert (concat "G = " (number-to-string g) "\n"))
      (insert (concat "B = " (number-to-string b) " (only known by Bob!)\n"))
      (insert (concat "Beta = " (number-to-string bb) "\n"))
      (insert (concat "Alpha = " (number-to-string aa) " (sent by Alice to Bob)\n"))
      (insert (concat "Secret Key = " (number-to-string kb) " (Alpha^B mod P == (G^A)^B mod P\n"))
      )
    ;; (kill-buffer "*Public*")
    (when (get-buffer buf-p) (kill-buffer buf-p))
    (generate-new-buffer buf-p)
    (with-current-buffer buf-p
      (insert "XxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXx\n")
      (insert "         This is a public transport buffer!\n")
      (insert "           Mean Hackerbois can wait here\n           and sniff the communication!!!\n")
      (insert "XxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXx\n\n")
      (insert (concat "P for GF(P) = " (number-to-string p) "\n"))
      (insert (concat "G = " (number-to-string g) "\n"))
      (insert (concat "Alpha = " (number-to-string aa) "\n"))
      (insert (concat "Beta = " (number-to-string bb) "\n"))
      )

    ;; Create Window setup lel that's soooo bad I am SORRY
    (delete-other-windows)
    (split-window-horizontally)
    (split-window-horizontally)
    (balance-windows)

    (set-window-buffer (nth 0 (window-list)) buf-a)
    (set-window-buffer (nth 1 (window-list)) buf-p)
    (set-window-buffer (nth 2 (window-list)) buf-b)
    )
  )

(defun phga/dh-get-random-prime-number (n)
  "Get a random prime number up to n (inclusive)"
  (interactive)
  (let (
        (q (+ 2 (random (- n 2))))
        )
    ;; p <= 1 -> not a prime number
    (if (phga/dh-is-prime q)
        q
      (phga/dh-get-random-prime-number n))
    )
  )

;; count from 2 to sqrt(p)
(defun phga/dh-is-prime (p &optional c)
  "Prime Number ye or ne?"
  (interactive)
  ;; default value for c (starting point for recursion)
  (let ((c (or c 2)))
    ;; stops in case of c <= sqrt(p) && p % c == 0 || c > sqrt(p)
    ;; first yields nil second yields t
    (or (> c (sqrt p))
        ;; p % c != 0 => is prime (for this recursion)
        (and (/= (mod p c) 0) ;; hopefully t every recursion so we get a prime
             (phga/dh-is-prime p (+ c 1)))
        )))

(defun phga/dh-get-generator-p (q)
  (interactive)
  ;; p = q*r + 1 -> test for prime
  (let (
        (p (+ 1 (* q (+ 1 (random 41))))))
    (if (phga/dh-is-prime p)
        p
      (phga/dh-get-generator-p q))
    ))

(defun phga/dh-get-generator-elem (p)
  (interactive)
  "Get the actual primitive root for GF(p)"
  (+ 1 (random (- p 2))))

(defun phga/dh-pretty-name (name)
  "Returns the name in a pretty format"
  (format "****************************\n    Hi my Name is %s!\n****************************\n\n" name))
;; (phga/dh-example)
;; (and nil t)

;; (phga/dh-get-generator-p (phga/dh-get-random-prime-number 20))

;; ;; Test
;; (setq phga/p (phga/dh-get-generator-p (phga/dh-get-random-prime-number 20)))
;; (setq phga/g (phga/dh-get-generator-elem phga/p))
;; (setq phga/a (+ 1 (random (- phga/p 2))))
;; (setq phga/b (+ 1 (random (- phga/p 2))))
;; (setq phga/aa (mod (expt phga/g phga/a) phga/p))
;; (setq phga/bb (mod (expt phga/g phga/b) phga/p))
;; (setq phga/ka (mod (expt phga/bb phga/a) phga/p))
;; (setq phga/kb (mod (expt phga/aa phga/b) phga/p))
;; ;; Tested if short-circuit and / ors
;; (or nil (and t (message "Hi")))

;; (phga/dh-get-random-prime-number 10)
;; (phga/dh-is-prime 0)