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feat: DH-Example in Elisp

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Toerd@archlinux 5 years ago
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diffie-hellman.el
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;; 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
(progn
(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
(progn
(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
(progn
(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)
(command-execute 'split-window-horizontally)
(command-execute 'split-window-horizontally)
(command-execute '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 (random n))
)
;; p <= 1 -> not a prime number
(if (and (> q 1)
(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))
;; Tests:
;; (phga/dh-get-generator-p (phga/dh-get-random-prime-number 20))
;; (and nil t)
;; (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)
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