grosse avancee, fin de cipher
This commit is contained in:
parent
968f4b16e8
commit
38346009e7
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@ -29,4 +29,8 @@ setup.log
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_opam/
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# Local files
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*~
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*~
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*.log
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*.cache
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*caml-toplevel*
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@ -0,0 +1,41 @@
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# OASIS_START
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# DO NOT EDIT (digest: a3c674b4239234cbbe53afe090018954)
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SETUP = ocaml setup.ml
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build: setup.data
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$(SETUP) -build $(BUILDFLAGS)
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doc: setup.data build
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$(SETUP) -doc $(DOCFLAGS)
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test: setup.data build
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$(SETUP) -test $(TESTFLAGS)
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all:
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$(SETUP) -all $(ALLFLAGS)
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install: setup.data
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$(SETUP) -install $(INSTALLFLAGS)
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uninstall: setup.data
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$(SETUP) -uninstall $(UNINSTALLFLAGS)
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reinstall: setup.data
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$(SETUP) -reinstall $(REINSTALLFLAGS)
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clean:
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$(SETUP) -clean $(CLEANFLAGS)
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distclean:
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$(SETUP) -distclean $(DISTCLEANFLAGS)
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setup.data:
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$(SETUP) -configure $(CONFIGUREFLAGS)
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configure:
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$(SETUP) -configure $(CONFIGUREFLAGS)
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.PHONY: build doc test all install uninstall reinstall clean distclean configure
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# OASIS_STOP
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@ -1,7 +1,8 @@
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(** Basic arithmetics with built-in integers *)
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(**#use "builtin.ml";;**)
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open Builtin
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(* Greater common divisor and smaller common multiple
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implemetations.
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*)
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@ -10,7 +11,11 @@ open Builtin
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@param a non-zero integers
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@param b non-zero integer
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*)
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let rec gcd a b = 0
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let rec gcd a b =
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let r = modulo (sign a*a) (sign b*b)
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in if r > 0 then
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gcd (sign b *b) r
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else b;;
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(* Extended Euclidean algorithm. Computing Bezout Coefficients. *)
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@ -20,4 +25,13 @@ let rec gcd a b = 0
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@param a non-zero integer
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@param b non-zero integer.
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*)
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let bezout a b = (0, 0, 0)
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let rec bezout a b =
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let rec bezout_rec u v r u1 v1 r1=
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if r1 = 0 then
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(u, v, a*u + b*v)
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else
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let q = r/r1 in
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bezout_rec u1 v1 r1 (u-q*u1) (v-q*v1) (r-q*r1)
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in bezout_rec 1 0 a 0 1 b;;
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@ -13,14 +13,31 @@ open Power
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@param m word to cipher.
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@param b base ; for ASCII codes should be set to 255.
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*)
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let encrypt_cesar k m b = []
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let encrypt_cesar k m b =
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let rec encrypt_cesar_rec l =
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match l with
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[] -> []
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| e::l -> begin
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let rot = modulo (e + k) b in
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rot::encrypt_cesar_rec l
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end
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in encrypt_cesar_rec m;;
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(** Cesar's cipher decryption
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@param k is an integer corresponding to key
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@param m encrypted word.
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@param b base ; for ASCII code should be set to 255.
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*)
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let decrypt_cesar k m b = []
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let decrypt_cesar k m b =
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let rec decrypt_cesar_rec l =
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match l with
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[] -> []
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| e::l -> begin
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let rot = modulo (e - k) b in
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rot::decrypt_cesar_rec l
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end
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in decrypt_cesar_rec m;;
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(********** RSA Cipher **********)
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@ -30,21 +47,25 @@ let decrypt_cesar k m b = []
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@param p prime number
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@param q prime number
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*)
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let generate_keys_rsa p q = ((0,0), (0,0))
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let generate_keys_rsa p q =
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let n = p * q in
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let phi = (p-1) * (q-1) in
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let e = phi - 1 in
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let (d, _, _) = bezout e phi in
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((n, e), (n, d));;
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(** Encryption using RSA cryptosystem.
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@param m integer hash of message
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@param pub_key a tuple (n, e) composing public key of RSA cryptosystem.
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*)
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let encrypt_rsa m (n, e) = 0
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let encrypt_rsa m (n, e) = mod_power m e n;;
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(** Decryption using RSA cryptosystem.
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@param m integer hash of encrypter message.
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@param pub_key a tuple (n, d) composing private key of RSA cryptosystem.
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*)
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let decrypt_rsa m (n , d) = 0
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;;
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let decrypt_rsa m (n , d) = mod_power m d n;;
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(********** ElGamal Cipher **********)
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@ -52,23 +73,32 @@ let decrypt_rsa m (n , d) = 0
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where p is prime and g having high enough order modulo p.
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@param p is prime having form 2*q + 1 for prime q.
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*)
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let rec public_data_g p = (0, 0)
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let rec public_data_g p =
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let g = (p - 1)/2 in
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(g, p);;
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(** Generate ElGamal public data.
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@param pub_data a tuple (g, p) of public data for ElGamal cryptosystem.
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*)
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let generate_keys_g (g, p) = (0, 0)
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let generate_keys_g (g, p) =
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let r = modulo (787581985456192323) g in
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let pub = mod_power g r p in (pub, r);;
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(** ElGamal encryption process.
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@param msg message to be encrypted.
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@param pub_data a tuple (g, p) of ElGamal public data.
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@param kA ElGamal public key.
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*)
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let encrypt_g msg (g, p) kA = (0, 0)
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let encrypt_g msg (g, p) kA =
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let r = modulo (787581985456192323) g in
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let c = mod_power g r p in
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let d = msg * mod_power kA r p in
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(c, d);;
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(** ElGamal decryption process.
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@param msg a tuple (msgA, msgB) forming an encrypted ElGamal message.
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@param a private key
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@param pub_data a tuple (g, p) of public data for ElGamal cryptosystem.
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*)
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let decrypt_g (msgA, msgB) a (g, p) = 0
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let decrypt_g (msgA, msgB) a (g, p) =
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msgB / (mod_power msgA a p);;
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@ -10,27 +10,61 @@ open Basic_arithmetics
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(** List composed of 2 and then odd integers starting at 3.
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@param n number of elements in the list of integers.
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*)
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let init_eratosthenes n = []
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let init_eratosthenes n =
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let rec init_eratosthenes_rec i =
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match i with
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i when i > n -> []
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| i when modulo i 2 = 1 -> i::init_eratosthenes_rec (i+2)
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| i -> init_eratosthenes_rec (i+1)
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in if n > 1 then
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2::init_eratosthenes_rec 3
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else [];;
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(* Eratosthenes sieve. *)
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(** Eratosthene sieve.
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@param n limit of list of primes, starting at 2.
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*)
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let eratosthenes n = []
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let rec remove_multiples_from_list e l =
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match l with
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[] -> []
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| e1::l1 -> begin
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match modulo e1 e with
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0 -> remove_multiples_from_list e l1
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| _ -> e1::remove_multiples_from_list e l1
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end;;
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let eratosthenes n =
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let list = init_eratosthenes n in
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let rec eratosthenes_rec l =
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match l with
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[] -> []
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| e::l1 -> begin
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let l1 = remove_multiples_from_list e l1 in
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e::eratosthenes_rec l1
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end
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in eratosthenes_rec list
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(* Write and read into file functions for lists. *)
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(** Write a list into a file. Element seperator is newline.
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@param file path to write to.
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*)
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let write_list li file = ()
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let write_list li file =
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let oc = open_out file in
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let rec write l =
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match l with
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[] -> close_out oc
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| e::l1 -> Printf.fprintf oc "%d\n" e; write l1
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in write li;;
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(** Write a list of prime numbers up to limit into a txt file.
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@param n limit of prime numbers up to which to build up a list of primes.
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@param file path to write to.
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*)
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let write_list_primes n file = ()
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let write_list_primes n file =
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let list = eratosthenes n in
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write_list list file;;
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(** Read file safely ; catch End_of_file exception.
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@param in_c input channel.
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@ -42,12 +76,23 @@ let input_line_opt in_c =
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(** Create a list out of reading a line per line channel.
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@param in_c input channel.
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*)
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let create_list in_c = ()
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let create_list in_c =
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let rec read acc =
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match input_line_opt in_c with
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None -> acc
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| Some l -> l::read acc
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in read [];;
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(** Load list of primes into OCaml environment.
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@param file path to load from.
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*)
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let read_list_primes file = []
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let read_list_primes file =
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let list = create_list (open_in file) in
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let rec put list =
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match list with
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[] -> []
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| e::l -> (int_of_string e)::put l
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in put list;;
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(* Auxiliary functions to extract big prime numbers for testing
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purposes.
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@ -80,11 +125,37 @@ let rec last_two l = match l with
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plus 1.
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@param limit positive integer bounding searched for primes.
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@param isprime function testing for (pseudo)primality.
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*)
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let double_primes limit isprime = []
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*)
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let double_primes limit isprime =
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let list = eratosthenes limit in
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let rec double_primes_rec l =
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match l with
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[] -> []
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| e::l1 -> begin
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let double = e * 2 + 1 in
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if isprime double then
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(e, double)::double_primes_rec l1
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else
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double_primes_rec l1
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end
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in double_primes_rec list;;
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(** Finding twin primes.
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@param limit positive integer bounding searched for primes.
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@param isprime function testing for (pseudo)primality.
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*)
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let twin_primes limit isprime = []
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let twin_primes limit isprime =
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let list = eratosthenes limit in
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let rec double_primes_rec l =
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match l with
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[] -> []
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| e::l1 -> begin
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let double = e + 2 in
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if isprime double then
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(e, double)::double_primes_rec l1
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else
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double_primes_rec l1
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end
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in double_primes_rec list;;
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@ -1,7 +1,7 @@
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(** Power function implementations for built-in integers *)
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open Builtin
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open Basic_arithmetics
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open Basic_arithmetics;;
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(* Naive and fast exponentiation ; already implemented in-class.
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*)
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@ -10,13 +10,25 @@ open Basic_arithmetics
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@param x base
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@param n exponent
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*)
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let pow x n = 0
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let pow x n =
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let rec pow_rec x1 n =
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match n with
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0 -> x1
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| n -> pow_rec (x1*x) (n-1)
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in pow_rec 1 n;;
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(** Fast integer exponentiation function. Logarithmic complexity.
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@param x base
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@param n exponent
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*)
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let power x n = 0
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let power x n =
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if n = 0 then 1 else
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let rec power_rec x1 n =
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match n with
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1 -> x1
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| n when modulo n 2 = 0 -> power_rec (x1 * x1) (n/2)
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| n -> x1 * power_rec (x1 * x1) ((n-1)/2)
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in power_rec x n;;
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(* Modular expnonentiation ; modulo a given natural number smaller
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max_int we never have integer-overflows if implemented properly.
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@ -27,7 +39,17 @@ let power x n = 0
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@param n exponent
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@param m modular base
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*)
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let mod_power x n m = 0
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let mod_power x n m =
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if n = 0 then
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1
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else
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let rec mod_power_rec c e =
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let c = modulo (x * c) m
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in if e < n then
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mod_power_rec c (e+1)
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else
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c
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in mod_power_rec 1 1;;
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||||
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(* Making use of Fermat Little Theorem for very quick exponentation
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modulo prime number.
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@ -39,4 +61,8 @@ let mod_power x n m = 0
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@param n exponent
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||||
@param p prime modular base
|
||||
*)
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||||
let prime_mod_power x n p = 0
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let prime_mod_power x n p =
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if x = 0 then
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0
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||||
else
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||||
mod_power x (modulo n (p - 1)) p;;
|
||||
|
|
|
|||
|
|
@ -5,10 +5,36 @@ open Basic_arithmetics
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|||
open Power
|
||||
|
||||
(** Deterministic primality test *)
|
||||
let is_prime n = true
|
||||
let is_prime n =
|
||||
if n = 2 || n = 3 then
|
||||
true
|
||||
else
|
||||
if modulo n 2 = 0 || modulo n 3 = 0 then
|
||||
false
|
||||
else
|
||||
let rec is_prime_rec k =
|
||||
if (6*k-1) * (6*k-1) > n then
|
||||
true
|
||||
else
|
||||
match (6*k-1, 6*k+1) with
|
||||
(a, b) when modulo n a = 0 || modulo n b = 0 -> false
|
||||
| _ -> is_prime_rec (k+1)
|
||||
in is_prime_rec 1;;
|
||||
|
||||
(** Pseudo-primality test based on Fermat's Little Theorem
|
||||
@param p tested integer
|
||||
@param testSeq sequence of integers againt which to test
|
||||
*)
|
||||
let is_pseudo_prime p test_seq = true
|
||||
|
||||
let is_pseudo_prime p test_seq =
|
||||
let rec is_pseudo_prime_rec l =
|
||||
match l with
|
||||
[] -> true
|
||||
| e::l1 when mod_power e (p-1) p <> 1 -> begin
|
||||
if gcd e p = 1 then
|
||||
false
|
||||
else
|
||||
is_pseudo_prime_rec l1
|
||||
end
|
||||
| _::l1 -> is_pseudo_prime_rec l1
|
||||
in is_pseudo_prime_rec test_seq;;
|
||||
|
|
|
|||
|
|
@ -0,0 +1,27 @@
|
|||
#!/bin/sh
|
||||
|
||||
# OASIS_START
|
||||
# DO NOT EDIT (digest: dc86c2ad450f91ca10c931b6045d0499)
|
||||
set -e
|
||||
|
||||
FST=true
|
||||
for i in "$@"; do
|
||||
if $FST; then
|
||||
set --
|
||||
FST=false
|
||||
fi
|
||||
|
||||
case $i in
|
||||
--*=*)
|
||||
ARG=${i%%=*}
|
||||
VAL=${i##*=}
|
||||
set -- "$@" "$ARG" "$VAL"
|
||||
;;
|
||||
*)
|
||||
set -- "$@" "$i"
|
||||
;;
|
||||
esac
|
||||
done
|
||||
|
||||
ocaml setup.ml -configure "$@"
|
||||
# OASIS_STOP
|
||||
|
|
@ -0,0 +1,39 @@
|
|||
(* setup.ml generated for the first time by OASIS v0.4.11 *)
|
||||
|
||||
(* OASIS_START *)
|
||||
(* DO NOT EDIT (digest: a426e2d026defb34183b787d31fbdcff) *)
|
||||
(******************************************************************************)
|
||||
(* OASIS: architecture for building OCaml libraries and applications *)
|
||||
(* *)
|
||||
(* Copyright (C) 2011-2016, Sylvain Le Gall *)
|
||||
(* Copyright (C) 2008-2011, OCamlCore SARL *)
|
||||
(* *)
|
||||
(* This library is free software; you can redistribute it and/or modify it *)
|
||||
(* under the terms of the GNU Lesser General Public License as published by *)
|
||||
(* the Free Software Foundation; either version 2.1 of the License, or (at *)
|
||||
(* your option) any later version, with the OCaml static compilation *)
|
||||
(* exception. *)
|
||||
(* *)
|
||||
(* This library is distributed in the hope that it will be useful, but *)
|
||||
(* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY *)
|
||||
(* or FITNESS FOR A PARTICULAR PURPOSE. See the file COPYING for more *)
|
||||
(* details. *)
|
||||
(* *)
|
||||
(* You should have received a copy of the GNU Lesser General Public License *)
|
||||
(* along with this library; if not, write to the Free Software Foundation, *)
|
||||
(* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA *)
|
||||
(******************************************************************************)
|
||||
|
||||
let () =
|
||||
try
|
||||
Topdirs.dir_directory (Sys.getenv "OCAML_TOPLEVEL_PATH")
|
||||
with Not_found -> ()
|
||||
;;
|
||||
#use "topfind";;
|
||||
#require "oasis.dynrun";;
|
||||
open OASISDynRun;;
|
||||
|
||||
let setup_t = BaseCompat.Compat_0_4.adapt_setup_t setup_t
|
||||
open BaseCompat.Compat_0_4
|
||||
(* OASIS_STOP *)
|
||||
let () = setup ();;
|
||||
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Reference in New Issue