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Task/RSA-code/Erlang/rsa-code.erl

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+%%% @author Tony Wallace <tony@tony.gen.nz>
+%%% @doc
+%%% For details of the algorithms used see
+%%% https://en.wikipedia.org/wiki/Modular_exponentiation
+%%% @end
+%%% Created : 21 Jul 2021 by Tony Wallace <tony@resurrection>
+
+-module mod.
+-export [mod_mult/3,mod_exp/3,binary_exp/2,test/0].
+
+mod_mult(I1,I2,Mod) when
+      I1 > Mod,
+      is_integer(I1), is_integer(I2), is_integer(Mod) ->
+    mod_mult(I1 rem Mod,I2,Mod);
+mod_mult(I1,I2,Mod) when
+      I2 > Mod,
+      is_integer(I1), is_integer(I2), is_integer(Mod) ->
+    mod_mult(I1,I2 rem Mod,Mod);
+mod_mult(I1,I2,Mod) when
+      is_integer(I1), is_integer(I2), is_integer(Mod) ->
+    (I1 * I2) rem Mod.
+
+mod_exp(Base,Exp,Mod) when
+      is_integer(Base),
+      is_integer(Exp),
+      is_integer(Mod),
+      Base > 0,
+      Exp > 0,
+      Mod > 0 ->
+    binary_exp_mod(Base,Exp,Mod);
+mod_exp(_,0,_) -> 1.
+
+
+binary_exp(Base,Exponent) when
+      is_integer(Base),
+      is_integer(Exponent),
+      Base > 0,
+      Exponent > 0 ->
+    binary_exp(Base,Exponent,1);
+binary_exp(_,0) ->
+    1.
+
+binary_exp(_,0,Result) ->
+    Result;
+binary_exp(Base,Exponent,Acc) ->
+    binary_exp(Base*Base,Exponent bsr 1,Acc * exp_factor(Base,Exponent)).
+
+
+binary_exp_mod(Base,Exponent,Mod) ->
+    binary_exp_mod(Base rem Mod,Exponent,Mod,1).
+binary_exp_mod(_,0,_,Result) ->
+   Result;
+binary_exp_mod(Base,Exponent,Mod,Acc) ->
+    binary_exp_mod((Base*Base) rem Mod,
+		   Exponent bsr 1,Mod,(Acc * exp_factor(Base,Exponent))rem Mod).
+
+exp_factor(_,0) ->
+    1;
+exp_factor(Base,1) ->
+    Base;
+exp_factor(Base,Exponent) ->
+    exp_factor(Base,Exponent band 1).
+
+test() ->
+    445 = mod_exp(4,13,497),
+    %% Rosetta code example:
+    R = 1527229998585248450016808958343740453059 =
+	mod_exp(2988348162058574136915891421498819466320163312926952423791023078876139,
+		2351399303373464486466122544523690094744975233415544072992656881240319,
+		binary_exp(10,40)),
+    R.
+
+%%%-------------------------------------------------------------------
+%%% @author Tony Wallace <tony@tony.gen.nz>
+%%% @doc
+%%% Blocking not implemented.  Runtime exception if message too long
+%%% Not a practical issue as RSA usually limited to symmetric key exchange
+%%% However as a key exchange tool no advantage in compressing plaintext
+%%% so that is not done either.
+%%% @end
+%%% Created : 24 Jul 2021 by Tony Wallace <tony@resurrection>
+%%%-------------------------------------------------------------------
+
+-module rsa.
+-export([key_gen/2,encrypt/2,decrypt/2,test/0]).
+-type key() :: {integer(),integer()}.
+key_gen({N,D},E) ->
+    {{E,N},{D,N}}.
+-spec encrypt(key(),integer()) -> integer().
+encrypt({E,N},MessageInt)
+  when MessageInt < N ->
+    mod:mod_exp(MessageInt,E,N).
+-spec decrypt(key(),integer()) -> integer().
+decrypt({D,N},Message) ->
+    mod:mod_exp(Message,D,N).
+test() ->
+    PlainText=10722935,
+    N = 9516311845790656153499716760847001433441357,
+    E = 65537,
+    D = 5617843187844953170308463622230283376298685,
+    {PublicKey,PrivateKey} = key_gen({N,D},E),
+    PlainText =:= decrypt(PrivateKey,
+			  encrypt(PublicKey,PlainText)).