# RSA code

Given an RSA key (n,e,d), construct a program to encrypt and decrypt plaintext messages strings.

RSA code
You are encouraged to solve this task according to the task description, using any language you may know.

Background

RSA code is used to encode secret messages. It is named after Ron Rivest, Adi Shamir, and Leonard Adleman who published it at MIT in 1977. The advantage of this type of encryption is that you can distribute the number “${\displaystyle n}$” and “${\displaystyle e}$” (which makes up the Public Key used for encryption) to everyone. The Private Key used for decryption “${\displaystyle d}$” is kept secret, so that only the recipient can read the encrypted plaintext.

The process by which this is done is that a message, for example “Hello World” is encoded as numbers (This could be encoding as ASCII or as a subset of characters ${\displaystyle a=01,b=02,...,z=26}$). This yields a string of numbers, generally referred to as "numerical plaintext", “${\displaystyle P}$”. For example, “Hello World” encoded with a=1,...,z=26 by hundreds would yield ${\displaystyle 08051212152315181204}$.

The plaintext must also be split into blocks so that the numerical plaintext is smaller than ${\displaystyle n}$ otherwise the decryption will fail.

The ciphertext, ${\displaystyle C}$, is then computed by taking each block of ${\displaystyle P}$, and computing

${\displaystyle C\equiv P^{e}\mod n}$

Similarly, to decode, one computes

${\displaystyle P\equiv C^{d}\mod n}$

To generate a key, one finds 2 (ideally large) primes ${\displaystyle p}$ and ${\displaystyle q}$. the value “${\displaystyle n}$” is simply: ${\displaystyle n=p\times q}$. One must then choose an “${\displaystyle e}$” such that ${\displaystyle \gcd(e,(p-1)\times (q-1))=1}$. That is to say, ${\displaystyle e}$ and ${\displaystyle (p-1)\times (q-1)}$ are relatively prime to each other.

The decryption value ${\displaystyle d}$ is then found by solving

${\displaystyle d\times e\equiv 1\mod (p-1)\times (q-1)}$

The security of the code is based on the secrecy of the Private Key (decryption exponent) “${\displaystyle d}$” and the difficulty in factoring “${\displaystyle n}$”. Research into RSA facilitated advances in factoring and a number of factoring challenges. Keys of 829 bits have been successfully factored, and NIST now recommends 2048 bit keys going forward (see Asymmetric algorithm key lengths).

• Encrypt and Decrypt a short message or two using RSA with a demonstration key.
• Implement RSA do not call a library.
• Encode and decode the message using any reversible method of your choice (ASCII or a=1,..,z=26 are equally fine).
• Either support blocking or give an error if the message would require blocking)
• Demonstrate that your solution could support real keys by using a non-trivial key that requires large integer support (built-in or libraries). There is no need to include library code but it must be referenced unless it is built into the language. The following keys will be meet this requirement;however, they are NOT long enough to be considered secure:
n = 9516311845790656153499716760847001433441357
e = 65537
d = 5617843187844953170308463622230283376298685
• Messages can be hard-coded into the program, there is no need for elaborate input coding.
• Demonstrate that your implementation works by showing plaintext, intermediate results, encrypted text, and decrypted text.
 WarningRosetta Code is not a place you should rely on for examples of code in critical roles, including security.Cryptographic routines should be validated before being used.For a discussion of limitations and please refer to Talk:RSA_code#Difference_from_practical_cryptographical_version.

## 11l

Translation of: D
V n = BigInt(‘9516311845790656153499716760847001433441357’)
V e = BigInt(65537)
V d = BigInt(‘5617843187844953170308463622230283376298685’)

V txt = ‘Rosetta Code’

print(‘Plain text:             ’txt)

V txtN = txt.reduce(BigInt(0), (a, b) -> a * 256 + b.code)
print(‘Plain text as a number: ’txtN)

V enc = pow(txtN, e, n)
print(‘Encoded:                ’enc)

V dec = pow(enc, d, n)
print(‘Decoded:                ’dec)

V decTxt = ‘’
L dec != 0
decTxt ‘’= Char(code' dec % 256)
dec I/= 256

print(‘Decoded number as text: ’reversed(decTxt))
Output:
Plain text:             Rosetta Code
Plain text as a number: 25512506514985639724585018469
Encoded:                916709442744356653386978770799029131264344
Decoded:                25512506514985639724585018469
Decoded number as text: Rosetta Code


The code below uses a thik and a thin binding of gmp.

WITH GMP, GMP.Integers, Ada.Text_IO, GMP.Integers.Aliased_Internal_Value, Interfaces.C;

PROCEDURE Main IS
FUNCTION "+" (U : Unbounded_Integer) RETURN Mpz_T IS (Aliased_Internal_Value (U));
FUNCTION "+" (S : String) RETURN Unbounded_Integer IS (To_Unbounded_Integer (S));
FUNCTION Image_Cleared (M : Mpz_T) RETURN String IS (Image (To_Unbounded_Integer (M)));
N                 : Unbounded_Integer := +"9516311845790656153499716760847001433441357";
E                 : Unbounded_Integer := +"65537";
D                 : Unbounded_Integer := +"5617843187844953170308463622230283376298685";
Plain_Text        : CONSTANT String := "Rosetta Code";
M, M_C, M_D       : Mpz_T;
-- We import two C functions from the GMP library which are not in the specs of the gmp package
PROCEDURE Mpz_Import
(Rop   : Mpz_T; Count : Size_T; Order : Int; Size : Size_T; Endian : Int;
Nails : Size_T; Op : Char_Array);
PRAGMA Import (C, Mpz_Import, "__gmpz_import");

PROCEDURE Mpz_Export
(Rop    : OUT Char_Array; Count : ACCESS Size_T; Order : Int; Size : Size_T;
Endian : Int; Nails : Size_T; Op : Mpz_T);
PRAGMA Import (C, Mpz_Export, "__gmpz_export");
BEGIN
Mpz_Init (M);
Mpz_Init (M_C);
Mpz_Init (M_D);
Mpz_Import (M, Plain_Text'Length + 1, 1, 1, 0, 0, To_C (Plain_Text));
Mpz_Powm (M_C, M, +E, +N);
Mpz_Powm (M_D, M_C, +D, +N);
Put_Line ("Encoded plain text: " & Image_Cleared (M));
DECLARE Decrypted : Char_Array (1 .. Mpz_Sizeinbase (M_C, 256));
BEGIN
Put_Line ("Encryption of this encoding: " & Image_Cleared (M_C));
Mpz_Export (Decrypted, NULL, 1, 1, 0, 0, M_D);
Put_Line ("Decryption of the encoding: " & Image_Cleared (M_D));
Put_Line ("Final decryption: " &  To_Ada (Decrypted));
END;
END Main;

Output:
Encoded plain text: 6531201667836323769493764728064
Encryption of this encoding: 8527003485686414372697775926080309566820293
Decryption of the encoding: 6531201667836323769493764728064
Final decryption: Rosetta Code


## ALGOL 68

The code below uses Algol 68 Genie which provides arbitrary precision arithmetic for LONG LONG modes.

COMMENT
First cut.  Doesn't yet do blocking and deblocking.  Also, as
encryption and decryption are identical operations but for the
reciprocal exponents used, only one has been implemented below.

A later release will address these issues.
COMMENT

BEGIN
PR precision=1000 PR
MODE LLI = LONG LONG INT;    CO For brevity CO
PROC mod power = (LLI base, exponent, modulus) LLI :
BEGIN
LLI result := 1, b := base, e := exponent;
IF exponent < 0
THEN
put (stand error, (("Negative exponent", exponent, newline)))
ELSE
WHILE e > 0
DO
(ODD e | result := (result * b) MOD modulus);
e OVERAB 2; b := (b * b) MOD modulus
OD
FI;
result
END;
PROC modular inverse = (LLI a, m) LLI :
BEGIN
PROC extended gcd = (LLI x, y) []LLI :
BEGIN
LLI v := 1, a := 1, u := 0, b := 0, g := x, w := y;
WHILE w>0
DO
LLI q := g % w, t := a - q * u;
a := u; u := t;
t := b - q * v;
b := v; v := t;
t := g - q * w;
g := w; w := t
OD;
a PLUSAB (a < 0 | u | 0);
(a, b, g)
END;
[] LLI egcd = extended gcd (a, m);
(egcd[3] > 1 | 0 | egcd[1] MOD m)
END;
PROC number to string = (LLI number) STRING :
BEGIN
[] CHAR map = (blank + "ABCDEFGHIJKLMNOPQRSTUVWXYZ")[@0];
LLI local number := number;
INT length := SHORTEN SHORTEN ENTIER long long log(number) + 1;
(ODD length | length PLUSAB 1);
[length % 2] CHAR text;
FOR i FROM length % 2 BY -1 TO 1
DO
INT index = SHORTEN SHORTEN (local number MOD 100);
text[i] := (index > 26 | "?" | map[index]);
local number := local number % 100
OD;
text
END;
CO The parameters of a particular RSA cryptosystem CO
LLI p = 3490529510847650949147849619903898133417764638493387843990820577;
LLI q = 32769132993266709549961988190834461413177642967992942539798288533;
LLI n = p * q;
LLI phi n = (p-1) * (q-1);
LLI e = 9007;
LLI d = modular inverse (e, phi n);
CO A ciphertext CO
LLI cipher text = 96869613754622061477140922254355882905759991124574319874695120930816298225145708356931476622883989628013391990551829945157815154;
CO Print out the corresponding plain text CO
print (number to string (mod power (ciphertext, d, n)))
END
Output:
THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE


## C

Library: GMP
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <gmp.h>

int main(void)
{
mpz_t n, d, e, pt, ct;

mpz_init(pt);
mpz_init(ct);
mpz_init_set_str(n, "9516311845790656153499716760847001433441357", 10);
mpz_init_set_str(e, "65537", 10);
mpz_init_set_str(d, "5617843187844953170308463622230283376298685", 10);

const char *plaintext = "Rossetta Code";
mpz_import(pt, strlen(plaintext), 1, 1, 0, 0, plaintext);

if (mpz_cmp(pt, n) > 0)
abort();

mpz_powm(ct, pt, e, n);
gmp_printf("Encoded:   %Zd\n", ct);

mpz_powm(pt, ct, d, n);
gmp_printf("Decoded:   %Zd\n", pt);

char buffer[64];
mpz_export(buffer, NULL, 1, 1, 0, 0, pt);
printf("As String: %s\n", buffer);

mpz_clears(pt, ct, n, e, d, NULL);
return 0;
}

Output:
Encoded:   5278143020249600501803788468419399384934220
Decoded:   6531201733672758787904906421349
As String: Rossetta Code


## C#

using System;
using System.Numerics;
using System.Text;

class Program
{
static void Main(string[] args)
{
BigInteger n = BigInteger.Parse("9516311845790656153499716760847001433441357");
BigInteger e = 65537;
BigInteger d = BigInteger.Parse("5617843187844953170308463622230283376298685");

const string plaintextstring = "Hello, Rosetta!";
byte[] plaintext = ASCIIEncoding.ASCII.GetBytes(plaintextstring);
BigInteger pt = new BigInteger(plaintext);
if (pt > n)
throw new Exception();

BigInteger ct = BigInteger.ModPow(pt, e, n);
Console.WriteLine("Encoded:  " + ct);

BigInteger dc = BigInteger.ModPow(ct, d, n);
Console.WriteLine("Decoded:  " + dc);

string decoded = ASCIIEncoding.ASCII.GetString(dc.ToByteArray());
Console.WriteLine("As ASCII: " + decoded);
}
}

Output:
Encoded:  8545729659809274764853392532557102329563535
Decoded:  173322416552962951144796590453843272
As ASCII: Hello, Rosetta!

## Common Lisp

In this example, the functions encode-string and decode-string are responsible for converting the string to an integer (which can be encoded) and back. They are not very important to the RSA algorithm, which happens in encode-rsa, decode-rsa, and mod-exp.

The string is encoded as follows: each character is converted into 2 digits based on ASCII value (subtracting 32, so that SPACE=00, and so on.) To decode we simply read every 2 digits from the given integer in order, adding 32 and converting back into characters.

(defparameter *n* 9516311845790656153499716760847001433441357)
(defparameter *e* 65537)
(defparameter *d* 5617843187844953170308463622230283376298685)

;; magic
(defun encode-string (message)
(parse-integer (reduce #'(lambda (x y) (concatenate 'string x y))
(loop for c across message collect (format nil "~2,'0d" (- (char-code c) 32))))))

;; sorcery
(defun decode-string (message) (coerce (loop for (a b) on
(loop for char across (write-to-string message) collect char)
by #'cddr collect (code-char (+ (parse-integer (coerce (list a b) 'string)) 32))) 'string))

;; ACTUAL RSA ALGORITHM STARTS HERE ;;

;; fast modular exponentiation: runs in O(log exponent)
;; acc is initially 1 and contains the result by the end
(defun mod-exp (base exponent modulus acc)
(if (= exponent 0) acc
(mod-exp (mod (* base base) modulus) (ash exponent -1) modulus
(if (= (mod exponent 2) 1) (mod (* acc base) modulus) acc))))

;; to encode a message, we first convert it to its integer form.
;; then, we raise it to the *e* power, modulo *n*
(defun encode-rsa (message)
(mod-exp (encode-string message) *e* *n* 1))

;; to decode a message, we raise it to *d* power, modulo *n*
;; and then convert it back into a string
(defun decode-rsa (message)
(decode-string (mod-exp message *d* *n* 1)))


Interpreter output (the star * represents the interpreter prompt):

* (load "rsa.lisp")

T
* (encode-rsa "Rosetta Code")

4330737636866106722999010287941987299297557
* (decode-rsa 4330737636866106722999010287941987299297557)

"Rosetta Code"


## D

This used the D module of the Modular Exponentiation Task.

Translation of: Go
void main() {
import std.stdio, std.bigint, std.algorithm, std.string, std.range,
modular_exponentiation;

immutable txt = "Rosetta Code";
writeln("Plain text:             ", txt);

// A key set big enough to hold 16 bytes of plain text in
// a single block (to simplify the example) and also big enough
// to demonstrate efficiency of modular exponentiation.
immutable BigInt n = "2463574872878749457479".BigInt *
"3862806018422572001483".BigInt;
immutable BigInt e = 2 ^^ 16 + 1;
immutable BigInt d = "5617843187844953170308463622230283376298685";

// Convert plain text to a number.
immutable txtN = reduce!q{ (a << 8) | uint(b) }(0.BigInt, txt);
if (txtN >= n)
return writeln("Plain text message too long.");
writeln("Plain text as a number: ", txtN);

// Encode a single number.
immutable enc = txtN.powMod(e, n);
writeln("Encoded:                ", enc);

// Decode a single number.
auto dec = enc.powMod(d, n);
writeln("Decoded:                ", dec);

// Convert number to text.
char[] decTxt;
for (; dec; dec >>= 8)
decTxt ~= (dec & 0xff).toInt;
writeln("Decoded number as text: ", decTxt.retro);
}

Output:
Plain text:             Rosetta Code
Plain text as a number: 25512506514985639724585018469
Encoded:                916709442744356653386978770799029131264344
Decoded:                25512506514985639724585018469
Decoded number as text: Rosetta Code

## Delphi

Translation of: Go

Thanks for Rudy Velthuis, BigIntegers library

program RSA_code;

{$APPTYPE CONSOLE} uses System.SysUtils, Velthuis.BigIntegers; type TRSA = record private n, e, d: BigInteger; class function PlainTextAsNumber(data: AnsiString): BigInteger; static; class function NumberAsPlainText(Num: BigInteger): AnsiString; static; public constructor Create(n, e, d: string); function Encode(data: AnsiString): string; function Decode(code: string): AnsiString; end; function EncodeRSA(data: AnsiString): string; var n, e, d, bb, ptn, etn, dtn: BigInteger; begin // a key set big enough to hold 16 bytes of plain text in // a single block (to simplify the example) and also big enough // to demonstrate efficiency of modular exponentiation. n := '9516311845790656153499716760847001433441357'; e := '65537'; d := '5617843187844953170308463622230283376298685'; for var c in data do begin bb := ord(c); ptn := (ptn shl 8) or bb; end; if BigInteger.Compare(ptn, n) >= 0 then begin Writeln('Plain text message too long'); exit; end; writeln('Plain text as a number:', ptn.ToString); writeln(ptn.ToString); // encode a single number etn := BigInteger.ModPow(ptn, e, n); Writeln('Encoded: ', etn.ToString); // decode a single number dtn := BigInteger.ModPow(etn, d, n); Writeln('Decoded: ', dtn.ToString); // convert number to text var db: AnsiString; var bff: BigInteger :=$FF;
while dtn.BitLength > 0 do
begin
db := ansichar((dtn and bff).AsInteger) + db;
dtn := dtn shr 8;
end;
Write('Decoded number as text:"', db, '"');
end;

const
pt = 'Rosetta Code';

{ TRSA }

constructor TRSA.Create(n, e, d: string);
begin
self.n := n;
self.e := e;
self.d := d;
end;

function TRSA.Decode(code: string): AnsiString;
var
etn, dtn: BigInteger;
begin
// decode a single number
etn := code;
dtn := BigInteger.ModPow(etn, d, n);
Result := NumberAsPlainText(dtn);
end;

function TRSA.Encode(data: AnsiString): string;
var
ptn: BigInteger;
begin
ptn := PlainTextAsNumber(data);

// encode a single number
Result := BigInteger.ModPow(ptn, e, n).ToString;
end;

class function TRSA.NumberAsPlainText(Num: BigInteger): AnsiString;
var
bff: BigInteger;
begin
// convert number to text
bff := $FF; Result := ''; while Num.BitLength > 0 do begin Result := ansichar((Num and bff).AsInteger) + Result; Num := Num shr 8; end; end; class function TRSA.PlainTextAsNumber(data: AnsiString): BigInteger; var c: AnsiChar; bb, n: BigInteger; begin Result := 0; n := '9516311845790656153499716760847001433441357'; for c in data do begin bb := ord(c); Result := (Result shl 8) or bb; end; if BigInteger.Compare(Result, n) >= 0 then raise Exception.Create('Plain text message too long'); end; var RSA: TRSA; Encoded: string; const n = '9516311845790656153499716760847001433441357'; e = '65537'; d = '5617843187844953170308463622230283376298685'; TEST_WORD = 'Rosetta Code'; begin RSA := TRSA.Create(n, e, d); Encoded := RSA.Encode(TEST_WORD); writeln('Plain text: ', TEST_WORD); writeln('Encoded: ', Encoded); writeln('Decoded: ', RSA.Decode(Encoded)); Readln; end.  Output: Plain text: Rosetta Code Encoded: 916709442744356653386978770799029131264344 Decoded: Rosetta Code ## Erlang Solution split into 2 modules, the mod module does the modulo aritmetic as per separate Rosetta Code entry. %%% @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)).  Running test: 8> rsa:test(). rsa:test(). true 9> ## F# //Nigel Galloway February 12th., 2018 let RSA n g l = bigint.ModPow(l,n,g) let encrypt = RSA 65537I 9516311845790656153499716760847001433441357I let m_in = System.Text.Encoding.ASCII.GetBytes "The magic words are SQUEAMISH OSSIFRAGE"|>Array.chunkBySize 16|>Array.map(Array.fold(fun n g ->(n*256I)+(bigint(int g))) 0I) let n = Array.map encrypt m_in let decrypt = RSA 5617843187844953170308463622230283376298685I 9516311845790656153499716760847001433441357I let g = Array.map decrypt n let m_out = Array.collect(fun n->Array.unfold(fun n->if n>0I then Some(byte(int (n%256I)),n/256I) else None) n|>Array.rev) g|>System.Text.Encoding.ASCII.GetString printfn "'The magic words are SQUEAMISH OSSIFRAGE' as numbers -> %A\nEncrypted -> %A\nDecrypted -> %A\nAs text -> %A" m_in n g m_out  Output: 'The magic words are SQUEAMISH OSSIFRAGE' as numbers -> [|112197201611743344895286521511035564832; 129529088517466560781735691575334293331; 23442989443532613|] Encrypted -> [|3493129515654757560886946157927565680562316; 5582490186309277335090560762784439391588703; 8700785834706594190338047528968122486721264|] Decrypted -> [|112197201611743344895286521511035564832; 129529088517466560781735691575334293331; 23442989443532613|] As text -> "The magic words are SQUEAMISH OSSIFRAGE"  ## FreeBASIC Translation of: C ' version 17-01-2017 ' compile with: fbc -s console #Include Once "gmp.bi" Dim As Mpz_ptr e, d, n, pt, ct e = Allocate(Len(__mpz_struct)) d = Allocate(Len(__mpz_struct)) n = Allocate(Len(__mpz_struct)) pt = Allocate(Len(__mpz_struct)) : mpz_init(pt) ct = Allocate(Len(__mpz_struct)) : mpz_init(ct) mpz_init_set_str(e, "65537", 10) mpz_init_set_str(d, "5617843187844953170308463622230283376298685", 10) mpz_init_set_str(n, "9516311845790656153499716760847001433441357", 10) Dim As ZString Ptr plaintext : plaintext = Allocate(1000) Dim As ZString Ptr text : text = Allocate(1000) *plaintext = "Rosetta Code" mpz_import(pt, Len(*plaintext), 1, 1, 0, 0, plaintext) If mpz_cmp(pt, n) > 0 Then GoTo clean_up mpz_powm(ct, pt, e, n) gmp_printf(!" Encoded: %Zd\n", ct) mpz_powm(pt, ct, d, n) gmp_printf(!" Decoded: %Zd\n", pt) mpz_export(text, NULL, 1, 1, 0, 0, pt) Print "As string: "; *text clean_up: DeAllocate(plaintext) : DeAllocate(text) mpz_clear(e) : mpz_clear(d) : mpz_clear(n) mpz_clear(pt) : mpz_clear(ct) ' empty keyboard buffer While Inkey <> "" : Wend Print : Print "hit any key to end program" Sleep End Output:  Encoded: 916709442744356653386978770799029131264344 Decoded: 25512506514985639724585018469 As string: Rosetta Code ## Go Note: see the crypto/rsa package included with Go for a full implementation. package main import ( "fmt" "math/big" ) func main() { var n, e, d, bb, ptn, etn, dtn big.Int pt := "Rosetta Code" fmt.Println("Plain text: ", pt) // a key set big enough to hold 16 bytes of plain text in // a single block (to simplify the example) and also big enough // to demonstrate efficiency of modular exponentiation. n.SetString("9516311845790656153499716760847001433441357", 10) e.SetString("65537", 10) d.SetString("5617843187844953170308463622230283376298685", 10) // convert plain text to a number for _, b := range []byte(pt) { ptn.Or(ptn.Lsh(&ptn, 8), bb.SetInt64(int64(b))) } if ptn.Cmp(&n) >= 0 { fmt.Println("Plain text message too long") return } fmt.Println("Plain text as a number:", &ptn) // encode a single number etn.Exp(&ptn, &e, &n) fmt.Println("Encoded: ", &etn) // decode a single number dtn.Exp(&etn, &d, &n) fmt.Println("Decoded: ", &dtn) // convert number to text var db [16]byte dx := 16 bff := big.NewInt(0xff) for dtn.BitLen() > 0 { dx-- db[dx] = byte(bb.And(&dtn, bff).Int64()) dtn.Rsh(&dtn, 8) } fmt.Println("Decoded number as text:", string(db[dx:])) }  Output: Plain text: Rosetta Code Plain text as a number: 25512506514985639724585018469 Encoded: 916709442744356653386978770799029131264344 Decoded: 25512506514985639724585018469 Decoded number as text: Rosetta Code  ## Haskell module RSAMaker where import Data.Char ( chr ) encode :: String -> [Integer] encode s = map (toInteger . fromEnum ) s rsa_encode :: Integer -> Integer -> [Integer] -> [Integer] rsa_encode n e numbers = map (\num -> mod ( num ^ e ) n ) numbers rsa_decode :: Integer -> Integer -> [Integer] -> [Integer] rsa_decode d n ciphers = map (\c -> mod ( c ^ d ) n ) ciphers decode :: [Integer] -> String decode encoded = map ( chr . fromInteger ) encoded divisors :: Integer -> [Integer] divisors n = [m | m <- [1..n] , mod n m == 0 ] isPrime :: Integer -> Bool isPrime n = divisors n == [1,n] totient :: Integer -> Integer -> Integer totient prime1 prime2 = (prime1 - 1 ) * ( prime2 - 1 ) myE :: Integer -> Integer myE tot = head [n | n <- [2..tot - 1] , gcd n tot == 1] myD :: Integer -> Integer -> Integer -> Integer myD e n phi = head [d | d <- [1..n] , mod ( d * e ) phi == 1] main = do putStrLn "Enter a test text!" text <- getLine let primes = take 90$ filter isPrime [1..]
p1     = last primes
p2     = last $init primes tot = totient p1 p2 e = myE tot n = p1 * p2 rsa_encoded = rsa_encode n e$ encode text
d  =  myD e n tot
encrypted = concatMap show rsa_encoded
decrypted = decode $rsa_decode d n rsa_encoded putStrLn ("Encrypted: " ++ encrypted ) putStrLn ("And now decrypted: " ++ decrypted )  Output: Enter a test text! Rosettacode Encrypted: 65646265111107071564791028551028551458331139502651145035156479 And now decrypted: Rosettacode  ## Icon and Unicon Please read talk pages. procedure main() # rsa demonstration n := 9516311845790656153499716760847001433441357 e := 65537 d := 5617843187844953170308463622230283376298685 b := 2^integer(log(n,2)) # for blocking write("RSA Demo using\n n = ",n,"\n e = ",e,"\n d = ",d,"\n b = ",b) every m := !["Rosetta Code", "Hello Word!", "This message is too long.", repl("x",*decode(n+1))] do { write("\nMessage = ",image(m)) write( "Encoded = ",m := encode(m)) if m := rsa(m,e,n) then { # unblocked write( "Encrypt = ",m) write( "Decrypt = ",m := rsa(m,d,n)) } else { # blocked every put(C := [], rsa(!block(m,b),e,n)) writes("Encrypt = ") ; every writes(!C," ") ; write() every put(P := [], rsa(!C,d,n)) writes("Decrypt = ") ; every writes(!P," ") ; write() write("Unblocked = ",m := unblock(P,b)) } write( "Decoded = ",image(decode(m))) } end procedure mod_power(base, exponent, modulus) # fast modular exponentation result := 1 while exponent > 0 do { if exponent % 2 = 1 then result := (result * base) % modulus exponent /:= 2 base := base ^ 2 % modulus } return result end procedure rsa(text,e,n) # return rsa encryption of numerically encoded message; fail if text < n return mod_power(text,e,text < n) end procedure encode(text) # numerically encode ascii text as int every (message := 0) := ord(!text) + 256 * message return message end procedure decode(message) # numerically decode int to ascii text text := "" while text ||:= char((0 < message) % 256) do message /:= 256 return reverse(text) end procedure block(m,b) # break lg int into blocks of size b M := [] while push(M, x := (0 < m) % b) do m /:= b return M end procedure unblock(M,b) # reassemble blocks of size b into lg int every (m := 0) := !M + b * m return m end  Output: RSA Demo using n = 9516311845790656153499716760847001433441357 e = 65537 d = 5617843187844953170308463622230283376298685 b = 5575186299632655785383929568162090376495104 Message = "Rosetta Code" Encoded = 25512506514985639724585018469 Encrypt = 916709442744356653386978770799029131264344 Decrypt = 25512506514985639724585018469 Decoded = "Rosetta Code" Message = "Hello Word!" Encoded = 87521618088882533792113697 Encrypt = 1798900477268307339588642263628429901019383 Decrypt = 87521618088882533792113697 Decoded = "Hello Word!" Message = "This message is too long." Encoded = 529836718428469753460978059376661024804668788418205881100078 Encrypt = 3376966937987363040878203966915676619521252 7002174816151673360605669161609885530980579 Decrypt = 95034800624219541 4481988526688939374478063610382714873472814 Unblocked = 529836718428469753460978059376661024804668788418205881100078 Decoded = "This message is too long." Message = "xxxxxxxxxxxxxxxxxx" Encoded = 10494468328720293243075632128305111296931960 Encrypt = 1 829820657892505002815717051746917810425013 Decrypt = 1 4919282029087637457691702560143020920436856 Unblocked = 10494468328720293243075632128305111296931960 Decoded = "xxxxxxxxxxxxxxxxxx" ## J Note, for an implementation with blocking (and a much smaller key) see [1]  N=: 9516311845790656153499716760847001433441357x E=: 65537x D=: 5617843187844953170308463622230283376298685x ] text=: 'Rosetta Code' Rosetta Code ] num=: 256x #. a.i.text 25512506514985639724585018469 num >: N NB. check if blocking is necessary (0 means no) 0 ] enc=: N&|@^&E num 916709442744356653386978770799029131264344 ] dec=: N&|@^&D enc 25512506514985639724585018469 ] final=: a. {~ 256x #.inv dec Rosetta Code  Note: as indicated at http://www.jsoftware.com/help/dictionary/special.htm, N&|@^ does not bother with creating the exponential intermediate result. ## Java public static void main(String[] args) { /* This is probably not the best method...or even the most optimized way...however it works since n and d are too big to be ints or longs This was also only tested with 'Rosetta Code' and 'Hello World' It's also pretty limited on plainText size (anything bigger than the above will fail) */ BigInteger n = new BigInteger("9516311845790656153499716760847001433441357"); BigInteger e = new BigInteger("65537"); BigInteger d = new BigInteger("5617843187844953170308463622230283376298685"); Charset c = Charsets.UTF_8; String plainText = "Rosetta Code"; System.out.println("PlainText : " + plainText); byte[] bytes = plainText.getBytes(); BigInteger plainNum = new BigInteger(bytes); System.out.println("As number : " + plainNum); BigInteger Bytes = new BigInteger(bytes); if (Bytes.compareTo(n) == 1) { System.out.println("Plaintext is too long"); return; } BigInteger enc = plainNum.modPow(e, n); System.out.println("Encoded: " + enc); BigInteger dec = enc.modPow(d, n); System.out.println("Decoded: " + dec); String decText = new String(dec.toByteArray(), c); System.out.println("As text: " + decText); }  ### Alternative solution - convert to byte array then to BigInteger: import java.math.BigInteger; import java.util.Random; public class rsaCode { public static void main(String[]args){ //Size of primes int BIT_LENGTH = 4096; Random rand = new Random(); //Generate primes and other necessary values BigInteger p = BigInteger.probablePrime(BIT_LENGTH / 2, rand); BigInteger q = BigInteger.probablePrime(BIT_LENGTH / 2, rand); BigInteger n = p.multiply(q); BigInteger phi = p.subtract(BigInteger.valueOf(1)).multiply(q.subtract(BigInteger.valueOf(1))); BigInteger e; BigInteger d; do { e = new BigInteger(phi.bitLength(), rand); } while (e.compareTo(BigInteger.valueOf(1)) <= 0 || e.compareTo(phi) >= 0 || !e.gcd(phi).equals(BigInteger.valueOf(1))); d = e.modInverse(phi); //Convert message to byte array and then to a BigInteger BigInteger message = new BigInteger("Hello World! - From Rosetta Code".getBytes()); BigInteger cipherText = message.modPow(e, n); BigInteger decryptedText = cipherText.modPow(d, n); System.out.println("Message: " + message); System.out.println("Prime 1: " + p); System.out.println("Prime 2: " + q); System.out.println("Phi p1 * p2: " + phi); System.out.println("p1 * p2: " + n); System.out.println("Public key: " + e); System.out.println("Private key: " + d); System.out.println("Ciphertext: " + cipherText); System.out.println("Decrypted message(number form): " + decryptedText); //Convert BigInteger to byte array then to String System.out.println("Decrypted message(string): " + new String(decryptedText.toByteArray())); } }  Output: Message: 32745724963520459128167607565116331713761641910444445962992228853365120918629 Prime 1: 19236082984974163990952162748173714068049389803543876908591023542434008581726901827775282361343539027357627272183474081300821830594665417249999421476471444612045376319151307819458083226682409477411524022807762467877933511178646356355356721278159329226472299570078614830307335816363768128995044913560110586093645150502887099142708810425659608200567299323058631080348801201371891024721397456687923823598994147721120698707559677560198153919129668778208924015134166710369131053236474139106999881687335966483688956493993503452781613364724067448118712996621139377805320411264206346354690147839668674568385780953439324061827 Prime 2: 17979329033868078796981009025342087899891110883452413861085335446537232859657584956199529432436753743100057017453176958641563538906032576785591580481524960405796753482749211728790206586594224271803757384485305551705171358489679998051039658612346599741622638134691446099105450988669667758655426868708523266671158484337114750111466361420411180131539156350206088712722069263680478398363920580976741655559629459204726096055804150577131670026585406567505359058210528861172448235138919989250928848721850118962177309953951127503325970279819172102106621073790956566530104217789478786634899278802600883073967446382373644250257 Phi p1 * p2: 345851865309641725173652598401242058900566653910908938475312921380066114219124630361012048649340940349701681628058518630535276222954695692233147670047674008455691941733381178283159719985229687501019788350058464636500196522521346408404768715926660411771389935137989577763538670548607053837834611583177259789432946335846775973340201166384784256821490809726897985505537384164828673170953111807028144501567927080933277305734847328999516054393161305269105612852357562678721346577533872335946654435942111678921979428611842390495534195723208415846942969477148117377158823876687230703157218761840307200229212313941422321195051355226377851222163854147510935258095666300221082823130614374400292194084084333352100386386600651725502133645428505729406848959785973133150969119775159790464605612595258587741654065352840099419921194642121733262659814580729725479879031162109276830902575494117198577188807279359692336933181285455336126206772237317229756148090589146421446485136412385682723586947367965091078676401379642267664924847358476052429919297388821038943132363371365451994109675932621652038431036384121653367832798502022879709943736316295610602665722391298109723459179009548775436875778616030750642493163185541967992915955989097200396360327456 p1 * p2: 345851865309641725173652598401242058900566653910908938475312921380066114219124630361012048649340940349701681628058518630535276222954695692233147670047674008455691941733381178283159719985229687501019788350058464636500196522521346408404768715926660411771389935137989577763538670548607053837834611583177259789432946335846775973340201166384784256821490809726897985505537384164828673170953111807028144501567927080933277305734847328999516054393161305269105612852357562678721346577533872335946654435942111678921979428611842390495534195723208415846942969477148117377158823876687230703157218761840307200229212313941422321195088570638396693464951787319284451060063606800908079113900290733389263435525468820136075198180380944495959817935065156769349234329286671127186560121733156195482447742397159107289902355166116733169136476049414801282242919450398051834285427541999782759870670431821968638118220066164725772820831757237604760059537040952069757997344764318267517273468518841355988306740438835556131045824464960305329590326517099659355766092152184867080462187317080527339823959005966347609972615672497047496190727232432065795389602582743555233621829974942652963009404343619187532820114040659804327626152774968610262473598342324536209328639539 Public key: 193579940416764762032781091221143757801413904551984303885407040026321908965197971867687112770438003048686335467825121571041736775396425178706013366881005246973351188647629560663037810331045292388828497048500842585316962463760854316963245076613682542629780184301654965436793943481122744003077197338402843407520722504896640189710671321124115630104805979401188537742997889316213029383963089439143905748656345056757946693819634971714186428073990059096062771479710217863926284515341443931092854041306087536208153864059633604334787035313177701948799425284530371404018395643074910533253129726213643193854656336232925658951811658248314007700619000559672273590950586652099230800733098520827807590026231300954320448333065980082309254977488081625340716095420728271744505284703847569933308644755417715559811180764086973488668246118187715534944871349843316776293048731714297576612062481854912918664986385922123428018736434561518771685854566894264705876397229699222060976725454055036743075458563364307745597456824543609383372429743649103452964024219143956601668222718087847554469024737873441872945480724976527827721060219946775750776694792509727838512629661637130805269017888622785492890741411798087685393616016451666522802755139926311245306229041 Private key: 219036175169203544315490853999486820834618560996816043411987210664248102884377915567272406198057873662330646577076795355640818453754512006948660586443609679011052139043660581484406998357727395227184641632029033848943507736672039637904589489626534363470520344933214278535075666039716685014892551021861132000517572948046870070641407067319704943583671179776670601874690644590228314092730047599467716558027443683253737751585758991176998516378325292822247842855150355043416320003512453741917219948896684868393696007264717697967091707113384847407621846752255898098912112528872599250195047315005253431619786863325536528182598792588704861531564144935586585480994816595663012912390628905402008731003235520424397350241617043412307761990786711273480686856614955176903059108533627807572077696388568308581773433971401736018773723311485647784158083000913638874130114372027510789163873963163280849749880619112666293979830817843596818936327354256104400652111217685523782967475741729222155996255475772715455781288940265345618022791173798222315117453828105848080873781770073614996444414329484314974671715475986173113744470587849073918357399130907446602201256421236363869748993676713228862789197394591401079130691347928057018496258825068434610372879057 Ciphertext: 751802077965963630324549365263121640277689482825128224616526073196054301029392106215761462171255492597878612184351606323296123153021421277191908278007450520130118453205040455128556435393691729542297181525367763857641211099694558032110059874156910175402903627759175935900055257215548262301358748652386044838566618270488287858766869634274195146217020325014127218881028662056032737660265341221411932659292844178938078127559747544470249139600492686861162904399444542749100026596955221740375230453344396141534329779530430928001439479395156999496805099234924399049952788417632216512939528956109220706809364166228124854558311835437452608371779980805227059349785343399382366770619320980575920634550115026075376299109862825119723058827075167366432962208711425854647134395509013075755502864140908914499073909257771585668395445413050111450415828406012614877021632277223689796818643848597729370856433117827304201297547912764020996146635163811573223631120712910083451904964228318515972103019499763177402019351409722785807448842923761649884358555226283418059099812653679780193380193208207168410802721122329377467373427784070234188000453256581358361888268040964222190110448131244743936030485464773996914221120717918807573232494076059754978713933 Decrypted message(number form): 32745724963520459128167607565116331713761641910444445962992228853365120918629 Decrypted message(string): Hello World! - From Rosetta Code ## jq Adapted from Wren after correcting for a bug in the decode-to-text algorithm as of 2023-02-07 Works with gojq, the Go implementation of jq, and with fq The following assumes unbounded-precision integer arithmetic. # If$j is 0, then an error condition is raised;
# otherwise, assuming infinite-precision integer arithmetic,
# if the input and $j are integers, then the result will be an integer. def idivide($j): (. - (. % $j)) /$j ;

# shift left
def left8: 256 * .;

# shift right
def right8: idivide(256);

def modPow($b;$e; $m): if ($m == 1) then 0
else {b: ($b %$m), $e, r: 1} | until( .e <= 0 or .return; if .b == 0 then .return = 0 else if .e % 2 == 1 then .r = (.r * .b) %$m else . end
| .e |= idivide(2)
| .b = (.b * .b) % $m end) | if .return then .return else .r end end; # Convert the input integer to a stream of 8-bit integers, most significant first def bytes: def stream: recurse(if . >= 256 then ./256|floor else empty end) | . % 256 ; [stream] | reverse ; # convert ASCII plain text to a number def ptn: reduce explode[] as$b (0; left8 + $b); def n: 9516311845790656153499716760847001433441357; def e: 65537; def d: 5617843187844953170308463622230283376298685; # encode a single number def etn: . as$ptn | modPow($ptn; e; n); # decode a single number def dtn: . as$etn | modPow($etn; d; n); def decode: [recurse(right8 | select(.>0)) % 256] | reverse | implode; def task($pt):
($pt|ptn) as$ptn
| if ($ptn >= n) then "Plain text message too long" | error else . end | ($ptn|etn) as $etn | ($etn|dtn) as $dtn | ($ptn|decode) as $text | "Plain text: : \($pt)",
"Plain text as a number : \($ptn)", "Encoded : \($etn)",
"Decoded                : \($dtn)", "Decoded number as text : \($text)"
;

"",
task("Hello, Rosetta!!!!")

Invocation: gojq -nr -f rsa-code.jq

Output:
Plain text:            : Rosetta Code
Plain text as a number : 25512506514985639724585018469
Encoded                : 916709442744356653386978770799029131264344
Decoded                : 25512506514985639724585018469
Decoded number as text : Rosetta Code

Plain text:            : Hello, Rosetta!!!!
Plain text as a number : 6306597225792201544376884997106189304144161
Encoded                : 3763881655974029977658577646869029457590896
Decoded                : 6306597225792201544376884997106189304144161
Decoded number as text : Hello, Rosetta!!!!


## Julia

Works with: Julia version 0.6
function rsaencode(clearmsg::AbstractString, nmod::Integer, expub::Integer)
bytes = parse(BigInt, "0x" * bytes2hex(collect(UInt8, clearmsg)))
return powermod(bytes, expub, nmod)
end

decoded = powermod(encoded, dsecr, nmod)
return join(Char.(hex2bytes(hex(decoded))))
end

msg = "Rosetta Code."
nmod = big"9516311845790656153499716760847001433441357"
expub = 65537
dsecr = big"5617843187844953170308463622230283376298685"

encoded = rsaencode(msg, nmod, expub)
println("\n# $msg\n -> ENCODED:$encoded\n -> DECODED: $decoded")  Output: # Rosetta Code. -> ENCODED: 2440331969632134446717000067136916252596373 -> DECODED: Rosetta Code. ## Kotlin // version 1.1.4-3 import java.math.BigInteger fun main(args: Array<String>) { val n = BigInteger("9516311845790656153499716760847001433441357") val e = BigInteger("65537") val d = BigInteger("5617843187844953170308463622230283376298685") val c = Charsets.UTF_8 val plainText = "Rosetta Code" println("PlainText :$plainText")
val bytes = plainText.toByteArray(c)
val plainNum = BigInteger(bytes)
println("As number : $plainNum") if (plainNum > n) { println("Plaintext is too long") return } val enc = plainNum.modPow(e, n) println("Encoded :$enc")

val dec = enc.modPow(d, n)
println("Decoded   : $dec") val decText = dec.toByteArray().toString(c) println("As text :$decText")
}

Output:
PlainText : Rosetta Code
As number : 25512506514985639724585018469
Encoded   : 916709442744356653386978770799029131264344
Decoded   : 25512506514985639724585018469
As text   : Rosetta Code


## Mathematica/Wolfram Language

Does not support blocking.

toNumPlTxt[s_] := FromDigits[ToCharacterCode[s], 256];
fromNumPlTxt[plTxt_] := FromCharacterCode[IntegerDigits[plTxt, 256]];
enc::longmess = "Message '' is too long for n = .";
enc[n_, _, mess_] /;
toNumPlTxt[mess] >= n := (Message[enc::longmess, mess, n]; Failed); enc[n_, e_, mess_] := PowerMod[toNumPlTxt[mess], e, n]; dec[n_, d_, en_] := fromNumPlTxt[PowerMod[en, d, n]]; text = "The cake is a lie!"; n = 9516311845790656153499716760847001433441357; e = 65537; d = 5617843187844953170308463622230283376298685; en = enc[n, e, text]; de = dec[n, d, en]; Print["Text: '" <> text <> "'"]; Print["n = " <> IntegerString[n]]; Print["e = " <> IntegerString[e]]; Print["d = " <> IntegerString[d]]; Print["Numeric plaintext: " <> IntegerString[toNumPlTxt[text]]]; Print["Encoded: " <> IntegerString[en]]; Print["Decoded: '" <> de <> "'"];  Output: Text: 'The cake is a lie!' n = 9516311845790656153499716760847001433441357 e = 65537 d = 5617843187844953170308463622230283376298685 Numeric plaintext: 7352955804624388987810264523908743852287265 Encoded: 199505409518408949879682159958576932863989 Decoded: 'The cake is a lie!' ## Nim import strutils, streams, strformat # nimble install stint import stint const messages = ["PPAP", "I have a pen, I have a apple\nUh! Apple-pen!", "I have a pen, I have pineapple\nUh! Pineapple-pen!", "Apple-pen, pineapple-pen\nUh! Pen-pineapple-apple-pen\nPen-pineapple-apple-pen\nDance time!", "\a\0"] const n = u256("9516311845790656153499716760847001433441357") e = u256("65537") d = u256("5617843187844953170308463622230283376298685") proc pcount(s: string, c: char): int{.inline.} = for ch in s: if ch != c: break result+=1 func powmodHexStr(s: string, key, divisor: UInt256): string{.inline.} = toHex(powmod(UInt256.fromHex(s), key, divisor)) proc translate(hexString: string, key, divisor: UInt256, encrypt = true): string = var strm = newStringStream(hexString) chunk, residue, tempChunk: string let chunkSize = len(toHex(divisor)) while true: tempChunk = strm.peekStr(chunkSize-int(encrypt)*3) if len(chunk) > 0: if len(tempChunk) == 0: if encrypt: result&=powmodHexStr(pcount(chunk, '0').toHex(2)&align(chunk, chunkSize-3, '0'), key, divisor) else: tempChunk = align(powmodHexStr(chunk, key, divisor), chunkSize-1, '0') residue = tempChunk[2..^1].strip(trailing = false, chars = {'0'}) result&=align(residue, fromHex[int](tempChunk[0..1])+len(residue), '0') break result&=align(powmodHexStr(chunk, key, divisor), chunkSize-3+int( encrypt)*3, '0') discard strm.readStr(chunkSize-int(encrypt)*3) chunk = tempChunk strm.close() for message in messages: echo(&"plaintext:\n{message}") var numPlaintext = message.toHex() echo(&"numerical plaintext in hex:\n{numPlaintext}") var ciphertext = translate(numPlaintext, e, n) echo(&"ciphertext is: \n{ciphertext}") var deciphertext = translate(ciphertext, d, n, false) echo(&"deciphered numerical plaintext in hex is:\n{deciphertext}") echo(&"deciphered plaintext is:\n{parseHexStr(deciphertext)}\n\n")  Output: plaintext: PPAP numerical plaintext in hex: 50504150 ciphertext is: 6c55b71c718b8921555eaa9754b7bfd7018b deciphered numerical plaintext in hex is: 50504150 deciphered plaintext is: PPAP plaintext: I have a pen, I have a apple Uh! Apple-pen! numerical plaintext in hex: 49206861766520612070656E2C204920686176652061206170706C650A556821204170706C652D70656E21 ciphertext is: 4614caba02ac33654130c10485dcceeec4a2443f4bffb46e389c2705d4ebd7ac7185a206ae0294575f283841baad236fa90d5c5536b deciphered numerical plaintext in hex is: 49206861766520612070656e2c204920686176652061206170706c650a556821204170706c652d70656e21 deciphered plaintext is: I have a pen, I have a apple Uh! Apple-pen! plaintext: I have a pen, I have pineapple Uh! Pineapple-pen! numerical plaintext in hex: 49206861766520612070656E2C204920686176652070696E656170706C650A5568212050696E656170706C652D70656E21 ciphertext is: 4614caba02ac33654130c10485dcceeec4a21c96dd7a5048e412a16c65e274609964ffb14231b9d6a70a59380d4bbaef3c40e88afa3d deciphered numerical plaintext in hex is: 49206861766520612070656e2c204920686176652070696e656170706c650a5568212050696e656170706c652d70656e21 deciphered plaintext is: I have a pen, I have pineapple Uh! Pineapple-pen! plaintext: Apple-pen, pineapple-pen Uh! Pen-pineapple-apple-pen Pen-pineapple-apple-pen Dance time! numerical plaintext in hex: 4170706C652D70656E2C2070696E656170706C652D70656E0A5568212050656E2D70696E656170706C652D6170706C652D70656E0A50656E2D70696E656170706C652D6170706C652D70656E0A44616E63652074696D6521 ciphertext is: 5d733e3979b0b43207dace453c3ec65baaff54571a3127be4ccd120dff94fb2e1b9258d6067cee2669e868ee4390c5e16f61016a171f6585ad4cd58ca3335bc9faa96da943bfedad0dd0ac7cbc83a256bf9f6f65d755865aed232e1e0a467512a6744f3f470ee283c8b4e2e5 deciphered numerical plaintext in hex is: 4170706c652d70656e2c2070696e656170706c652d70656e0a5568212050656e2d70696e656170706c652d6170706c652d70656e0a50656e2d70696e656170706c652d6170706c652d70656e0a44616e63652074696d6521 deciphered plaintext is: Apple-pen, pineapple-pen Uh! Pen-pineapple-apple-pen Pen-pineapple-apple-pen Dance time! plaintext: (shell terminal cannot display "\a\0") numerical plaintext in hex: 0700 ciphertext is: 2177c0b1865ac16e47807e4f4d82e421bbdf deciphered numerical plaintext in hex is: 0700 deciphered plaintext is: (shell terminal cannot display "\a\0")  ## PARI/GP stigid(V,b)=subst(Pol(V),'x,b); \\ inverse function digits(...) n = 9516311845790656153499716760847001433441357; e = 65537; d = 5617843187844953170308463622230283376298685; text = "Rosetta Code" inttext = stigid(Vecsmall(text),256) \\ message as an integer encoded = lift(Mod(inttext, n) ^ e) \\ encrypted message decoded = lift(Mod(encoded, n) ^ d) \\ decrypted message message = Strchr(digits(decoded, 256)) \\ readable message Output: text: "Rosetta Code" inttext: 25512506514985639724585018469 encoded: 916709442744356653386978770799029131264344 decoded: 25512506514985639724585018469 message: "Rosetta Code"  If inttext is equal or greater than b = 2^(log(n)/log(2)\1) use block = inttext % b; inttext /= b; to break inttext into blocks and encode piece by piece. Decode in reverse order. As a check: it's easy to crack this weak encrypted message without knowing secret key 'd' f = factor(n); \\ factorize public key 'n' crack = Strchr(digits(lift(Mod(encoded,n) ^ lift(Mod(1,(f[1,1]-1)*(f[2,1]-1)) / e)),256)) Output: crack: "Rosetta Code" ## Perl Translation of: Raku use bigint;n = 9516311845790656153499716760847001433441357;
$e = 65537;$d = 5617843187844953170308463622230283376298685;

package Message {
my @alphabet;
push @alphabet, $_ for 'A' .. 'Z', ' '; my$rad = +@alphabet;
$code{$alphabet[$_]} =$_ for 0..$rad-1; sub encode { my($t) = @_;
my $cnt = my$sum = 0;
for (split '', reverse $t) {$sum += $code{$_} * $rad**$cnt;
$cnt++; }$sum;
}

sub decode {
my($n) = @_; my(@i); while () { push @i,$n % $rad; last if$n < $rad;$n = int $n /$rad;
}
reverse join '', @alphabet[@i];
}

sub expmod {
my($a,$b, $n) = @_; my$c = 1;
do {
($c *=$a) %= $n if$b % 2;
($a *=$a) %= $n; } while ($b = int $b/2);$c;
}

}

my $secret_message = "ROSETTA CODE";$numeric_message  = Message::encode $secret_message;$numeric_cipher   = Message::expmod $numeric_message,$e, $n;$text_cipher      = Message::decode $numeric_cipher;$numeric_cipher2  = Message::encode $text_cipher;$numeric_message2 = Message::expmod $numeric_cipher2,$d, $n;$secret_message2  = Message::decode $numeric_message2; print <<"EOT"; Secret message is$secret_message
Secret message in integer form is $numeric_message After exponentiation with public exponent we get:$numeric_cipher
This turns into the string $text_cipher If we re-encode it in integer form we get$numeric_cipher2
After exponentiation with SECRET exponent we get: $numeric_message2 This turns into the string$secret_message2
EOT

Output:
Secret message is ROSETTA CODE
Secret message in integer form is 97525102075211938
After exponentiation with public exponent we get: 8326171774113983822045243488956318758396426
This turns into the string ZULYDCEZOWTFXFRRNLIMGNUPHVCJSX
If we re-encode it in integer form we get 8326171774113983822045243488956318758396426
After exponentiation with SECRET exponent we get: 97525102075211938
This turns into the string ROSETTA CODE

## Phix

Library: Phix/mpfr
Translation of: C
without javascript_semantics
include builtins/mpfr.e

mpz n = mpz_init("9516311845790656153499716760847001433441357"),
e = mpz_init("65537"),
d = mpz_init("5617843187844953170308463622230283376298685"),
pt = mpz_init(),
ct = mpz_init()

string plaintext = "Rossetta Code" -- matches C/zkl
--                 "Rosetta Code" -- matches D/FreeBasic/Go/Icon/J/Kotlin/Seed7.

mpz_import(pt, length(plaintext), 1, 1, 0, 0, plaintext)

if mpz_cmp(pt, n)>0 then ?9/0 end if

mpz_powm(ct, pt, e, n);
printf(1,"Encoded:   %s\n", {mpz_get_str(ct)})

mpz_powm(pt, ct, d, n);
printf(1,"Decoded:   %s\n", {mpz_get_str(pt)})

integer size =floor((mpz_sizeinbase(pt,2)+7)/8)
atom pMem = allocate(size,true)
integer count = mpz_export(pMem, 1, 1, 0, 0, pt)
if count>size then ?9/0 end if

printf(1,"As String: %s\n", {peek({pMem,count})})

{pt, ct, n, e, d} = mpz_free({pt, ct, n, e, d})


(mpz_import() and mpz_export() are not supported under pwa/p2js)

Output:
Encoded:   5278143020249600501803788468419399384934220
Decoded:   6531201733672758787904906421349
As String: Rossetta Code


## PicoLisp

PicoLisp comes with an RSA library:

### This is a copy of "lib/rsa.l" ###

# Generate long random number
(de longRand (N)
(use (R D)
(while (=0 (setq R (abs (rand)))))
(until (> R N)
(unless (=0 (setq D (abs (rand))))
(setq R (* R D)) ) )
(% R N) ) )

# X power Y modulus N
(de **Mod (X Y N)
(let M 1
(loop
(when (bit? 1 Y)
(setq M (% (* M X) N)) )
(T (=0 (setq Y (>> 1 Y)))
M )
(setq X (% (* X X) N)) ) ) )

# Probabilistic prime check
(de prime? (N)
(and
(> N 1)
(bit? 1 N)
(let (Q (dec N)  K 0)
(until (bit? 1 Q)
(setq
Q  (>> 1 Q)
K  (inc K) ) )
(do 50
(NIL (_prim? N Q K))
T ) ) ) )

# (Knuth Vol.2, p.379)
(de _prim? (N Q K)
(use (X J Y)
(while (> 2 (setq X (longRand N))))
(setq
J 0
Y (**Mod X Q N) )
(loop
(T
(or
(and (=0 J) (= 1 Y))
(= Y (dec N)) )
T )
(T
(or
(and (> J 0) (= 1 Y))
(<= K (inc 'J)) )
NIL )
(setq Y (% (* Y Y) N)) ) ) )

# Find a prime number with Len' digits
(de prime (Len)
(let P (longRand (** 10 (*/ Len 2 3)))
(unless (bit? 1 P)
(inc 'P) )
(until (prime? P)  # P: Prime number of size 2/3 Len
(inc 'P 2) )
# R: Random number of size 1/3 Len
(let (R (longRand (** 10 (/ Len 3)))  K (+ R (% (- P R) 3)))
(when (bit? 1 K)
(inc 'K 3) )
(until (prime? (setq R (inc (* K P))))
(inc 'K 6) )
R ) ) )

# Generate RSA key
(de rsaKey (N)  #> (Encrypt . Decrypt)
(let (P (prime (*/ N 5 10))  Q (prime (*/ N 6 10)))
(cons
(* P Q)
(/
(inc (* 2 (dec P) (dec Q)))
3 ) ) ) )

# Encrypt a list of characters
(de encrypt (Key Lst)
(let Siz (>> 1 (size Key))
(make
(while Lst
(let N (char (pop 'Lst))
(while (> Siz (size N))
(setq N (>> -16 N))
(inc 'N (char (pop 'Lst))) )
(link (**Mod N 3 Key)) ) ) ) ) )

# Decrypt a list of numbers
(de decrypt (Keys Lst)
(mapcan
'((N)
(let Res NIL
(setq N (**Mod N (cdr Keys) (car Keys)))
(until (=0 N)
(push 'Res (char (& (dec (** 2 16)) N)))
(setq N (>> 16 N)) )
Res ) )
Lst ) )
### End of "lib/rsa.l" ###

# Generate 100-digit keys (private . public)
: (setq Keys (rsaKey 100))
-> (14394597526321726957429995133376978449624406217727317004742182671030....

# Encrypt
: (setq CryptText
(encrypt (car Keys)
(chop "The quick brown fox jumped over the lazy dog's back") ) )
-> (72521958974980041245760752728037044798830723189142175108602418861716...

# Decrypt
: (pack (decrypt Keys CryptText))
-> "The quick brown fox jumped over the lazy dog's back"

## PowerShell

Translation of: C#
$n = [BigInt]::Parse("9516311845790656153499716760847001433441357")$e = [BigInt]::new(65537)
$d = [BigInt]::Parse("5617843187844953170308463622230283376298685")$plaintextstring = "Hello, Rosetta!"
$plaintext = [Text.ASCIIEncoding]::ASCII.GetBytes($plaintextstring)
[BigInt]$pt = [BigInt]::new($plaintext)
if ($n -lt$pt) {throw "$n =$n < $pt = $pt"}
$ct = [BigInt]::ModPow($pt, $e,$n)
"Encoded:  $ct"$dc = [BigInt]::ModPow($ct,$d, $n) "Decoded:$dc"
$decoded = [Text.ASCIIEncoding]::ASCII.GetString($dc.ToByteArray())
"As ASCII: $decoded"  Output: Encoded: 8545729659809274764853392532557102329563535 Decoded: 173322416552962951144796590453843272 As ASCII: Hello, Rosetta!  ## Python import binascii n = 9516311845790656153499716760847001433441357 # p*q = modulus e = 65537 d = 5617843187844953170308463622230283376298685 message='Rosetta Code!' print('message ', message) hex_data = binascii.hexlify(message.encode()) print('hex data ', hex_data) plain_text = int(hex_data, 16) print('plain text integer ', plain_text) if plain_text > n: raise Exception('plain text too large for key') encrypted_text = pow(plain_text, e, n) print('encrypted text integer ', encrypted_text) decrypted_text = pow(encrypted_text, d, n) print('decrypted text integer ', decrypted_text) print('message ', binascii.unhexlify(hex(decrypted_text)[2:]).decode()) # [2:] slicing, to strip the 0x part  Output: message Rosetta Code! hex data b'526f736574746120436f646521' plain text integer 6531201667836323769493764728097 encrypted text integer 5307878626309103053766094186556322974789734 decrypted text integer 6531201667836323769493764728097 message Rosetta Code!  ## Racket This implementation does key generation and demonstrates digital signature as a freebie. Thanks again to the wonderful math/number-theory package (distributed as standard). Cutting messages into blocks has not been done. #lang racket (require math/number-theory) (define-logger rsa) (current-logger rsa-logger) ;; -| STRING TO NUMBER MAPPING |---------------------------------------------------------------------- (define (bytes->number B) ; We'll need our data in numerical form .. (for/fold ((rv 0)) ((b B)) (+ b (* rv 256)))) (define (number->bytes N) ; .. and back again (define (inr n b) (if (zero? n) b (inr (quotient n 256) (bytes-append (bytes (modulo n 256)) b)))) (inr N (bytes))) ;; -| RSA PUBLIC / PRIVATE FUNCTIONS |---------------------------------------------------------------- ;; The basic definitions... pretty well lifted from the text book! (define ((C e n) p) ;; Just do the arithmetic to demonstrate RSA... ;; breaking large messages into blocks is something for another day. (unless (< p n) (raise-argument-error 'C (format "(and/c integer? (</c ~a))" n) p)) (modular-expt p e n)) (define ((P d n) c) (modular-expt c d n)) ;; -| RSA KEY GENERATION |---------------------------------------------------------------------------- ;; Key generation ;; Full description of the steps can be found on Wikipedia (define (RSA-keyset function-base-name) (log-info "RSA-keyset: ~s" function-base-name) (define max-k 4294967087) ;; I'm guessing this RNG is about as cryptographically strong as replacing spaces with tabs. (define (big-random n-rolls) (for/fold ((rv 1)) ((roll (in-range n-rolls 0 -1))) (+ (* rv (add1 max-k)) 1 (random max-k)))) (define (big-random-prime) (define start-number (big-random (/ 1024 32))) (log-debug "got large (possibly non-prime) number, finding next prime") (next-prime (match start-number ((? odd? o) o) ((app add1 e) e)))) ;; [1] Choose two distinct prime numbers p and q. (log-debug "generating p") (define p (big-random-prime)) (log-debug "p generated") (log-debug "generating q") (define q (big-random-prime)) (log-debug "q generated") (log-info "primes generated") ;; [2] Compute n = pq. (define n (* p q)) ;; [3] Compute φ(n) = φ(p)φ(q) = (p − 1)(q − 1) = n - (p + q -1), ;; where φ is Euler's totient function. (define φ (- n (+ p q -1))) ;; [4] Choose an integer e such that 1 < e < φ(n) and gcd(e, φ(n)) = 1; i.e., e and φ(n) are ;; coprime. ... most commonly 2^16 + 1 = 65,537 ... (define e (+ (expt 2 16) 1)) ;; [5] Determine d as d ≡ e−1 (mod φ(n)); i.e., d is the multiplicative inverse of e (modulo φ(n)). (log-debug "generating d") (define d (modular-inverse e φ)) (log-info "d generated") (values n e d)) ;; -| GIVE A USABLE SET OF PRIVATE STUFF TO A USER |-------------------------------------------------- ;; six values: the public (encrypt) function (numeric) ;; the private (decrypt) function (numeric) ;; the public (encrypt) function (bytes) ;; the private (decrypt) function (bytes) ;; private (list n e d) ;; public (list n e) (define (RSA-key-pack #:function-base-name function-base-name) (define (rnm-fn f s) (procedure-rename f (string->symbol (format "~a-~a" function-base-name s)))) (define-values (n e d) (RSA-keyset function-base-name)) (define my-C (rnm-fn (C e n) "C")) (define my-P (rnm-fn (P d n) "P")) (define my-encrypt (rnm-fn (compose number->bytes my-C bytes->number) "encrypt")) (define my-decrypt (rnm-fn (compose number->bytes my-P bytes->number) "decrypt")) (values my-C my-P my-encrypt my-decrypt (list n e d) (list n e))) ;; -| HEREON IS JUST A LOAD OF CHATTY DEMOS |--------------------------------------------------------- (define (narrated-encrypt-bytes C who plain-text) (define plain-n (bytes->number plain-text)) (define cypher-n (C plain-n)) (define cypher-text (number->bytes cypher-n)) (printf #<<EOS ~a wants to send plain text: ~s as number: ~s cyphered number: ~s sent by ~a over the public interwebs: ~s ... EOS who plain-text plain-n cypher-n who cypher-text) cypher-text) (define (narrated-decrypt-bytes P who cypher-text) (define cypher-n (bytes->number cypher-text)) (define plain-n (P cypher-n)) (define plain-text (number->bytes plain-n)) (printf #<<EOS ... ~s received by ~a as number: ~s decyphered (with P) number: ~s decyphered text: ~s EOS cypher-text who cypher-n plain-n plain-text) plain-text) ;; ENCRYPT AND DECRYPT A MESSAGE WITH THE e.g. KEYS (define-values (given-n given-e given-d) (values 9516311845790656153499716760847001433441357 65537 5617843187844953170308463622230283376298685)) ;; Get the keys specific RSA functions (for ((message-text (list #"hello world" #"TOP SECRET!"))) (define Bobs-public-function (C given-e given-n)) (define Bobs-private-function (P given-d given-n)) (define cypher-text (narrated-encrypt-bytes Bobs-public-function "Alice" message-text)) (define plain-text (narrated-decrypt-bytes Bobs-private-function "Bob" cypher-text)) plain-text) ;; Demonstrate with larger keys. ;; (And include a free recap on digital signatures, too) (define-values (A-pub-C A-pvt-P A-pub-encrypt A-pvt-decrypt A-pvt-keys A-pub-keys) (RSA-key-pack #:function-base-name 'Alice)) (define-values (B-pub-C B-pvt-P B-pub-encrypt B-pvt-decrypt B-pvt-keys B-pub-keys) (RSA-key-pack #:function-base-name 'Bob)) ;; Since p and q are random, it is possible that message' = "message modulo {A,B}-key-n" will be too ;; big for "message' modulo {B,A}-key-n", if that happens then I run the program again until it ;; works. Strictly, we need blocking of the signed message -- which is not yet implemented. (let* ((plain-A-to-B #"Dear Bob, meet you in Lymm at 1200, Alice") (signed-A-to-B (A-pvt-decrypt plain-A-to-B)) (unsigned-A-to-B (A-pub-encrypt signed-A-to-B)) (crypt-signed-A-to-B (B-pub-encrypt signed-A-to-B)) (decrypt-signed-A-to-B (B-pvt-decrypt crypt-signed-A-to-B)) (decrypt-verified-B (A-pub-encrypt decrypt-signed-A-to-B))) (printf #<<EOS Alice wants to send ~s to Bob. She "encrypts" with her private "decryption" key. (A-prv msg) -> ~s Only she could have done this (only she has the her private key data) -- so this is a signature on the message. Anyone can verify the signature by "decrypting" the message with the public "encryption" key. (A-pub (A-prv msg)) -> ~s But anyone is able to do this, so there is no privacy here. Everyone knows that it can only be Alice at Lymm at noon, but this message is for Bob's eyes only. We need to encrypt this with his public key: (B-pub (A-prv msg)) -> ~s Which is what gets posted to alt.chat.secret-rendezvous Bob decrypts this to get the signed message from Alice: (B-prv (B-pub (A-prv msg))) -> ~s And verifies Alice's signature: (A-pub (B-prv (B-pub (A-prv msg)))) -> ~s Alice genuinely sent the message. And nobody else (on a.c.s-r, at least) has read it. KEYS: Alice's full set: ~s Bob's full set: ~s EOS plain-A-to-B signed-A-to-B unsigned-A-to-B crypt-signed-A-to-B decrypt-signed-A-to-B decrypt-verified-B A-pvt-keys B-pvt-keys))  Output: Alice wants to send plain text: #"hello world" as number: 126207244316550804821666916 cyphered number: 4109627268073579506944196826730512948879423 sent by Alice over the public interwebs: #"/-\e\355\225\327\244\222<R@\20\4\233\275\333?" ... ... #"/-\e\355\225\327\244\222<R@\20\4\233\275\333?" received by Bob as number: 4109627268073579506944196826730512948879423 decyphered (with P) number: 126207244316550804821666916 decyphered text: #"hello world" Alice wants to send plain text: #"TOP SECRET!" as number: 101924313868583037137409057 cyphered number: 5346093164296793050289700489360581430628365 sent by Alice over the public interwebs: #"=^\301{\17p\201AE\341D\357 \237IPP\r" ... ... #"=^\301{\17p\201AE\341D\357 \237IPP\r" received by Bob as number: 5346093164296793050289700489360581430628365 decyphered (with P) number: 101924313868583037137409057 decyphered text: #"TOP SECRET!" Alice wants to send #"Dear Bob, meet you in Lymm at 1200, Alice" to Bob. She "encrypts" with her private "decryption" key. (A-prv msg) -> #"B}\4<G\373-\217\350;\0214\226\233\236\333\215\226\225=\236\350\277X\241*J\356\302\250\350fO\5\375u\367\365\315\270\312\334\204U\332\224\322\357u=\262\326\274e\31\301\321\210:i\361\361g\361\16\5a\304X\306\313\350(^\374 \353\350t\2662\305\346a\300\244b\337JI\343\335\21j\202\236\242\335<rA\a\233\375\23\t\32(d\237i\267\336\270\340L\26\f\260\346&\t\301\326\331k@\253\242\241VKw\365 \204U\270*\r,\334h=\257\230\320V\357\304\242\4B\240\356\200\204\252\35\20c\220LJ}\275x!\25\23\262\325{\246\304?\36\272\343\17\230\2449Q[y\334(m1\252N<\253?^#\236p\311\3006\f\245M*<\273H\333\225\256\317\322\363\273\335\303\243\354\a\253\342\312\302\372vTQ\247\r\210\343\264\323*E\364\2\ba\305Z79\273M\327\310F\301,\235\32\323" Only she could have done this (only she has the her private key data) -- so this is a signature on the message. Anyone can verify the signature by "decrypting" the message with the public "encryption" key. (A-pub (A-prv msg)) -> #"Dear Bob, meet you in Lymm at 1200, Alice" But anyone is able to do this, so there is no privacy here. Everyone knows that it can only be Alice at Lymm at noon, but this message is for Bob's eyes only. We need to encrypt this with his public key: (B-pub (A-prv msg)) -> #"\eXq\4/\207\250hs\244<ym\3716\210\357'0\351E\202D\360\177\361\325\24\310+s\340j1\36\0\213\353\254\314*\212a;\300\210\\\347\371z\226\230 \230A\337d\31\262nwp\6m\312\320D@h\232d]{sN\312xAW\216'c\27V\5\270\267>@\305\312\210\262|tGU?\266\325\250\227\270X\235\6C\307\323D\301q{\266S\351,i\211,~X\341\225z4\320F\353\361I\313M\270&d\267m\207 \2736s_\272\307\275\31T\301\247\317@\16D\263X\"\340\262\204\277g\30\337\311o\205\236\34\370)\323\275\5\1\301>\226Q,\255\213\\\2\307\215c\342\323\16\226a\3U\254\214\275\274\214\325\f\226\347\325\225\354~\32z)\340re5I\321\254\34'T\n\220p\316#\1\347\6;*\347\303\351\342\221\244\eey\31\275y\271\2605y\344\261\202B\321E\335\212" Which is what gets posted to alt.chat.secret-rendezvous Bob decrypts this to get the signed message from Alice: (B-prv (B-pub (A-prv msg))) -> #"B}\4<G\373-\217\350;\0214\226\233\236\333\215\226\225=\236\350\277X\241*J\356\302\250\350fO\5\375u\367\365\315\270\312\334\204U\332\224\322\357u=\262\326\274e\31\301\321\210:i\361\361g\361\16\5a\304X\306\313\350(^\374 \353\350t\2662\305\346a\300\244b\337JI\343\335\21j\202\236\242\335<rA\a\233\375\23\t\32(d\237i\267\336\270\340L\26\f\260\346&\t\301\326\331k@\253\242\241VKw\365 \204U\270*\r,\334h=\257\230\320V\357\304\242\4B\240\356\200\204\252\35\20c\220LJ}\275x!\25\23\262\325{\246\304?\36\272\343\17\230\2449Q[y\334(m1\252N<\253?^#\236p\311\3006\f\245M*<\273H\333\225\256\317\322\363\273\335\303\243\354\a\253\342\312\302\372vTQ\247\r\210\343\264\323*E\364\2\ba\305Z79\273M\327\310F\301,\235\32\323" And verifies Alice's signature: (A-pub (B-prv (B-pub (A-prv msg)))) -> #"Dear Bob, meet you in Lymm at 1200, Alice" Alice genuinely sent the message. And nobody else (on a.c.s-r, at least) has read it. KEYS: Alice's full set: (104685401856522903402850023081275254628934665755538824520013952439504139625115997713509448983980532229245117213463882915048453185855818576471069794363975118091990355601850994380420233190180031768156385491949949615002445375960925665247160785747787333124376845288066200576472845984390877385677186819996627676676634639097055255729270941154875343472575964213139374388405182305309760553726485659960423106167598201105611690471457085541574734821426421348095213778701793437599877207476950721505461275161623234401077010666082709757697115644957960465476529769011591060857755043525709942747005873747546230596592939772042294065813 65537 2717089103223300710869400327467677924284264864888101995949520623458451584636500177162207191689440855119183734075439291369721208922299577316283774359722319847940485449116507338466741179127763462435479373816422239271238530669843516739939583694050479174276592059981393826091830737132442474221232201364332570578846365932454353567371199951546467136016124284306002875511872761969350668537869576342139916560099770887726733315363999637008436783521647128919138309876487426046116064403375745886449924998134881929018589019826525209406457786746758225025770316010686323085528641486882271019011944746635302695471929361680924424193) Bob's full set: (66453628687555934925745945778628604864426900808865010224295559035622434292221884343034084372211796572669001844069872620681089178469116242843088008182594366670325110214571956032739850447309116856946000976960287962443982329056724158946509616005091553738944083845350969457626620995817549009173612137879065054069514627974682257866567361928526254468372096924822844681482943840826594855542477801468633973217959659919448029041762191501507078772425126221108904380853918736930072466664169841898502073182029626689571748335731893924787111612947107622008163390629359277338946499436753837554940480109336784185532913066463754681017 65537 40065645823449313467522156271281139875308606308813084959528059327930012759030216763756439504389958618427304726562596348031980052624474573194667691034359998325290386803002604616043604539794698176121997293172282195706991070204897106862588071733664686557012032668284371518061563321600604452438728297053809260134398419618573423334221995863281726034127469856978901426632431740449516515840848181614406772903883730243825332015822633960435748349249507976445585019837204822017018926054553157019477128528700400452557614873387735038266042290443427594857847964184247833486305612600841625002197933394323058877499979801727736278613) The burden seems to be in finding (proving) the next large prime after the big random number. However, once keys are generated, things are pretty snappy. ## Raku (formerly Perl 6) No blocking here. Algorithm doesn't really work if either red or black text begins with 'A'. class RSA-message { has ($.n, $.e,$.d); # the 3 elements that define an RSA key

my @alphabet = |('A' .. 'Z'), ' ';
my $rad = +@alphabet; my %code = @alphabet Z=> 0 .. *; subset Text of Str where /^^ @alphabet+$$/; method encode(Text$t) {
[+] %code{$t.flip.comb} Z× (1,$rad, $rad×$rad … *);
}

method decode(Int $n is copy) { @alphabet[ gather loop { take$n % $rad; last if$n < $rad;$n div= $rad; } ].join.flip; } } constant$n = 9516311845790656153499716760847001433441357;
constant $e = 65537; constant$d = 5617843187844953170308463622230283376298685;

my $fmt = "%48s %s\n"; my$message = 'ROSETTA CODE';
printf $fmt, 'Secret message is',$message;

my $rsa = RSA-message.new: n =>$n, e => $e, d =>$d;
printf $fmt, 'Secret message in integer form is', my$numeric-message = $rsa.encode:$message;

printf $fmt, 'After exponentiation with public exponent we get', my$numeric-cipher = expmod $numeric-message,$e, $n; printf$fmt, 'This turns into the string',
my $text-cipher =$rsa.decode: $numeric-cipher; printf$fmt, 'If we re-encode it in integer form we get',
my $numeric-cipher2 =$rsa.encode: $text-cipher; printf$fmt, 'After exponentiation with SECRET exponent we get',
my $numeric-message2 = expmod$numeric-cipher2, $d,$n;

printf $fmt, 'This turns into the string', my$message2 = $rsa.decode:$numeric-message2;

Output:
                               Secret message is ROSETTA CODE
Secret message in integer form is 97525102075211938
After exponentiation with public exponent we get 8326171774113983822045243488956318758396426
This turns into the string ZULYDCEZOWTFXFRRNLIMGNUPHVCJSX
If we re-encode it in integer form we get 8326171774113983822045243488956318758396426
After exponentiation with SECRET exponent we get 97525102075211938
This turns into the string ROSETTA CODE

## Ruby

#!/usr/bin/ruby

require 'openssl' # for mod_exp only
require 'prime'

def rsa_encode blocks, e, n
blocks.map{|b| b.to_bn.mod_exp(e, n).to_i}
end

def rsa_decode ciphers, d, n
rsa_encode ciphers, d, n
end

# all numbers in blocks have to be < modulus, or information is lost
# for secure encryption only use big modulus and blocksizes
def text_to_blocks text, blocksize=64 # 1 hex = 4 bit => default is 256bit
text.each_byte.reduce(""){|acc,b| acc << b.to_s(16).rjust(2, "0")} # convert text to hex (preserving leading 0 chars)
.each_char.each_slice(blocksize).to_a                          # slice hexnumbers in pieces of blocksize
.map{|a| a.join("").to_i(16)}                                  # convert each slice into internal number
end

def blocks_to_text blocks
blocks.map{|d| d.to_s(16)}.join("")                                # join all blocks into one hex-string
.each_char.each_slice(2).to_a                                # group into pairs
.map{|s| s.join("").to_i(16)}                                # number from 2 hexdigits is byte
.flatten.pack("C*")                                          # pack bytes into ruby-string
.force_encoding(Encoding::default_external)                  # reset encoding
end

def generate_keys p1, p2
n = p1 * p2
t = (p1 - 1) * (p2 - 1)
e = 2.step.each do |i|
break i if i.gcd(t) == 1
end
d = 1.step.each do |i|
break i if (i * e) % t == 1
end
return e, d, n
end

p1, p2 = Prime.take(100).last(2)
public_key, private_key, modulus =
generate_keys p1, p2

print "Message: "
message = gets
blocks = text_to_blocks message, 4 # very small primes
print "Numbers: "; p blocks
encoded = rsa_encode(blocks, public_key, modulus)
print "Encrypted as: "; p encoded
decoded = rsa_decode(encoded, private_key, modulus)
print "Decrypted to: "; p decoded
final = blocks_to_text(decoded)
print "Decrypted Message: "; puts final

Output:
% echo "☆ rosettacode.org ✓" | ./rsa.rb
Message: Numbers: [58008, 34336, 29295, 29541, 29812, 24931, 28516, 25902, 28530, 26400, 58012, 37642]
Encrypted as: [8509, 99626, 21784, 139807, 81066, 67678, 183438, 147659, 261822, 85962, 150227, 167121]
Decrypted to: [58008, 34336, 29295, 29541, 29812, 24931, 28516, 25902, 28530, 26400, 58012, 37642]
Decrypted Message: ☆ rosettacode.org ✓


## Rust

extern crate num;

use num::bigint::BigUint;
use num::integer::Integer;
use num::traits::{One, Zero};

fn mod_exp(b: &BigUint, e: &BigUint, n: &BigUint) -> Result<BigUint, &'static str> {
if n.is_zero() {
return Err("modulus is zero");
}
if b >= n {
// base is too large and should be split into blocks
return Err("base is >= modulus");
}
if b.gcd(n) != BigUint::one() {
return Err("base and modulus are not relatively prime");
}

let mut bb = b.clone();
let mut ee = e.clone();
let mut result = BigUint::one();
while !ee.is_zero() {
if ee.is_odd() {
result = (result * &bb) % n;
}
ee >>= 1;
bb = (&bb * &bb) % n;
}
Ok(result)
}

fn main() {
let msg = "Rosetta Code";

let n = "9516311845790656153499716760847001433441357"
.parse()
.unwrap();
let e = "65537".parse().unwrap();
let d = "5617843187844953170308463622230283376298685"
.parse()
.unwrap();

let msg_int = BigUint::from_bytes_be(msg.as_bytes());
let enc = mod_exp(&msg_int, &e, &n).unwrap();
let dec = mod_exp(&enc, &d, &n).unwrap();
let msg_dec = String::from_utf8(dec.to_bytes_be()).unwrap();

println!("msg as txt: {}", msg);
println!("msg as num: {}", msg_int);
println!("enc as num: {}", enc);
println!("dec as num: {}", dec);
println!("dec as txt: {}", msg_dec);
}

Output:
msg as txt: Rosetta Code
msg as num: 25512506514985639724585018469
enc as num: 916709442744356653386978770799029131264344
dec as num: 25512506514985639724585018469
dec as txt: Rosetta Code


## Scala

The code below demonstrates RSA encryption and decryption in Scala. Text to integer encryption using ASCII code.

object RSA_saket{
val d = BigInt("5617843187844953170308463622230283376298685")
val n = BigInt("9516311845790656153499716760847001433441357")
val e = 65537
val text = "Rosetta Code"
val encode = (msg:BigInt) => pow_mod(msg,e,n)
val decode = (msg:BigInt) => pow_mod(msg,d,n)
val getmsg = (txt:String) => BigInt(txt.map(x => "%03d".format(x.toInt)).reduceLeft(_+_))
def pow_mod(p:BigInt, q:BigInt, n:BigInt):BigInt = {
if(q==0)            BigInt(1)
else if(q==1)       p
else if(q%2 == 1)   pow_mod(p,q-1,n)*p % n
else                pow_mod(p*p % n,q/2,n)
}
def gettxt(num:String) = {
if(num.size%3==2)
("0" + num).grouped(3).toList.foldLeft("")(_ + _.toInt.toChar)
else
num.grouped(3).toList.foldLeft("")(_ + _.toInt.toChar)
}
def main(args: Array[String]): Unit = {
println(f"Original String \t: "+text)
val msg = getmsg(text)
println(f"Converted Signal \t: "+msg)
val enc_sig = encode(msg)
println("Encoded Signal \t\t: "+ enc_sig)
val dec_sig = decode(enc_sig)
println("Decoded String \t\t: "+ dec_sig)
val rec_msg = gettxt(dec_sig.toString)
println("Retrieved Signal \t: "+rec_msg)
}
}

Output:
    Ouput:
Original String         : Rosetta Code
Converted String        : 82111115101116116097032067111100101
Encoded Signal          : 5902559240035849005218240192859088445397686
Decoded String          : 82111115101116116097032067111100101
Retrieved String        : Rosetta Code


$include "seed7_05.s7i"; include "bigint.s7i"; include "bytedata.s7i"; const proc: main is func local const string: plainText is "Rosetta Code"; # Use a key big enough to hold 16 bytes of plain text in a single block. const bigInteger: modulus is 9516311845790656153499716760847001433441357_; const bigInteger: encode is 65537_; const bigInteger: decode is 5617843187844953170308463622230283376298685_; var bigInteger: plainTextNumber is 0_; var bigInteger: encodedNumber is 0_; var bigInteger: decodedNumber is 0_; var string: decodedText is ""; begin writeln("Plain text: " <& plainText); plainTextNumber := bytes2BigInt(plainText, UNSIGNED, BE); if plainTextNumber >= modulus then writeln("Plain text message too long"); else writeln("Plain text as a number: " <& plainTextNumber); encodedNumber := modPow(plainTextNumber, encode, modulus); writeln("Encoded: " <& encodedNumber); decodedNumber := modPow(encodedNumber, decode, modulus); writeln("Decoded: " <& decodedNumber); decodedText := bytes(decodedNumber, UNSIGNED, BE); writeln("Decoded number as text: " <& decodedText); end if; end func; Output: Plain text: Rosetta Code Plain text as a number: 25512506514985639724585018469 Encoded: 916709442744356653386978770799029131264344 Decoded: 25512506514985639724585018469 Decoded number as text: Rosetta Code  ## Sidef Translation of: Raku const n = 9516311845790656153499716760847001433441357 const e = 65537 const d = 5617843187844953170308463622230283376298685 module Message { var alphabet = [('A' .. 'Z')..., ' '] var rad = alphabet.len var code = Hash(^rad -> map {|i| (alphabet[i], i) }...) func encode(String t) { [code{t.reverse.chars...}] ~Z* t.len.range.map { |i| rad**i } -> sum(0) } func decode(Number n) { ''.join(alphabet[ gather { loop { var (d, m) = n.divmod(rad) take(m) break if (n < rad) n = d } }...] ).reverse } } var secret_message = "ROSETTA CODE" say "Secret message is #{secret_message}" var numeric_message = Message::encode(secret_message) say "Secret message in integer form is #{numeric_message}" var numeric_cipher = expmod(numeric_message, e, n) say "After exponentiation with public exponent we get: #{numeric_cipher}" var text_cipher = Message::decode(numeric_cipher) say "This turns into the string #{text_cipher}" var numeric_cipher2 = Message::encode(text_cipher) say "If we re-encode it in integer form we get #{numeric_cipher2}" var numeric_message2 = expmod(numeric_cipher2, d, n) say "After exponentiation with SECRET exponent we get: #{numeric_message2}" var secret_message2 = Message::decode(numeric_message2) say "This turns into the string #{secret_message2}"  Output: Secret message is ROSETTA CODE Secret message in integer form is 97525102075211938 After exponentiation with public exponent we get: 8326171774113983822045243488956318758396426 This turns into the string ZULYDCEZOWTFXFRRNLIMGNUPHVCJSX If we re-encode it in integer form we get 8326171774113983822045243488956318758396426 After exponentiation with SECRET exponent we get: 97525102075211938 This turns into the string ROSETTA CODE  ## Tcl This code is careful to avoid the assumption that the input string is in a single-byte encoding, instead forcing the encryption to be performed on the UTF-8 form of the text. package require Tcl 8.5 # This is a straight-forward square-and-multiply implementation that relies on # Tcl 8.5's bignum support (based on LibTomMath) for speed. proc modexp {b expAndMod} { lassign$expAndMod -> e n
if {$b >=$n} {puts stderr "WARNING: modulus too small"}
for {set r 1} {$e != 0} {set e [expr {$e >> 1}]} {
if {$e & 1} { set r [expr {($r * $b) %$n}]
}
set b [expr {($b ** 2) %$n}]
}
return $r } # Assumes that messages are shorter than the modulus proc rsa_encrypt {message publicKey} { if {[lindex$publicKey 0] ne "publicKey"} {error "key handling"}
set toEnc 0
foreach char [split [encoding convertto utf-8 $message] ""] { set toEnc [expr {$toEnc * 256 + [scan $char "%c"]}] } return [modexp$toEnc $publicKey] } proc rsa_decrypt {encrypted privateKey} { if {[lindex$privateKey 0] ne "privateKey"} {error "key handling"}
set toDec [modexp $encrypted$privateKey]
for {set message ""} {$toDec > 0} {set toDec [expr {$toDec >> 8}]} {
append message [format "%c" [expr {$toDec & 255}]] } return [encoding convertfrom utf-8 [string reverse$message]]
}

# Assemble packaged public and private keys
set e 65537
set n 9516311845790656153499716760847001433441357
set d 5617843187844953170308463622230283376298685
set publicKey  [list "publicKey"  $e$n]
set privateKey [list "privateKey" $d$n]

# Test on some input strings
foreach input {"Rosetta Code" "UTF-8 \u263a test"} {
set enc [rsa_encrypt $input$publicKey]
set dec [rsa_decrypt $enc$privateKey]
puts "$input ->$enc -> $dec" }  Output: Rosetta Code -> 916709442744356653386978770799029131264344 -> Rosetta Code UTF-8 ☺ test -> 3905697186829810541171404594906488782823186 -> UTF-8 ☺ test  ## Visual Basic .NET Translation of: C# Imports System Imports System.Numerics Imports System.Text Module Module1 Sub Main() Dim n As BigInteger = BigInteger.Parse("9516311845790656153499716760847001433441357") Dim e As BigInteger = 65537 Dim d As BigInteger = BigInteger.Parse("5617843187844953170308463622230283376298685") Dim plainTextStr As String = "Hello, Rosetta!" Dim plainTextBA As Byte() = ASCIIEncoding.ASCII.GetBytes(plainTextStr) Dim pt As BigInteger = New BigInteger(plainTextBA) If pt > n Then Throw New Exception() ' Blocking not implemented Dim ct As BigInteger = BigInteger.ModPow(pt, e, n) Console.WriteLine(" Encoded: " & ct.ToString("X")) Dim dc As BigInteger = BigInteger.ModPow(ct, d, n) Console.WriteLine(" Decoded: " & dc.ToString("X")) Dim decoded As String = ASCIIEncoding.ASCII.GetString(dc.ToByteArray()) Console.WriteLine("As ASCII: " & decoded) End Sub End Module  Output:  Encoded: 6219A470D8B319A31C8E13F612B31337098F Decoded: 2161747465736F52202C6F6C6C6548 As ASCII: Hello, Rosetta! ## V (Vlang) Translation of: Go /*import math.big fn main() { //var bb, ptn, etn, dtn big.Int pt := "Rosetta Code" println("Plain text:$pt")

// a key set big enough to hold 16 bytes of plain text in
// a single block (to simplify the example) and also big enough
// to demonstrate efficiency of modular exponentiation.
n := big.integer_from_string("9516311845790656153499716760847001433441357")?
e := big.integer_from_string("65537")?
d := big.integer_from_string("5617843187844953170308463622230283376298685")?

mut ptn := big.zero_int
// convert plain text to a number
for b in pt.bytes() {
bb := big.integer_from_i64(i64(b))
ptn = ptn.lshift(8).bitwise_or(bb)
}
if ptn >= n {
println("Plain text message too long")
return
}
println("Plain text as a number:$ptn") // encode a single number etn := ptn.big_mod_pow(e,n) println("Encoded:$etn")

// decode a single number
mut dtn := etn.big_mod_pow(d,n)
println("Decoded:               $dtn") // convert number to text mut db := [16]u8{} mut dx := 16 bff := big.integer_from_int(0xff) for dtn.bit_len() > 0 { dx-- bb := dtn.bitwise_and(bff) db[dx] = u8(i64(bb.int())) dtn = dtn.rshift(8) println('${db[0..].bytestr()} ${dtn.bit_len()}') } println("Decoded number as text:${db[dx..].bytestr()}")
}*/

import math.big
fn main() {
//var bb, ptn, etn, dtn big.Int
pt := "Hello World"
println("Plain text:            $pt") // a key set big enough to hold 16 bytes of plain text in // a single block (to simplify the example) and also big enough // to demonstrate efficiency of modular exponentiation. n := big.integer_from_string("9516311845790656153499716760847001433441357")? e := big.integer_from_string("65537")? d := big.integer_from_string("5617843187844953170308463622230283376298685")? mut ptn := big.zero_int // convert plain text to a number for b in pt.bytes() { bb := big.integer_from_i64(i64(b)) ptn = ptn.lshift(8).bitwise_or(bb) } if ptn >= n { println("Plain text message too long") return } println("Plain text as a number:$ptn")

// encode a single number
etn := ptn.big_mod_pow(e,n)
println("Encoded:               $etn") // decode a single number mut dtn := etn.big_mod_pow(d,n) println("Decoded:$dtn")

// convert number to text
mut db := [16]u8{}
mut dx := 16
bff := big.integer_from_int(0xff)
for dtn.bit_len() > 0 {
dx--
bb := dtn.bitwise_and(bff)
db[dx] = u8(i64(bb.int()))
dtn = dtn.rshift(8)
}
println("Decoded number as text: \${db[dx..].bytestr()}")
}
Output:
Plain text:            Hello World
Plain text as a number:87521618088882533792115812
Encoded:               8455179966388263657372423602482472996174613
Decoded:               87521618088882533792115812
Decoded number as text: Hello World


## Wren

Translation of: Go
Library: Wren-big
import "./big" for BigInt

var pt = "Rosetta Code"
System.print("Plain text:            : %(pt)")
var n = BigInt.new("9516311845790656153499716760847001433441357")
var e = BigInt.new("65537")
var d = BigInt.new("5617843187844953170308463622230283376298685")
var ptn = BigInt.zero
// convert plain text to a number
for (b in pt.bytes) {
ptn = (ptn << 8) | BigInt.new(b)
}
if (ptn >= n) {
System.print("Plain text message too long")
return
}
System.print("Plain text as a number : %(ptn)")

// encode a single number
var etn = ptn.modPow(e, n)
System.print("Encoded                : %(etn)")

// decode a single number
var dtn = etn.modPow(d, n)
System.print("Decoded                : %(dtn)")

// convert number to text
var db = List.filled(16, 0)
var dx = 16
var bff = BigInt.new(255)
while (dtn.bitLength > 0) {
dx = dx - 1
db[dx] = (dtn & bff).toSmall
dtn = dtn >> 8
}
var s = ""
for (i in dx..15) s = s + String.fromByte(db[i])
System.print("Decoded number as text : %(s)")

Output:
Plain text:            : Rosetta Code
Plain text as a number : 25512506514985639724585018469
Encoded                : 916709442744356653386978770799029131264344
Decoded                : 25512506514985639724585018469
Decoded number as text : Rosetta Code


## zkl

Translation of: C
Library: GMP

No blocking.

var BN=Import.lib("zklBigNum");

n:=BN("9516311845790656153499716760847001433441357");
e:=BN("65537");
d:=BN("5617843187844953170308463622230283376298685");

const plaintext="Rossetta Code";
pt:=BN(Data(Int,0,plaintext));  // convert string (as stream of bytes) to big int
if(pt>n) throw(Exception.ValueError("Message is too large"));

println("Plain text: ",plaintext);
println("As Int:     ",pt);
ct:=pt.powm(e,n);  println("Encoded:    ",ct);
pt =ct.powm(d,n);  println("Decoded:    ",pt);
txt:=pt.toData().text; // convert big int to bytes, treat as string
println("As String:  ",txt);
Output:
Plain text: Rossetta Code
As Int:     6531201733672758787904906421349
Encoded:    5278143020249600501803788468419399384934220
Decoded:    6531201733672758787904906421349
As String:  Rossetta Code
`