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#!/usr/bin/perl -sw |
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## |
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## Crypt::RSA - Pure-perl implementation of RSA encryption/signing |
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## algorithms. |
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## |
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## Copyright (c) 2000-2001, Vipul Ved Prakash. All rights reserved. |
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## This code is free software; you can redistribute it and/or modify |
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## it under the same terms as Perl itself. |
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## |
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## $Id: RSA.pm,v 1.48 2001/09/25 12:44:55 vipul Exp $ |
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package Crypt::RSA; |
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use FindBin qw($Bin); |
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use lib "$Bin/../../lib"; |
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use strict; |
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use base 'Class::Loader'; |
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use base 'Crypt::RSA::Errorhandler'; |
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use Crypt::RSA::Key; |
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use Crypt::RSA::DataFormat qw(steak octet_len); |
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use Convert::ASCII::Armour; |
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use Carp; |
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$Crypt::RSA::VERSION = '1.99'; # change this elsewhere too! |
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my %DEFAULTS = ( |
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'ES' => { Name => 'OAEP_ES' }, |
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'SS' => { Name => 'PSS_SS' }, |
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'PP' => { Name => 'ASCII_PP' }, |
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); |
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my %KNOWNMAP = ( |
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# ENCRYPTION SCHEMES |
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OAEP_ES => { Module => "Crypt::RSA::ES::OAEP" }, |
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PKCS1v21_ES => { Module => "Crypt::RSA::ES::OAEP" }, |
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PKCS1v15_ES => { Module => "Crypt::RSA::ES::PKCS1v15" }, |
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# SIGNATURE SCHEMES |
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PSS_SS => { Module => "Crypt::RSA::SS::PSS" }, |
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PKCS1v21_SS => { Module => "Crypt::RSA::SS::PSS" }, |
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PKCS1v15_SS => { Module => "Crypt::RSA::SS::PKCS1v15" }, |
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# POST PROCESSORS |
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ASCII_PP => { Module => "Convert::ASCII::Armour" }, |
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); |
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sub new { |
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my ($class, %params) = @_; |
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my %self = (%DEFAULTS, %params); |
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my $self = bless \%self, $class; |
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$self->_storemap (%KNOWNMAP); |
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for (qw(ES SS PP)) { |
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$$self{$_} = { Name => $$self{$_} . "_$_" } unless ref $$self{$_}; |
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$$self{lc($_)} = $self->_load ( %{$$self{$_}} ); |
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} |
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$$self{keychain} = new Crypt::RSA::Key; |
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return bless \%self, $class; |
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} |
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sub keygen { |
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my ($self, %params) = @_; |
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$params{KF} = $$self{KF} if $$self{KF}; |
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my @keys; |
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return (@keys = $self->{keychain}->generate (%params)) |
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? @keys |
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: $self->error ($self->{keychain}->errstr); |
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} |
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sub encrypt { |
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my ($self, %params) = @_; |
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my $plaintext = $params{Message} || $params{Plaintext}; |
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my $key = $params{Key}; |
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return $self->error ($key->errstr, \%params, $key, \$plaintext) |
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unless $key->check(); |
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my $blocksize = blocksize ( $$self{es}->encryptblock (Key => $key), |
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length($plaintext) |
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); |
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return $self->error("Message too long.", \$key, \%params) if $blocksize <= 0; |
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my $cyphertext; |
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my @segments = steak ($plaintext, $blocksize); |
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for (@segments) { |
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$cyphertext .= $self->{es}->encrypt (Message => $_, Key => $key) |
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|| return $self->error ($self->{es}->errstr, \$key, \%params); |
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} |
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if ($params{Armour} || $params{Armor}) { |
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$cyphertext = $self->{pp}->armour ( |
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Object => 'RSA ENCRYPTED MESSAGE', |
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Headers => { |
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Scheme => $$self{ES}{Module} || ${$KNOWNMAP{$$self{ES}{Name}}}{Module}, |
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Version => $self->{es}->version() |
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}, |
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Content => { Cyphertext => $cyphertext }, |
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Compress => 1, |
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); |
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} |
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return $cyphertext; |
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} |
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sub decrypt { |
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my ($self , %params) = @_; |
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my $cyphertext = $params{Cyphertext} || $params{Ciphertext}; |
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my $key = $params{Key}; |
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return $self->error ($key->errstr, \%params, $key) unless $key->check(); |
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if ($params{Armour} || $params{Armor}) { |
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my $decoded = $self->{pp}->unarmour ($cyphertext) || |
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return $self->error ($self->{pp}->errstr()); |
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$cyphertext = $$decoded{Content}{Cyphertext} |
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} |
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my $plaintext; |
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my $blocksize = blocksize ( $$self{es}->decryptblock (Key => $key), |
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length($cyphertext) |
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); |
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return $self->error("Message too long.") if $blocksize <= 0; |
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my @segments = steak ($cyphertext, $blocksize); |
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for (@segments) { |
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$plaintext .= $self->{es}->decrypt (Cyphertext=> $_, Key => $key) |
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|| return $self->error ($self->{es}->errstr, \$key, \%params); |
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} |
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return $plaintext; |
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} |
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sub sign { |
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my ($self, %params) = @_; |
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my $signature = $self->{ss}->sign (%params) |
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|| return $self->error ($self->{ss}->errstr, |
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$params{Key}, \%params); |
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if ($params{Armour} || $params{Armor}) { |
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$signature = $self->{pp}->armour ( |
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Object => "RSA SIGNATURE", |
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Headers => { |
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Scheme => $$self{SS}{Module} || ${$KNOWNMAP{$$self{SS}{Name}}}{Module}, |
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Version => $self->{ss}->version() }, |
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Content => { Signature => $signature }, |
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); |
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} |
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return $signature; |
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} |
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sub verify { |
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my ($self, %params) = @_; |
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if ($params{Armour} || $params{Armor}) { |
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my $decoded = $self->{pp}->unarmour ($params{Signature}) || |
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return $self->error ($self->{pp}->errstr()); |
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$params{Signature} = $$decoded{Content}{Signature} |
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} |
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my $verify = $self->{ss}->verify (%params) || |
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return $self->error ($self->{ss}->errstr, $params{Key}, \%params); |
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return $verify; |
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} |
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sub blocksize { |
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my ($blocksize, $ptsize) = @_; |
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return $ptsize if $blocksize == -1; |
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return 0 if $blocksize < 1; |
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return $blocksize; |
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} |
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1; |
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=head1 NAME |
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Crypt::RSA - RSA public-key cryptosystem. |
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213
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=head1 SYNOPSIS |
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215
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my $rsa = new Crypt::RSA; |
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217
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my ($public, $private) = |
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$rsa->keygen ( |
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Identity => 'Lord Macbeth ', |
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Size => 1024, |
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Password => 'A day so foul & fair', |
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Verbosity => 1, |
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) or die $rsa->errstr(); |
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226
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my $cyphertext = |
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$rsa->encrypt ( |
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Message => $message, |
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Key => $public, |
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Armour => 1, |
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) || die $rsa->errstr(); |
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233
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234
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my $plaintext = |
235
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$rsa->decrypt ( |
236
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Cyphertext => $cyphertext, |
237
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Key => $private, |
238
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Armour => 1, |
239
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) || die $rsa->errstr(); |
240
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241
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242
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my $signature = |
243
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$rsa->sign ( |
244
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Message => $message, |
245
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Key => $private |
246
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) || die $rsa->errstr(); |
247
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248
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249
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my $verify = |
250
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$rsa->verify ( |
251
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Message => $message, |
252
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Signature => $signature, |
253
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Key => $public |
254
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) || die $rsa->errstr(); |
255
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256
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=head1 NOTE |
257
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258
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This manual assumes familiarity with public-key cryptography and the RSA |
259
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algorithm. If you don't know what these are or how they work, please refer |
260
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to the sci.crypt FAQ[15]. A formal treatment of RSA can be found in [1]. |
261
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262
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=head1 DESCRIPTION |
263
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264
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Crypt::RSA is a pure-perl, cleanroom implementation of the RSA public-key |
265
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cryptosystem. It uses Math::Pari(3), a perl interface to the blazingly |
266
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fast PARI library, for big integer arithmetic and number theoretic |
267
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computations. |
268
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269
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Crypt::RSA provides arbitrary size key-pair generation, plaintext-aware |
270
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encryption (OAEP) and digital signatures with appendix (PSS). For |
271
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compatibility with SSLv3, RSAREF2, PGP and other applications that follow |
272
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the PKCS #1 v1.5 standard, it also provides PKCS #1 v1.5 encryption and |
273
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signatures. |
274
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275
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Crypt::RSA is structured as bundle of modules that encapsulate different |
276
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parts of the RSA cryptosystem. The RSA algorithm is implemented in |
277
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Crypt::RSA::Primitives(3). Encryption schemes, located under |
278
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Crypt::RSA::ES, and signature schemes, located under Crypt::RSA::SS, use |
279
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the RSA algorithm to build encryption/signature schemes that employ secure |
280
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padding. (See the note on Security of Padding Schemes.) |
281
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282
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The key generation engine and other functions that work on both components |
283
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of the key-pair are encapsulated in Crypt::RSA::Key(3). |
284
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Crypt::RSA::Key::Public(3) & Crypt::RSA::Key::Private(3) provide |
285
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mechanisms for storage & retrival of keys from disk, decoding & encoding |
286
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of keys in certain formats, and secure representation of keys in memory. |
287
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Finally, the Crypt::RSA module provides a convenient, DWIM wrapper around |
288
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the rest of the modules in the bundle. |
289
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290
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=head1 SECURITY OF PADDING SCHEMES |
291
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292
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It has been conclusively shown that textbook RSA is insecure[3,7]. Secure |
293
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RSA requires that plaintext is padded in a specific manner before |
294
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encryption and signing. There are four main standards for padding: PKCS |
295
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#1 v1.5 encryption & signatures, and OAEP encryption & PSS signatures. |
296
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Crypt::RSA implements these as four modules that |
297
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provide overloaded encrypt(), decrypt(), sign() and verify() methods that |
298
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add padding functionality to the basic RSA operations. |
299
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300
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Crypt::RSA::ES::PKCS1v15(3) implements PKCS #1 v1.5 encryption, |
301
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|
Crypt::RSA::SS::PKCS1v15(3) implements PKCS #1 v1.5 signatures, |
302
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|
Crypt::RSA::ES::OAEP(3) implements Optimal Asymmetric Encryption and |
303
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|
Crypt::RSA::SS::PSS(3) Probabilistic Signatures. |
304
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305
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PKCS #1 v1.5 schemes are older and hence more widely deployed, but PKCS #1 |
306
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|
v1.5 encryption has certain flaws that make it vulnerable to |
307
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|
chosen-cyphertext attacks[9]. Even though Crypt::RSA works around these |
308
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|
vulnerabilities, it is recommended that new applications use OAEP and PSS, |
309
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|
both of which are provably secure[13]. In any event, |
310
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|
Crypt::RSA::Primitives (without padding) should never be used directly. |
311
|
|
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312
|
|
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|
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|
That said, there exists a scheme called Simple RSA[16] that provides |
313
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|
|
security without padding. However, Crypt::RSA doesn't implement this |
314
|
|
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|
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|
|
scheme yet. |
315
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316
|
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|
=head1 METHODS |
317
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318
|
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|
=over 4 |
319
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320
|
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|
=item B |
321
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322
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|
The constructor. When no arguments are provided, new() returns an object |
323
|
|
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|
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|
|
loaded with default values. This object can be customized by specifying |
324
|
|
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|
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|
|
encryption & signature schemes, key formats and post processors. For |
325
|
|
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|
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|
|
details see the section on B
|
326
|
|
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|
|
|
|
object> later in this manpage. |
327
|
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328
|
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|
=item B |
329
|
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|
330
|
|
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|
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|
|
keygen() generates and returns an RSA key-pair of specified bitsize. |
331
|
|
|
|
|
|
|
keygen() is a synonym for Crypt::RSA::Key::generate(). Parameters and |
332
|
|
|
|
|
|
|
return values are described in the Crypt::RSA::Key(3) manpage. |
333
|
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|
334
|
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|
=item B |
335
|
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|
336
|
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|
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|
|
encrypt() performs RSA encryption on a string of arbitrary length with a |
337
|
|
|
|
|
|
|
public key using the encryption scheme bound to the object. The default |
338
|
|
|
|
|
|
|
scheme is OAEP. encrypt() returns cyphertext (a string) on success and |
339
|
|
|
|
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|
|
undef on failure. It takes a hash as argument with following keys: |
340
|
|
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|
|
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341
|
|
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|
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|
|
=over 4 |
342
|
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343
|
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|
=item B |
344
|
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345
|
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|
An arbitrary length string to be encrypted. |
346
|
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347
|
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|
=item B |
348
|
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|
349
|
|
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|
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|
|
Public key of the recipient, a Crypt::RSA::Key::Public(3) or |
350
|
|
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|
|
|
|
compatible object. |
351
|
|
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352
|
|
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|
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|
|
=item B |
353
|
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|
354
|
|
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|
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|
|
A boolean parameter that forces cyphertext through a post processor after |
355
|
|
|
|
|
|
|
encrpytion. The default post processor is Convert::ASCII::Armour(3) that |
356
|
|
|
|
|
|
|
encodes binary octets in 6-bit clean ASCII messages. The cyphertext is |
357
|
|
|
|
|
|
|
returned as-is, when the Armour key is not present. |
358
|
|
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|
|
|
|
|
359
|
|
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|
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|
=back |
360
|
|
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|
|
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|
|
361
|
|
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|
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|
|
=item B |
362
|
|
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|
363
|
|
|
|
|
|
|
decrypt() performs RSA decryption with a private key using the encryption |
364
|
|
|
|
|
|
|
scheme bound to the object. The default scheme is OAEP. decrypt() returns |
365
|
|
|
|
|
|
|
plaintext on success and undef on failure. It takes a hash as argument |
366
|
|
|
|
|
|
|
with following keys: |
367
|
|
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|
|
|
|
|
368
|
|
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|
|
|
|
=over 4 |
369
|
|
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|
|
|
|
|
370
|
|
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|
|
|
|
=item B |
371
|
|
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|
|
|
|
|
372
|
|
|
|
|
|
|
Cyphertext of arbitrary length. |
373
|
|
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|
|
|
|
|
374
|
|
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|
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|
|
=item B |
375
|
|
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|
|
|
|
|
376
|
|
|
|
|
|
|
Private key, a Crypt::RSA::Key::Private(3) or compatible object. |
377
|
|
|
|
|
|
|
|
378
|
|
|
|
|
|
|
=item B |
379
|
|
|
|
|
|
|
|
380
|
|
|
|
|
|
|
Boolean parameter that specifies whether the Cyphertext is encoded with a |
381
|
|
|
|
|
|
|
post processor. |
382
|
|
|
|
|
|
|
|
383
|
|
|
|
|
|
|
=back |
384
|
|
|
|
|
|
|
|
385
|
|
|
|
|
|
|
=item B |
386
|
|
|
|
|
|
|
|
387
|
|
|
|
|
|
|
sign() creates an RSA signature on a string with a private key using the |
388
|
|
|
|
|
|
|
signature scheme bound to the object. The default scheme is |
389
|
|
|
|
|
|
|
PSS. sign() returns a signature on success and undef on failure. It takes |
390
|
|
|
|
|
|
|
a hash as argument with following keys: |
391
|
|
|
|
|
|
|
|
392
|
|
|
|
|
|
|
=over 4 |
393
|
|
|
|
|
|
|
|
394
|
|
|
|
|
|
|
=item B |
395
|
|
|
|
|
|
|
|
396
|
|
|
|
|
|
|
A string of arbitrary length to be signed. |
397
|
|
|
|
|
|
|
|
398
|
|
|
|
|
|
|
=item B |
399
|
|
|
|
|
|
|
|
400
|
|
|
|
|
|
|
Private key of the sender, a Crypt::RSA::Key::Private(3) or |
401
|
|
|
|
|
|
|
compatible object. |
402
|
|
|
|
|
|
|
|
403
|
|
|
|
|
|
|
=item B |
404
|
|
|
|
|
|
|
|
405
|
|
|
|
|
|
|
A boolean parameter that forces the computed signature to be post |
406
|
|
|
|
|
|
|
processed. |
407
|
|
|
|
|
|
|
|
408
|
|
|
|
|
|
|
=back |
409
|
|
|
|
|
|
|
|
410
|
|
|
|
|
|
|
=item B |
411
|
|
|
|
|
|
|
|
412
|
|
|
|
|
|
|
verify() verifies an RSA signature with a public key using the signature |
413
|
|
|
|
|
|
|
scheme bound to the object. The default scheme is PSS. verify() returns a |
414
|
|
|
|
|
|
|
true value on success and undef on failure. It takes a hash as argument |
415
|
|
|
|
|
|
|
with following keys: |
416
|
|
|
|
|
|
|
|
417
|
|
|
|
|
|
|
=over 4 |
418
|
|
|
|
|
|
|
|
419
|
|
|
|
|
|
|
=item B |
420
|
|
|
|
|
|
|
|
421
|
|
|
|
|
|
|
A signed message, a string of arbitrary length. |
422
|
|
|
|
|
|
|
|
423
|
|
|
|
|
|
|
=item B |
424
|
|
|
|
|
|
|
|
425
|
|
|
|
|
|
|
Public key of the signer, a Crypt::RSA::Key::Public(3) or |
426
|
|
|
|
|
|
|
compatible object. |
427
|
|
|
|
|
|
|
|
428
|
|
|
|
|
|
|
=item B |
429
|
|
|
|
|
|
|
|
430
|
|
|
|
|
|
|
A signature computed with sign(). |
431
|
|
|
|
|
|
|
|
432
|
|
|
|
|
|
|
=item B |
433
|
|
|
|
|
|
|
|
434
|
|
|
|
|
|
|
Boolean parameter that specifies whether the Signature has been |
435
|
|
|
|
|
|
|
post processed. |
436
|
|
|
|
|
|
|
|
437
|
|
|
|
|
|
|
=back |
438
|
|
|
|
|
|
|
|
439
|
|
|
|
|
|
|
=back |
440
|
|
|
|
|
|
|
|
441
|
|
|
|
|
|
|
=head1 MODULES |
442
|
|
|
|
|
|
|
|
443
|
|
|
|
|
|
|
Apart from Crypt::RSA, the following modules are intended for application |
444
|
|
|
|
|
|
|
developer and end-user consumption: |
445
|
|
|
|
|
|
|
|
446
|
|
|
|
|
|
|
=over 4 |
447
|
|
|
|
|
|
|
|
448
|
|
|
|
|
|
|
=item B |
449
|
|
|
|
|
|
|
|
450
|
|
|
|
|
|
|
RSA key pair generator. |
451
|
|
|
|
|
|
|
|
452
|
|
|
|
|
|
|
=item B |
453
|
|
|
|
|
|
|
|
454
|
|
|
|
|
|
|
RSA Public Key Management. |
455
|
|
|
|
|
|
|
|
456
|
|
|
|
|
|
|
=item B |
457
|
|
|
|
|
|
|
|
458
|
|
|
|
|
|
|
RSA Private Key Management. |
459
|
|
|
|
|
|
|
|
460
|
|
|
|
|
|
|
=item B |
461
|
|
|
|
|
|
|
|
462
|
|
|
|
|
|
|
Plaintext-aware encryption with RSA. |
463
|
|
|
|
|
|
|
|
464
|
|
|
|
|
|
|
=item B |
465
|
|
|
|
|
|
|
|
466
|
|
|
|
|
|
|
Probabilistic Signature Scheme based on RSA. |
467
|
|
|
|
|
|
|
|
468
|
|
|
|
|
|
|
=item B |
469
|
|
|
|
|
|
|
|
470
|
|
|
|
|
|
|
PKCS #1 v1.5 encryption scheme. |
471
|
|
|
|
|
|
|
|
472
|
|
|
|
|
|
|
=item B |
473
|
|
|
|
|
|
|
|
474
|
|
|
|
|
|
|
PKCS #1 v1.5 signature scheme. |
475
|
|
|
|
|
|
|
|
476
|
|
|
|
|
|
|
=back |
477
|
|
|
|
|
|
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478
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=head1 CUSTOMISING A CRYPT::RSA OBJECT |
479
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480
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A Crypt::RSA object can be customized by passing any of the following keys |
481
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in a hash to new(): ES to specify the encryption scheme, SS to specify the |
482
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signature scheme, PP to specify the post processor, and KF to specify the |
483
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key format. The value associated with these keys can either be a name (a |
484
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string) or a hash reference that specifies a module name, its constructor, |
485
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and constructor arguments. For example: |
486
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487
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my $rsa = new Crypt::RSA ( ES => 'OAEP' ); |
488
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489
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or |
490
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491
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my $rsa = new Crypt::RSA ( ES => { Module => 'Crypt::RSA::ES::OAEP' } ); |
492
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493
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A module thus specified need not be included in the Crypt::RSA bundle, but |
494
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it must be interface compatible with the ones provided with Crypt::RSA. |
495
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496
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As of this writing, the following names are recognised: |
497
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498
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=over 4 |
499
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500
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=item B (Encryption Scheme) |
501
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502
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'OAEP', 'PKCS1v15' |
503
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504
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=item B (Signature Scheme) |
505
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506
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'PSS', 'PKCS1v15' |
507
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508
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=item B (Key Format) |
509
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510
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'Native', 'SSH' |
511
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512
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=item B (Post Processor) |
513
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514
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'ASCII' |
515
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516
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=back |
517
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518
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=head1 ERROR HANDLING |
519
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520
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All modules in the Crypt::RSA bundle use a common error handling method |
521
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(implemented in Crypt::RSA::Errorhandler(3)). When a method fails it |
522
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returns undef and calls $self->error() with the error message. This error |
523
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message is available to the caller through the errstr() method. For more |
524
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details see the Crypt::RSA::Errorhandler(3) manpage. |
525
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526
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=head1 AUTHOR |
527
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528
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Vipul Ved Prakash, Email@vipul.netE |
529
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530
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=head1 ACKNOWLEDGEMENTS |
531
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532
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Thanks to Ilya Zakharevich for help with Math::Pari, Benjamin Trott for |
533
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several patches including SSH key support, Genèche Ramanoudjame for |
534
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extensive testing and numerous bug reports, Shizukesa on #perl for |
535
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suggesting the error handling method used in this module, and Dave Paris |
536
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for good advice. |
537
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538
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=head1 LICENSE |
539
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540
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Copyright (c) 2000-2008, Vipul Ved Prakash. This code is free software; |
541
|
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it is distributed under the same license as Perl itself. |
542
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543
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|
I have received requests for commercial licenses of |
544
|
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|
Crypt::RSA, from those who desire contractual support and |
545
|
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|
indemnification. I'd be happy to provide a commercial license |
546
|
|
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|
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|
if you need one. Please send me mail at C with |
547
|
|
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|
the subject "Crypt::RSA license". Please don't send me mail |
548
|
|
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|
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|
asking if you need a commercial license. You don't, if |
549
|
|
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|
Artistic of GPL suit you fine. |
550
|
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551
|
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=head1 SEE ALSO |
552
|
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553
|
|
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|
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|
|
Crypt::RSA::Primitives(3), Crypt::RSA::DataFormat(3), |
554
|
|
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|
|
Crypt::RSA::Errorhandler(3), Crypt::RSA::Debug(3), Crypt::Primes(3), |
555
|
|
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|
|
Crypt::Random(3), Crypt::CBC(3), Crypt::Blowfish(3), |
556
|
|
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|
Tie::EncryptedHash(3), Convert::ASCII::Armour(3), Math::Pari(3), |
557
|
|
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|
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|
|
Class::Loader(3), crypt-rsa-interoperability(3), |
558
|
|
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|
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|
|
crypt-rsa-interoperability-table(3). |
559
|
|
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560
|
|
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|
|
=head1 REPORTING BUGS |
561
|
|
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562
|
|
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|
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|
|
All bug reports related to Crypt::RSA should go to rt.cpan.org |
563
|
|
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|
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|
|
at C |
564
|
|
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|
|
565
|
|
|
|
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|
|
Crypt::RSA is considered to be stable. If you are running into a |
566
|
|
|
|
|
|
|
problem, it's likely of your own making. Please check your code |
567
|
|
|
|
|
|
|
and consult the documentation before posting a bug report. A |
568
|
|
|
|
|
|
|
google search with the error message might also shed light if it |
569
|
|
|
|
|
|
|
is a common mistake that you've made. |
570
|
|
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|
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|
|
571
|
|
|
|
|
|
|
If the module installation fails with a "Segmentation Fault" or |
572
|
|
|
|
|
|
|
"Bus Error", it is likely a Math::Pari issue. Please consult |
573
|
|
|
|
|
|
|
Math::Pari bugs on rt.cpan.org or open a bug there. There have |
574
|
|
|
|
|
|
|
been known issues on HP-UX and SunOS systems (with Math::Pari), |
575
|
|
|
|
|
|
|
so if you are on those OSes, please consult Math::Pari |
576
|
|
|
|
|
|
|
resources before opening a Crypt::RSA bug. |
577
|
|
|
|
|
|
|
|
578
|
|
|
|
|
|
|
=head1 BIBLIOGRAPHY |
579
|
|
|
|
|
|
|
|
580
|
|
|
|
|
|
|
Chronologically sorted (for the most part). |
581
|
|
|
|
|
|
|
|
582
|
|
|
|
|
|
|
=over 4 |
583
|
|
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|
|
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|
|
584
|
|
|
|
|
|
|
=item 1 B A Method for Obtaining Digital Signatures and Public-Key Cryptosystems (1978). |
585
|
|
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|
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|
|
586
|
|
|
|
|
|
|
=item 2 B Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters (1994). |
587
|
|
|
|
|
|
|
|
588
|
|
|
|
|
|
|
=item 3 B Optimal Asymmetric Encryption - How to Encrypt with RSA (1995). |
589
|
|
|
|
|
|
|
|
590
|
|
|
|
|
|
|
=item 4 B The Exact Security of Digital Signatures - How to sign with RSA and Rabin (1996). |
591
|
|
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|
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|
|
592
|
|
|
|
|
|
|
=item 5 B Applied Cryptography, Second Edition (1996). |
593
|
|
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|
|
594
|
|
|
|
|
|
|
=item 6 B Handbook of Applied Cryptography (1997). |
595
|
|
|
|
|
|
|
|
596
|
|
|
|
|
|
|
=item 7 B Twenty Years of Attacks on the RSA Cryptosystem (1998). |
597
|
|
|
|
|
|
|
|
598
|
|
|
|
|
|
|
=item 8 B A New and Optimal Chosen-message Attack on RSA-type Cryptosystems (1998). |
599
|
|
|
|
|
|
|
|
600
|
|
|
|
|
|
|
=item 9 B Recent Results on PKCS #1: RSA Encryption Standard, RSA Labs Bulletin Number 7 (1998). |
601
|
|
|
|
|
|
|
|
602
|
|
|
|
|
|
|
=item 10 B PKCS #1: RSA Cryptography Specifications v2.0, RFC 2437 (1998). |
603
|
|
|
|
|
|
|
|
604
|
|
|
|
|
|
|
=item 11 B SSH 1.2.7 source code (1998). |
605
|
|
|
|
|
|
|
|
606
|
|
|
|
|
|
|
=item 12 B PGP DH vs. RSA FAQ v1.5 (1999). |
607
|
|
|
|
|
|
|
|
608
|
|
|
|
|
|
|
=item 13 B Draft I, PKCS #1 v2.1: RSA Cryptography Standard (1999). |
609
|
|
|
|
|
|
|
|
610
|
|
|
|
|
|
|
=item 14 B OpenSSL 0.9.5a source code (2000). |
611
|
|
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|
|
|
|
|
612
|
|
|
|
|
|
|
=item 15 B The sci.crypt FAQ at |
613
|
|
|
|
|
|
|
http://www.faqs.org/faqs/cryptography-faq/part01/index.html |
614
|
|
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|
|
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|
|
615
|
|
|
|
|
|
|
=item 16 B A Proposal for an ISO Standard for Public Key Encryption (2001). |
616
|
|
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|
|
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|
|
617
|
|
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|
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|
|
=cut |