|  line  | 
 stmt  | 
 bran  | 
 cond  | 
 sub  | 
 pod  | 
 time  | 
 code  | 
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1
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 package Crypt::RSA;  | 
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2
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1
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1
  
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19122
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 use strict;  | 
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2
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23
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3
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1
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5
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 use warnings;  | 
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2
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 ##  | 
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6
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 ## Crypt::RSA - Pure-perl implementation of RSA encryption/signing  | 
| 
7
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 ##              algorithms.  | 
| 
8
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 ##  | 
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9
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 ## Copyright (c) 2000-2001, Vipul Ved Prakash.  All rights reserved.  | 
| 
10
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 ## This code is free software; you can redistribute it and/or modify  | 
| 
11
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 ## it under the same terms as Perl itself.  | 
| 
12
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    | 
| 
13
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1
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1
  
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5
 | 
 use base 'Class::Loader';  | 
| 
 
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1
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1
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    | 
| 
 
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1
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 | 
762
 | 
    | 
| 
14
 | 
1
 | 
 
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1
  
 | 
 
 | 
11100
 | 
 use base 'Crypt::RSA::Errorhandler';  | 
| 
 
 | 
1
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3
 | 
    | 
| 
 
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1
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 | 
525
 | 
    | 
| 
15
 | 
1
 | 
 
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1
  
 | 
 
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510
 | 
 use Crypt::RSA::Key;  | 
| 
 
 | 
1
 | 
 
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3
 | 
    | 
| 
 
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1
 | 
 
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 | 
34
 | 
    | 
| 
16
 | 
1
 | 
 
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 | 
  
1
  
 | 
 
 | 
5
 | 
 use Crypt::RSA::DataFormat qw(steak octet_len);  | 
| 
 
 | 
1
 | 
 
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1
 | 
    | 
| 
 
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1
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 | 
50
 | 
    | 
| 
17
 | 
1
 | 
 
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1
  
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 | 
743
 | 
 use Convert::ASCII::Armour;  | 
| 
 
 | 
1
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 | 
130465
 | 
    | 
| 
 
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1
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 | 
33
 | 
    | 
| 
18
 | 
1
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1
  
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9
 | 
 use Carp;  | 
| 
 
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1
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3
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    | 
| 
 
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1
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1121
 | 
    | 
| 
19
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    | 
| 
20
 | 
 
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 | 
 
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 | 
 
 | 
 
 | 
 $Crypt::RSA::VERSION = '1.99';  # change this elsewhere too!  | 
| 
21
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    | 
| 
22
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 | 
 my %DEFAULTS = (   | 
| 
23
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
     'ES'    => { Name  => 'OAEP_ES'    },  | 
| 
24
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 | 
 
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 | 
     'SS'    => { Name  => 'PSS_SS'     },  | 
| 
25
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 | 
     'PP'    => { Name  => 'ASCII_PP'   },  | 
| 
26
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 );  | 
| 
27
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    | 
| 
28
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    | 
| 
29
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 my %KNOWNMAP = (  | 
| 
30
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    | 
| 
31
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 | 
   # ENCRYPTION SCHEMES  | 
| 
32
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    | 
| 
33
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
             OAEP_ES =>  { Module => "Crypt::RSA::ES::OAEP"      },  | 
| 
34
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         PKCS1v21_ES =>  { Module => "Crypt::RSA::ES::OAEP"      },  | 
| 
35
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         PKCS1v15_ES =>  { Module => "Crypt::RSA::ES::PKCS1v15"  },  | 
| 
36
 | 
 
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    | 
| 
37
 | 
 
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   # SIGNATURE SCHEMES  | 
| 
38
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    | 
| 
39
 | 
 
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 | 
              PSS_SS =>  { Module => "Crypt::RSA::SS::PSS"       },  | 
| 
40
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         PKCS1v21_SS =>  { Module => "Crypt::RSA::SS::PSS"       },  | 
| 
41
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         PKCS1v15_SS =>  { Module => "Crypt::RSA::SS::PKCS1v15"  },  | 
| 
42
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    | 
| 
43
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   # POST PROCESSORS  | 
| 
44
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    | 
| 
45
 | 
 
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 | 
            ASCII_PP =>  { Module => "Convert::ASCII::Armour"    },  | 
| 
46
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    | 
| 
47
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 | 
 
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 | 
 
 | 
 
 | 
 );  | 
| 
48
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    | 
| 
49
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    | 
| 
50
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 sub new {   | 
| 
51
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    | 
| 
52
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
  
1
  
 | 
 
 | 
     my ($class, %params) = @_;  | 
| 
53
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my %self = (%DEFAULTS, %params);  | 
| 
54
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $self = bless \%self, $class;  | 
| 
55
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
56
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     $self->_storemap (%KNOWNMAP);   | 
| 
57
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
       | 
| 
58
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     for (qw(ES SS PP)) {   | 
| 
59
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $$self{$_} = { Name => $$self{$_} . "_$_" } unless ref $$self{$_};  | 
| 
60
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $$self{lc($_)} = $self->_load ( %{$$self{$_}} );  | 
| 
 
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
61
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 
 | 
     }  | 
| 
62
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 
 | 
    | 
| 
63
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     $$self{keychain} = new Crypt::RSA::Key;   | 
| 
64
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
65
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return bless \%self, $class;   | 
| 
66
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
    | 
| 
67
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 
 | 
 }  | 
| 
68
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
69
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
    | 
| 
70
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub keygen {   | 
| 
71
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
72
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
  
1
  
 | 
 
 | 
     my ($self, %params) = @_;  | 
| 
73
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     $params{KF} = $$self{KF} if $$self{KF};  | 
| 
74
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
75
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my @keys;  | 
| 
76
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return (@keys = $self->{keychain}->generate (%params))  | 
| 
77
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                   ? @keys   | 
| 
78
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                   : $self->error ($self->{keychain}->errstr);  | 
| 
79
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
80
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }   | 
| 
81
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
82
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
83
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub encrypt {   | 
| 
84
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
85
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
  
1
  
 | 
 
 | 
     my ($self, %params)   = @_;  | 
| 
86
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
     my $plaintext         = $params{Message} || $params{Plaintext};  | 
| 
87
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $key               = $params{Key};   | 
| 
88
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
89
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $self->error ($key->errstr, \%params, $key, \$plaintext)   | 
| 
90
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         unless $key->check();  | 
| 
91
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
92
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $blocksize = blocksize ( $$self{es}->encryptblock (Key => $key),  | 
| 
93
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                 length($plaintext)  | 
| 
94
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                               );  | 
| 
95
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
96
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $self->error("Message too long.", \$key, \%params) if $blocksize <= 0;  | 
| 
97
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
98
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $cyphertext;  | 
| 
99
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my @segments = steak ($plaintext, $blocksize);  | 
| 
100
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     for (@segments) {  | 
| 
101
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $cyphertext .= $self->{es}->encrypt (Message => $_, Key => $key)  | 
| 
102
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
             || return $self->error ($self->{es}->errstr, \$key, \%params);  | 
| 
103
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
104
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
105
 | 
  
0
  
 | 
  
  0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
     if ($params{Armour} || $params{Armor}) {   | 
| 
106
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $cyphertext = $self->{pp}->armour (   | 
| 
107
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
              Object   => 'RSA ENCRYPTED MESSAGE',   | 
| 
108
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
              Headers  => {    | 
| 
109
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                 Scheme  => $$self{ES}{Module} || ${$KNOWNMAP{$$self{ES}{Name}}}{Module},  | 
| 
110
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                 Version => $self->{es}->version()   | 
| 
111
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
              },   | 
| 
112
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
              Content  => { Cyphertext => $cyphertext },  | 
| 
113
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
              Compress => 1,   | 
| 
114
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         );  | 
| 
115
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }   | 
| 
116
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
117
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $cyphertext;  | 
| 
118
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
119
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
120
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
121
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
122
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub decrypt {   | 
| 
123
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
124
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
  
1
  
 | 
 
 | 
     my ($self , %params) = @_;  | 
| 
125
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
     my $cyphertext       = $params{Cyphertext} || $params{Ciphertext};  | 
| 
126
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $key              = $params{Key};   | 
| 
127
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
128
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $self->error ($key->errstr, \%params, $key) unless $key->check();  | 
| 
129
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
130
 | 
  
0
  
 | 
  
  0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
     if ($params{Armour} || $params{Armor}) {   | 
| 
131
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         my $decoded = $self->{pp}->unarmour ($cyphertext) ||  | 
| 
132
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
             return $self->error ($self->{pp}->errstr());  | 
| 
133
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $cyphertext = $$decoded{Content}{Cyphertext}  | 
| 
134
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
135
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
136
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $plaintext;  | 
| 
137
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $blocksize = blocksize ( $$self{es}->decryptblock (Key => $key),  | 
| 
138
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                                 length($cyphertext)  | 
| 
139
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                               );  | 
| 
140
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
141
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $self->error("Message too long.") if $blocksize <= 0;  | 
| 
142
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
143
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my @segments = steak ($cyphertext, $blocksize);  | 
| 
144
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     for (@segments) {  | 
| 
145
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $plaintext .= $self->{es}->decrypt (Cyphertext=> $_, Key => $key)  | 
| 
146
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
             || return $self->error ($self->{es}->errstr, \$key, \%params);  | 
| 
147
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
148
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
149
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $plaintext;  | 
| 
150
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
151
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
152
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
153
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
154
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub sign {   | 
| 
155
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
156
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
  
1
  
 | 
 
 | 
     my ($self, %params) = @_;  | 
| 
157
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $signature = $self->{ss}->sign (%params)   | 
| 
158
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                  || return $self->error ($self->{ss}->errstr,  | 
| 
159
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
                         $params{Key}, \%params);  | 
| 
160
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
161
 | 
  
0
  
 | 
  
  0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
     if ($params{Armour} || $params{Armor}) {   | 
| 
162
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $signature      = $self->{pp}->armour (   | 
| 
163
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                Object   => "RSA SIGNATURE",   | 
| 
164
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                Headers  => {    | 
| 
165
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                     Scheme  => $$self{SS}{Module} || ${$KNOWNMAP{$$self{SS}{Name}}}{Module},  | 
| 
166
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
                     Version => $self->{ss}->version() },   | 
| 
167
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                Content  => { Signature => $signature },  | 
| 
168
 | 
 
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 | 
 
 | 
 
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 | 
         );  | 
| 
169
 | 
 
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 | 
     }  | 
| 
170
 | 
 
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 | 
 
 | 
 
 | 
 
 | 
    | 
| 
171
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $signature;  | 
| 
172
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
173
 | 
 
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 | 
 
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 | 
 }   | 
| 
174
 | 
 
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    | 
| 
175
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    | 
| 
176
 | 
 
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 sub verify {   | 
| 
177
 | 
 
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 | 
 
 | 
 
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 | 
    | 
| 
178
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
  
1
  
 | 
 
 | 
     my ($self, %params) = @_;  | 
| 
179
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
180
 | 
  
0
  
 | 
  
  0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
     if ($params{Armour} || $params{Armor}) {   | 
| 
181
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         my $decoded  = $self->{pp}->unarmour ($params{Signature}) ||  | 
| 
182
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
             return $self->error ($self->{pp}->errstr());  | 
| 
183
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $params{Signature} = $$decoded{Content}{Signature}  | 
| 
184
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     }  | 
| 
185
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
186
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $verify = $self->{ss}->verify (%params) ||   | 
| 
187
 | 
  
0
  
 | 
 
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
         return $self->error ($self->{ss}->errstr, $params{Key}, \%params);  | 
| 
188
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
189
 | 
  
0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $verify;  | 
| 
190
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
191
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
192
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
193
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
194
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sub blocksize {   | 
| 
195
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
196
 | 
  
0
  
 | 
 
 | 
 
 | 
  
0
  
 | 
  
0
  
 | 
 
 | 
     my ($blocksize, $ptsize) = @_;  | 
| 
197
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $ptsize if $blocksize == -1;  | 
| 
198
 | 
  
0
  
 | 
  
  0
  
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return 0 if $blocksize < 1;  | 
| 
199
 | 
0
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     return $blocksize;  | 
| 
200
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
           | 
| 
201
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 }  | 
| 
202
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
    | 
| 
203
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 1;   | 
| 
204
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
205
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =pod  | 
| 
206
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
207
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =encoding utf8  | 
| 
208
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
209
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 NAME  | 
| 
210
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
211
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA - RSA public-key cryptosystem.  | 
| 
212
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
213
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 SYNOPSIS  | 
| 
214
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
215
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $rsa = new Crypt::RSA;   | 
| 
216
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
217
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my ($public, $private) =   | 
| 
218
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $rsa->keygen (   | 
| 
219
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Identity  => 'Lord Macbeth ',  | 
| 
220
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Size      => 1024,    | 
| 
221
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Password  => 'A day so foul & fair',   | 
| 
222
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Verbosity => 1,  | 
| 
223
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         ) or die $rsa->errstr();  | 
| 
224
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
225
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
226
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $cyphertext =   | 
| 
227
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $rsa->encrypt (   | 
| 
228
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Message    => $message,  | 
| 
229
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Key        => $public,  | 
| 
230
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Armour     => 1,  | 
| 
231
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         ) || die $rsa->errstr();  | 
| 
232
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
233
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
234
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $plaintext =   | 
| 
235
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $rsa->decrypt (   | 
| 
236
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Cyphertext => $cyphertext,   | 
| 
237
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Key        => $private,  | 
| 
238
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Armour     => 1,  | 
| 
239
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         ) || die $rsa->errstr();  | 
| 
240
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
241
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
242
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $signature =   | 
| 
243
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $rsa->sign (   | 
| 
244
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Message    => $message,   | 
| 
245
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Key        => $private  | 
| 
246
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         ) || die $rsa->errstr();  | 
| 
247
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
248
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
249
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $verify =   | 
| 
250
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         $rsa->verify (  | 
| 
251
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Message    => $message,   | 
| 
252
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Signature  => $signature,   | 
| 
253
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
             Key        => $public  | 
| 
254
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
         ) || die $rsa->errstr();  | 
| 
255
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
256
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 NOTE  | 
| 
257
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
258
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 This manual assumes familiarity with public-key cryptography and the RSA  | 
| 
259
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 algorithm. If you don't know what these are or how they work, please refer  | 
| 
260
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 to the sci.crypt FAQ[15]. A formal treatment of RSA can be found in [1].  | 
| 
261
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
262
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 DESCRIPTION  | 
| 
263
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
264
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA is a pure-perl, cleanroom implementation of the RSA public-key  | 
| 
265
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 cryptosystem.  | 
| 
266
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
267
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA provides arbitrary size key-pair generation, plaintext-aware  | 
| 
268
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 encryption (OAEP) and digital signatures with appendix (PSS). For  | 
| 
269
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 compatibility with SSLv3, RSAREF2, PGP and other applications that follow  | 
| 
270
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the PKCS #1 v1.5 standard, it also provides PKCS #1 v1.5 encryption and  | 
| 
271
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 signatures.  | 
| 
272
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
273
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA is structured as bundle of modules that encapsulate different  | 
| 
274
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 parts of the RSA cryptosystem. The RSA algorithm is implemented in  | 
| 
275
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::Primitives(3). Encryption schemes, located under  | 
| 
276
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::ES, and signature schemes, located under Crypt::RSA::SS, use  | 
| 
277
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the RSA algorithm to build encryption/signature schemes that employ secure  | 
| 
278
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 padding. (See the note on Security of Padding Schemes.)  | 
| 
279
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
280
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The key generation engine and other functions that work on both components  | 
| 
281
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 of the key-pair are encapsulated in Crypt::RSA::Key(3).  | 
| 
282
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::Key::Public(3) & Crypt::RSA::Key::Private(3) provide  | 
| 
283
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 mechanisms for storage & retrival of keys from disk, decoding & encoding  | 
| 
284
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 of keys in certain formats, and secure representation of keys in memory.  | 
| 
285
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Finally, the Crypt::RSA module provides a convenient, DWIM wrapper around  | 
| 
286
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 the rest of the modules in the bundle.  | 
| 
287
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
288
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 SECURITY OF PADDING SCHEMES  | 
| 
289
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
290
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 It has been conclusively shown that textbook RSA is insecure[3,7]. Secure  | 
| 
291
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 RSA requires that plaintext is padded in a specific manner before  | 
| 
292
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 encryption and signing. There are four main standards for padding: PKCS  | 
| 
293
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 #1 v1.5 encryption & signatures, and OAEP encryption & PSS signatures.  | 
| 
294
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA implements these as four modules that   | 
| 
295
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 provide overloaded encrypt(), decrypt(), sign() and verify() methods that  | 
| 
296
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 add padding functionality to the basic RSA operations.  | 
| 
297
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
298
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::ES::PKCS1v15(3) implements PKCS #1 v1.5 encryption,  | 
| 
299
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::SS::PKCS1v15(3) implements PKCS #1 v1.5 signatures,  | 
| 
300
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::ES::OAEP(3) implements Optimal Asymmetric Encryption and  | 
| 
301
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::SS::PSS(3) Probabilistic Signatures.  | 
| 
302
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
303
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 PKCS #1 v1.5 schemes are older and hence more widely deployed, but PKCS #1  | 
| 
304
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 v1.5 encryption has certain flaws that make it vulnerable to  | 
| 
305
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 chosen-cyphertext attacks[9]. Even though Crypt::RSA works around these  | 
| 
306
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 vulnerabilities, it is recommended that new applications use OAEP and PSS,  | 
| 
307
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 both of which are provably secure[13]. In any event,  | 
| 
308
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Crypt::RSA::Primitives (without padding) should never be used directly.  | 
| 
309
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
310
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 That said, there exists a scheme called Simple RSA[16] that provides  | 
| 
311
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 security without padding. However, Crypt::RSA doesn't implement this  | 
| 
312
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 scheme yet.  | 
| 
313
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
314
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 METHODS  | 
| 
315
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
316
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
317
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
318
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
319
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
320
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 The constructor. When no arguments are provided, new() returns an object  | 
| 
321
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 loaded with default values. This object can be customized by specifying  | 
| 
322
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 encryption & signature schemes, key formats and post processors. For  | 
| 
323
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 details see the section on B
 | 
| 
324
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 object> later in this manpage.  | 
| 
325
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
326
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
327
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
328
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 keygen() generates and returns an RSA key-pair of specified bitsize.  | 
| 
329
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 keygen() is a synonym for Crypt::RSA::Key::generate(). Parameters and  | 
| 
330
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 return values are described in the Crypt::RSA::Key(3) manpage.  | 
| 
331
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
332
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
333
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
334
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 encrypt() performs RSA encryption on a string of arbitrary length with a  | 
| 
335
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 public key using the encryption scheme bound to the object. The default  | 
| 
336
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 scheme is OAEP. encrypt() returns cyphertext (a string) on success and  | 
| 
337
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 undef on failure. It takes a hash as argument with following keys:  | 
| 
338
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
339
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
340
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
341
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
342
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
343
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 An arbitrary length string to be encrypted.  | 
| 
344
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
345
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
346
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
347
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Public key of the recipient, a Crypt::RSA::Key::Public(3) or  | 
| 
348
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 compatible object.  | 
| 
349
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
350
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
351
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
352
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A boolean parameter that forces cyphertext through a post processor after  | 
| 
353
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 encrpytion. The default post processor is Convert::ASCII::Armour(3) that  | 
| 
354
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 encodes binary octets in 6-bit clean ASCII messages. The cyphertext is  | 
| 
355
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 returned as-is, when the Armour key is not present.  | 
| 
356
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
357
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
358
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
359
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
360
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
361
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 decrypt() performs RSA decryption with a private key using the encryption  | 
| 
362
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 scheme bound to the object. The default scheme is OAEP. decrypt() returns  | 
| 
363
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 plaintext on success and undef on failure. It takes a hash as argument  | 
| 
364
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 with following keys:  | 
| 
365
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
366
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
367
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
368
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
369
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
370
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Cyphertext of arbitrary length.   | 
| 
371
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
372
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
373
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
374
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Private key, a Crypt::RSA::Key::Private(3) or compatible object.  | 
| 
375
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
376
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B   | 
| 
377
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
378
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Boolean parameter that specifies whether the Cyphertext is encoded with a  | 
| 
379
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 post processor.  | 
| 
380
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
381
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
382
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
383
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
384
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
385
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 sign() creates an RSA signature on a string with a private key using the  | 
| 
386
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 signature scheme bound to the object. The default scheme is  | 
| 
387
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 PSS. sign() returns a signature on success and undef on failure. It takes  | 
| 
388
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 a hash as argument with following keys:  | 
| 
389
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
390
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
391
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
392
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
393
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
394
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A string of arbitrary length to be signed.  | 
| 
395
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
396
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
397
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
398
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Private key of the sender, a Crypt::RSA::Key::Private(3) or  | 
| 
399
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 compatible object.  | 
| 
400
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
401
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
402
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
403
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A boolean parameter that forces the computed signature to be post  | 
| 
404
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 processed.  | 
| 
405
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
406
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
407
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
408
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
409
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
410
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 verify() verifies an RSA signature with a public key using the signature  | 
| 
411
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 scheme bound to the object. The default scheme is PSS. verify() returns a  | 
| 
412
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 true value on success and undef on failure. It takes a hash as argument  | 
| 
413
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 with following keys:  | 
| 
414
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
415
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4   | 
| 
416
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
417
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
418
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
419
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A signed message, a string of arbitrary length.   | 
| 
420
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
421
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
422
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
423
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Public key of the signer, a Crypt::RSA::Key::Public(3) or  | 
| 
424
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 compatible object.  | 
| 
425
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
426
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B   | 
| 
427
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
428
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A signature computed with sign().  | 
| 
429
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
430
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
431
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
432
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Boolean parameter that specifies whether the Signature has been   | 
| 
433
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 post processed.  | 
| 
434
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
435
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
436
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
437
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
438
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
439
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 MODULES  | 
| 
440
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
441
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Apart from Crypt::RSA, the following modules are intended for application  | 
| 
442
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 developer and end-user consumption:  | 
| 
443
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
444
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
445
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
446
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
447
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
448
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 RSA key pair generator.  | 
| 
449
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
450
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
451
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
452
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 RSA Public Key Management.  | 
| 
453
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
454
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
455
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
456
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 RSA Private Key Management.  | 
| 
457
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
458
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
459
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
460
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Plaintext-aware encryption with RSA.  | 
| 
461
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
462
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
463
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
464
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 Probabilistic Signature Scheme based on RSA.  | 
| 
465
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
466
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
467
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
468
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 PKCS #1 v1.5 encryption scheme.   | 
| 
469
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
470
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B  | 
| 
471
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
472
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 PKCS #1 v1.5 signature scheme.   | 
| 
473
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
474
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back  | 
| 
475
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
476
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 CUSTOMISING A CRYPT::RSA OBJECT  | 
| 
477
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
478
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A Crypt::RSA object can be customized by passing any of the following keys  | 
| 
479
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 in a hash to new(): ES to specify the encryption scheme, SS to specify the  | 
| 
480
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 signature scheme, PP to specify the post processor, and KF to specify the  | 
| 
481
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 key format. The value associated with these keys can either be a name (a  | 
| 
482
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 string) or a hash reference that specifies a module name, its constructor,  | 
| 
483
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 and constructor arguments. For example:  | 
| 
484
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
485
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $rsa = new Crypt::RSA ( ES => 'OAEP' );  | 
| 
486
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
487
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
                     or   | 
| 
488
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
489
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     my $rsa = new Crypt::RSA ( ES => { Module => 'Crypt::RSA::ES::OAEP' } );  | 
| 
490
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
491
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 A module thus specified need not be included in the Crypt::RSA bundle, but  | 
| 
492
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 it must be interface compatible with the ones provided with Crypt::RSA.  | 
| 
493
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
494
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 As of this writing, the following names are recognised:  | 
| 
495
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
496
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =over 4  | 
| 
497
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
498
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B (Encryption Scheme)   | 
| 
499
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
500
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     'OAEP', 'PKCS1v15'  | 
| 
501
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
502
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B (Signature Scheme)   | 
| 
503
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
504
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     'PSS', 'PKCS1v15'  | 
| 
505
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
506
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B (Key Format)   | 
| 
507
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
508
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     'Native', 'SSH'  | 
| 
509
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
510
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item B (Post Processor)   | 
| 
511
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
512
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
     'ASCII'   | 
| 
513
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
514
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =back   | 
| 
515
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
516
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =head1 ERROR HANDLING  | 
| 
517
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
518
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 All modules in the Crypt::RSA bundle use a common error handling method  | 
| 
519
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 (implemented in Crypt::RSA::Errorhandler(3)). When a method fails it  | 
| 
520
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 returns undef and calls $self->error() with the error message. This error  | 
| 
521
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 message is available to the caller through the errstr() method. For more  | 
| 
522
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 details see the Crypt::RSA::Errorhandler(3) manpage.  | 
| 
523
 | 
 
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    | 
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524
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 =head1 AUTHOR  | 
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525
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526
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 Vipul Ved Prakash, Email@vipul.netE  | 
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527
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528
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 =head1 ACKNOWLEDGEMENTS  | 
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529
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530
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 Thanks to Ilya Zakharevich for help with Math::Pari, Benjamin Trott for  | 
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531
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 several patches including SSH key support, Genèche Ramanoudjame for  | 
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532
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 extensive testing and numerous bug reports, Shizukesa on #perl for  | 
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533
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 suggesting the error handling method used in this module, and Dave Paris  | 
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534
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 for good advice.  | 
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535
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536
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 =head1 LICENSE   | 
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537
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538
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 Copyright (c) 2000-2008, Vipul Ved Prakash. This code is free software;  | 
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539
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 it is distributed under the same license as Perl itself.  | 
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540
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541
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 I have received requests for commercial licenses of  | 
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542
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 Crypt::RSA, from those who desire contractual support and  | 
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543
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 indemnification. I'd be happy to provide a commercial license  | 
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544
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 if you need one. Please send me mail at C with  | 
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545
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 the subject "Crypt::RSA license". Please don't send me mail  | 
| 
546
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 asking if you need a commercial license. You don't, if  | 
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547
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 Artistic of GPL suit you fine.  | 
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548
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549
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 =head1 SEE ALSO  | 
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550
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551
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 Crypt::RSA::Primitives(3), Crypt::RSA::DataFormat(3),  | 
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552
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 Crypt::RSA::Errorhandler(3), Crypt::RSA::Debug(3),  | 
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553
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 Crypt::CBC(3), Crypt::Blowfish(3),  | 
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554
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 Tie::EncryptedHash(3), Convert::ASCII::Armour(3),  | 
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555
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 Class::Loader(3),  | 
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556
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 Math::Prime::Util, Bytes::Random::Secure.  | 
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557
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558
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 =head1 REPORTING BUGS  | 
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559
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560
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 All bug reports related to Crypt::RSA should go to rt.cpan.org   | 
| 
561
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 at C  | 
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562
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563
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 Crypt::RSA is considered to be stable. If you are running into a  | 
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564
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 problem, it's likely of your own making. Please check your code  | 
| 
565
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 and consult the documentation before posting a bug report. A  | 
| 
566
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 google search with the error message might also shed light if it  | 
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567
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 is a common mistake that you've made.  | 
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568
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    | 
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569
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 =head1 BIBLIOGRAPHY  | 
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570
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    | 
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571
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 Chronologically sorted (for the most part).  | 
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572
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    | 
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573
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 =over 4  | 
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574
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    | 
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575
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 =item 1 B A Method for Obtaining Digital Signatures and Public-Key Cryptosystems (1978).  | 
| 
576
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    | 
| 
577
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 =item 2 B Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters (1994).  | 
| 
578
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    | 
| 
579
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 =item 3 B Optimal Asymmetric Encryption - How to Encrypt with RSA (1995).  | 
| 
580
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    | 
| 
581
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 =item 4 B The Exact Security of Digital Signatures - How to sign with RSA and Rabin (1996).  | 
| 
582
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    | 
| 
583
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 =item 5 B Applied Cryptography, Second Edition (1996).  | 
| 
584
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    | 
| 
585
 | 
 
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 =item 6 B Handbook of Applied Cryptography (1997).  | 
| 
586
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    | 
| 
587
 | 
 
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 =item 7 B Twenty Years of Attacks on the RSA Cryptosystem (1998).  | 
| 
588
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    | 
| 
589
 | 
 
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 =item 8 B A New and Optimal Chosen-message Attack on RSA-type Cryptosystems (1998).  | 
| 
590
 | 
 
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    | 
| 
591
 | 
 
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 =item 9 B Recent Results on PKCS #1: RSA Encryption Standard, RSA Labs Bulletin Number 7 (1998).  | 
| 
592
 | 
 
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    | 
| 
593
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 =item 10 B PKCS #1: RSA Cryptography Specifications v2.0, RFC 2437 (1998).  | 
| 
594
 | 
 
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 | 
 
 | 
    | 
| 
595
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item 11 B SSH 1.2.7 source code (1998).  | 
| 
596
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
    | 
| 
597
 | 
 
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 =item 12 B PGP DH vs. RSA FAQ v1.5 (1999).  | 
| 
598
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
    | 
| 
599
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item 13 B Draft I, PKCS #1 v2.1: RSA Cryptography Standard (1999).  | 
| 
600
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 
 | 
    | 
| 
601
 | 
 
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 | 
 
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 | 
 
 | 
 
 | 
 =item 14 B OpenSSL 0.9.5a source code (2000).  | 
| 
602
 | 
 
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 | 
 
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 | 
 
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 | 
    | 
| 
603
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item 15 B The sci.crypt FAQ at  | 
| 
604
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 http://www.faqs.org/faqs/cryptography-faq/part01/index.html  | 
| 
605
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
    | 
| 
606
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 
 | 
 =item 16 B A Proposal for an ISO Standard for Public Key Encryption (2001).  | 
| 
607
 | 
 
 | 
 
 | 
 
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 | 
 
 | 
 
 | 
    | 
| 
608
 | 
 
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 | 
 
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 =cut  |