1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
|
# Copyright 2002 by the Massachusetts Institute of Technology.
# All Rights Reserved.
#
# Export of this software from the United States of America may
# require a specific license from the United States Government.
# It is the responsibility of any person or organization contemplating
# export to obtain such a license before exporting.
#
# WITHIN THAT CONSTRAINT, permission to use, copy, modify, and
# distribute this software and its documentation for any purpose and
# without fee is hereby granted, provided that the above copyright
# notice appear in all copies and that both that copyright notice and
# this permission notice appear in supporting documentation, and that
# the name of M.I.T. not be used in advertising or publicity pertaining
# to distribution of the software without specific, written prior
# permission. Furthermore if you modify this software you must label
# your software as modified software and not distribute it in such a
# fashion that it might be confused with the original M.I.T. software.
# M.I.T. makes no representations about the suitability of
# this software for any purpose. It is provided "as is" without express
# or implied warranty.
package CRC;
# CRC: implement a CRC using the Poly package (yes this is slow)
#
# message M(x) = m_0 * x^0 + m_1 * x^1 + ... + m_(k-1) * x^(k-1)
# generator P(x) = p_0 * x^0 + p_1 * x^1 + ... + p_n * x^n
# remainder R(x) = r_0 * x^0 + r_1 * x^1 + ... + r_(n-1) * x^(n-1)
#
# R(x) = (x^n * M(x)) % P(x)
#
# Note that if F(x) = x^n * M(x) + R(x), then F(x) = 0 mod P(x) .
#
# In MIT Kerberos 5, R(x) is taken as the CRC, as opposed to what
# ISO 3309 does.
#
# ISO 3309 adds a precomplement and a postcomplement.
#
# The ISO 3309 postcomplement is of the form
#
# A(x) = x^0 + x^1 + ... + x^(n-1) .
#
# The ISO 3309 precomplement is of the form
#
# B(x) = x^k * A(x) .
#
# The ISO 3309 FCS is then
#
# (x^n * M(x)) % P(x) + B(x) % P(x) + A(x) ,
#
# which is equivalent to
#
# (x^n * M(x) + B(x)) % P(x) + A(x) .
#
# In ISO 3309, the transmitted frame is
#
# F'(x) = x^n * M(x) + R(x) + R'(x) + A(x) ,
#
# where
#
# R'(x) = B(x) % P(x) .
#
# Note that this means that if a new remainder is computed over the
# frame F'(x) (treating F'(x) as the new M(x)), it will be equal to a
# constant.
#
# F'(x) = 0 + R'(x) + A(x) mod P(x) ,
#
# then
#
# (F'(x) + x^k * A(x)) * x^n
#
# = ((R'(x) + A(x)) + x^k * A(x)) * x^n mod P(x)
#
# = (x^k * A(x) + A(x) + x^k * A(x)) * x^n mod P(x)
#
# = (0 + A(x)) * x^n mod P(x)
#
# Note that (A(x) * x^n) % P(x) is a constant, and that this result
# depends on B(x) being x^k * A(x).
use Carp;
use Poly;
sub new {
my $self = shift;
my $class = ref($self) || $self;
my %args = @_;
$self = {bitsendian => "little"};
bless $self, $class;
$self->setpoly($args{"Poly"}) if exists $args{"Poly"};
$self->bitsendian($args{"bitsendian"})
if exists $args{"bitsendian"};
$self->{precomp} = $args{precomp} if exists $args{precomp};
$self->{postcomp} = $args{postcomp} if exists $args{postcomp};
return $self;
}
sub setpoly {
my $self = shift;
my($arg) = @_;
croak "need a polynomial" if !$arg->isa("Poly");
$self->{Poly} = $arg;
return $self;
}
sub crc {
my $self = shift;
my $msg = Poly->new(@_);
my($order, $r, $precomp);
$order = $self->{Poly}->order;
# B(x) = x^k * precomp
$precomp = $self->{precomp} ?
$self->{precomp} * Poly->powers2poly(scalar(@_)) : Poly->new;
# R(x) = (x^n * M(x)) % P(x)
$r = ($msg * Poly->powers2poly($order)) % $self->{Poly};
# B(x) % P(x)
$r += $precomp % $self->{Poly};
$r += $self->{postcomp} if exists $self->{postcomp};
return $r;
}
# endianness of bits of each octet
#
# Note that the message is always treated as being sent in big-endian
# octet order.
#
# Usually, the message will be treated as bits being little-endian,
# since that is the common case for serial implementations that
# present data in octets; e.g., most UARTs shift octets onto the line
# in little-endian order, and protocols such as ISO 3309, V.42,
# etc. treat individual octets as being sent LSB-first.
sub bitsendian {
my $self = shift;
my($arg) = @_;
croak "bad bit endianness" if $arg !~ /big|little/;
$self->{bitsendian} = $arg;
return $self;
}
sub crcstring {
my $self = shift;
my($arg) = @_;
my($packstr, @m);
{
$packstr = "B*", last if $self->{bitsendian} =~ /big/;
$packstr = "b*", last if $self->{bitsendian} =~ /little/;
croak "bad bit endianness";
};
@m = split //, unpack $packstr, $arg;
return $self->crc(@m);
}
1;
|
