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@mfukar
mfukar committed Feb 2, 2011
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71 changes: 71 additions & 0 deletions lfsr.c
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/*
* Galois LFSR software implementation.
*
* WARNING:
* Polynomial representation: x^4 + x^3 + 1 = 11001 = 0x19
*
* Well-known polynomials:
* CRC-12 : x^12 + x^11 + x^3 + x^2 + x + 1
* CRC-16-IBM : x^16 + x^15 + x^2 + 1
* CRC-16-DECT : x^16 + x^10 + x^8 + x^7 + x^3 + 1
* CCITT : x^16 + x^12 + x^5 + 1
* CRC-32-IEEE : x^32 + x^26 + x^23 + x^22 + x^16 + x^12 + x^11 + x^10 + x^8 + x^7 + x^5 + x^4 + x^2 + x + 1
*
* Spread-spectrum sequences:
* 7-bit : x^7 + x + 1
* 13-bit : x^13 + x^4 + x^3 + 1
* 19-bit : x^19 + x^5 + x^2 + x + 1
*
* Used in A5:
* x^19 + x^5 + x^2 + x + 1
* x^22 + x + 1
* x^23 + x^15 + x^2 + x + 1
* x^17 + x^5 + 1
*
* GPS satellites:
* x^10 + x^3 + 1
* x^10 + x^9 + x^8 + x^6 + x^3 + x^2 + 1
*
* Source of secure polynoms:
* http://homepage.mac.com/afj/taplist.html
* http://www.xilinx.com/support/documentation/application_notes/xapp052.pdf
*
* © 2010 Michael Foukarakis
*/
#include "lfsr.h"

void GLFSR_init(lfsr_t *glfsr, lfsr_data polynom, lfsr_data seed_value)
{
lfsr_data seed_mask;
unsigned int shift = 8 * sizeof(lfsr_data) - 1;

glfsr->polynomial = polynom | 1;
glfsr->data = seed_value;

seed_mask = 1;
seed_mask <<= shift;

while(shift--) {
if(polynom & seed_mask) {
glfsr->mask = seed_mask;
break;
}
seed_mask >>= 1;
}

return;
}

unsigned char GLFSR_next(lfsr_t *glfsr)
{
unsigned char retval = 0;

glfsr->data <<= 1;

if(glfsr->data & glfsr->mask) {
retval = 1;
glfsr->data ^= glfsr->polynomial;
}

return(retval);
}
17 changes: 17 additions & 0 deletions lfsr.h
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/*
* Galois LFSR software implementation.
*
* © 2010 Michael Foukarakis
*/
#include <stdint.h>

typedef uint64_t lfsr_data;

typedef struct {
lfsr_data data;
lfsr_data polynomial;
lfsr_data mask;
} lfsr_t;

void GLFSR_init(lfsr_t *, lfsr_data, lfsr_data);
unsigned char GLFSR_next(lfsr_t *);
172 changes: 172 additions & 0 deletions lfsr_table.txt
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Table of taps for maximum length GLFSRs

Bits are counted from 1 (one), ie. for taps 3,2 the polynomial is x^3 + x^2 + 1,
which in turn would be represented in hex as 0x0D.

BITS TAPS
3 3,2
4 4,3
5 5,3
6 6,5
7 7,6
8 8,6,5,4
9 9,5
10 10,7
11 11,9
12 12,6,4,1
13 13,4,3,1
14 14,5,3,1
15 15,14
16 16,15,13,4
17 17,14
18 18,11
19 19,6,2,1
20 20,17
21 21,19
22 22,21
23 23,18
24 24,23,22,17
25 25,22
26 26,6,2,1
27 27,5,2,1
28 28,25
29 29,27
30 30,6,4,1
31 31,28
32 32,22,2,1
33 33,20
34 34,27,2,1
35 35,33
36 36,25
37 37,5,4,3,2,1
38 38,6,5,1
39 39,35
40 40,38,21,19
41 41,38
42 42,41,20,19
43 43,42,38,37
44 44,43,18,17
45 45,44,42,41
46 46,45,26,25
47 47,42
48 48,47,21,20
49 49,40
50 50,49,24,23
51 51,50,36,35
52 52,49
53 53,52,38,37
54 54,53,18,17
55 55,31
56 56,55,35,34
57 57,50
58 58,39
59 59,58,38,37
60 60,59
61 61,60,46,45
62 62,61,6,5
63 63,62
64 64,63,61,60
65 65,47
66 66,65,57,56
67 67,66,58,57
68 68,59
69 69,67,42,40
70 70,69,55,54
71 71,65
72 72,66,25,19
73 73,48
74 74,73,59,58
75 75,74,65,64
76 76,75,41,40
77 77,76,47,46
78 78,77,59,58
79 79,70
80 80,79,43,42
81 81,77
82 82,79,47,44
83 83,82,38,37
84 84,71
85 85,84,58,57
86 86,85,74,73
87 87,74
88 88,87,17,16
89 89,51
90 90,89,72,71
91 91,90,8,7
92 92,91,80,79
93 93,91
94 94,73
95 95,84
96 96,94,49,47
97 97,91
98 98,87
99 99,97,54,52
100 100,63
101 101,100,95,94
102 102,101,36,35
103 103,94
104 104,103,94,93
105 105,89
106 106,91
107 107,105,44,42
108 108,77
109 109,108,103,102
110 110,109,98,97
111 111,101
112 112,110,69,67
113 113,104
114 114,113,33,32
115 115,114,101,100
116 116,115,46,45
117 117,115,99,97
118 118,85
119 119,111
120 120,113,9,2
121 121,103
122 122,121,63,62
123 123,121
124 124,87
125 125,124,18,17
126 126,125,90,89
127 127,126
128 128,126,101,99
129 129,124
130 130,127
131 131,130,84,83
132 132,103
133 133,132,82,81
134 134,77
135 135,124
136 136,135,11,10
137 137,116
138 138,137,131,130
139 139,136,134,131
140 140,111
141 141,140,110,109
142 142,121
143 143,142,123,122
144 144,143,75,74
145 145,93
146 146,145,87,86
147 147,146,110,109
148 148,121
149 149,148,40,39
150 150,97
151 151,148
152 152,151,87,86
153 153,152
154 154,152,27,25
155 155,154,124,123
156 156,155,41,40
157 157,156,131,130
158 158,157,132,131
159 159,128
160 160,159,142,141
161 161,143
162 162,161,75,74
163 163,162,104,103
164 164,163,151,150
165 165,164,135,134
166 166,165,128,127
167 167,161
168 168,166,153,151
78 changes: 78 additions & 0 deletions prng.c
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#include <stdio.h>
#include <stdlib.h>
#include "lfsr.h"

lfsr_t glfsr_d0;
lfsr_t glfsr_c0;

int main(int argc, char **argv) {
unsigned char bit0;
unsigned char bitc0;
unsigned char bitr = 0;
char byte = 0, bitpos = 7;
unsigned int bitcounter = 0, ones = 0, zeros = 0, dropped = 0;
unsigned int polynom_d, init_value_d;
unsigned int polynom_c, init_value_c;
FILE *f;

if (argc < 5) {
fprintf(stderr, "Too few arguments: data_polynom data_init_value control_polynom control_init_value\n");
exit(1);
}

f = fopen("output.bin", "w");

if (f == NULL) {
fprintf(stderr, "Cannot open output data file (output.bin)\n");
exit(2);
}

sscanf(argv[1], "%x", &polynom_d);
sscanf(argv[2], "%x", &init_value_d);
GLFSR_init(&glfsr_d0, polynom_d, init_value_d);
printf("GLFSR D0: using polynom 0x%X, initial value: 0x%X.\n", polynom_d, init_value_d);

sscanf(argv[3], "%x", &polynom_c);
sscanf(argv[4], "%x", &init_value_c);
GLFSR_init(&glfsr_c0, polynom_c, init_value_c);
printf("GLFSR C0: using polynom 0x%X, initial value: 0x%X.\n", polynom_c, init_value_c);

do {
bit0 = GLFSR_next(&glfsr_d0);
bitc0 = 1;//GLFSR_next(&glfsr_c0);

if (glfsr_d0.data == init_value_d)
printf("GLFSR D0 overflow at %d.\n", bitcounter);

if (glfsr_c0.data == init_value_c)
printf("GLFSR C0 overflow at %d.\n", bitcounter);

printf("Next bits: %d, %d\t= ", bit0, bitc0);

if (bitc0) {
bitr = bit0;
printf("%d\n", bitr);

if (bitpos < 0) {
fprintf(f, "%c", byte);
bitpos = 7;
byte = 0;
}

byte |= bitr << bitpos;
bitpos--;

bitr ? ones++ : zeros++;
} else {
printf("dropped\n");
dropped++;
}

bitcounter++;
} while (!((glfsr_d0.data == init_value_d) && (glfsr_c0.data == init_value_c)));

fclose(f);

printf("\nNumber of steps: %d (%d bytes), ones: %d, zeros: %d, dropped: %d\n", bitcounter, (zeros + ones) / 8, ones, zeros, dropped);
return 0;
}

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