7 # define BYTE_FORMAT "0x%02x"
8 # define BYTE_COLUMNS 8
10 # define BYTE_FORMAT "%3d"
11 # define BYTE_COLUMNS 0x10
14 #define WORD_FORMAT "0x%08lx"
15 #define WORD_COLUMNS 4
17 unsigned char sbox[0x100];
18 unsigned char isbox[0x100];
20 unsigned char gf2_log[0x100];
21 unsigned char gf2_exp[0x100];
23 unsigned long dtable[4][0x100];
24 unsigned long itable[4][0x100];
25 unsigned long mtable[4][0x100];
41 /* Computes the exponentiatiom and logarithm tables for GF_2, to the
42 * base x+1 (0x03). The unit element is 1 (0x01).*/
49 memset(gf2_log, 0, 0x100);
51 for (i = 0; i < 0x100; i++, x = x ^ xtime(x))
58 /* The loop above sets gf2_log[1] = 0xff, which is correct,
59 * but gf2_log[1] = 0 is nicer. */
64 mult(unsigned a, unsigned b)
66 return (a && b) ? gf2_exp[ (gf2_log[a] + gf2_log[b]) % 255] : 0;
72 return x ? gf2_exp[0xff - gf2_log[x]] : 0;
79 (0x63^x^(x>>4)^(x<<4)^(x>>5)^(x<<3)^(x>>6)^(x<<2)^(x>>7)^(x<<1));
86 for (i = 0; i<0x100; i++)
88 sbox[i] = affine(invert(i));
93 /* Generate little endian tables, i.e. the first row of the AES state
94 * arrays occupies the least significant byte of the words.
96 * The sbox values are multiplied with the column of GF2 coefficients
97 * of the polynomial 03 x^3 + x^2 + x + 02. */
102 for (i = 0; i<0x100; i++)
104 unsigned s = sbox[i];
106 unsigned long t =( ( (s ^ xtime(s)) << 24)
107 | (s << 16) | (s << 8)
110 for (j = 0; j<4; j++, t = (t << 8) | (t >> 24))
115 /* The inverse sbox values are multiplied with the column of GF2 coefficients
116 * of the polynomial inverse 0b x^3 + 0d x^2 + 09 x + 0e. */
121 for (i = 0; i<0x100; i++)
123 unsigned s = isbox[i];
125 unsigned long t = ( (mult(s, 0xb) << 24)
126 | (mult(s, 0xd) << 16)
127 | (mult(s, 0x9) << 8)
130 for (j = 0; j<4; j++, t = (t << 8) | (t >> 24))
135 /* Used for key inversion, inverse mix column. No sbox. */
140 for (i = 0; i<0x100; i++)
143 unsigned long t = ( (mult(i, 0xb) << 24)
144 | (mult(i, 0xd) << 16)
145 | (mult(i, 0x9) << 8)
148 for (j = 0; j<4; j++, t = (t << 8) | (t >> 24))
154 display_byte_table(const char *name, unsigned char *table)
158 printf("uint8_t %s[0x100] =\n{", name);
160 for (i = 0; i<0x100; i+= BYTE_COLUMNS)
163 for (j = 0; j<BYTE_COLUMNS; j++)
164 printf(BYTE_FORMAT ",", table[i + j]);
171 display_table(const char *name, unsigned long table[][0x100])
175 printf("uint32_t %s[4][0x100] =\n{\n ", name);
177 for (k = 0; k<4; k++)
180 for (i = 0; i<0x100; i+= WORD_COLUMNS)
183 for (j = 0; j<WORD_COLUMNS; j++)
184 printf(WORD_FORMAT ",", table[k][i + j]);
192 display_polynomial(const unsigned *p)
194 printf("(%x x^3 + %x x^2 + %x x + %x)",
195 p[3], p[2], p[1], p[0]);
199 main(int argc, char **argv)
204 display_byte_table("gf2_log", gf2_log);
205 display_byte_table("gf2_exp", gf2_exp);
208 display_byte_table("sbox", sbox);
209 display_byte_table("isbox", isbox);
212 display_table("dtable", dtable);
215 display_table("itable", itable);
218 display_table("mtable", mtable);
225 for (a = 1; a<0x100; a++)
227 unsigned a1 = invert(a);
231 printf("invert(%x) = 0 !\n", a);
235 printf("invert(%x) = %x; product = %x\n",
238 for (b = 1; b<0x100; b++)
240 unsigned b1 = invert(b);
241 unsigned c = mult(a, b);
244 printf("%x x %x = 0\n", a, b);
248 printf("%x x %x = %x, invert(%x) = %x, %x x %x = %x\n",
249 a, b, c, a, a1, c, a1, u);
253 printf("%x x %x = %x, invert(%x) = %x, %x x %x = %x\n",
254 a, b, c, b, b1, c, b1, u);
263 a = strtoul(argv[1], NULL, 16);
264 b = strtoul(argv[3], NULL, 16);
275 c = mult(a, invert(b));
280 printf("%x %c %x = %x\n", a, op, b, c);
286 /* Compute gcd(a, x^4+1) */
290 for (i = 0; i<4; i++)
291 a[i] = strtoul(argv[1+i], NULL, 16);
300 for (i = 0; i<4; i++)
302 a[i] = strtoul(argv[1+i], NULL, 16);
303 b[i] = strtoul(argv[5+i], NULL, 16);
306 c[0] = mult(a[0],b[0])^mult(a[3],b[1])^mult(a[2],b[2])^mult(a[1],b[3]);
307 c[1] = mult(a[1],b[0])^mult(a[0],b[1])^mult(a[3],b[2])^mult(a[2],b[3]);
308 c[2] = mult(a[2],b[0])^mult(a[1],b[1])^mult(a[0],b[2])^mult(a[3],b[3]);
309 c[3] = mult(a[3],b[0])^mult(a[2],b[1])^mult(a[1],b[2])^mult(a[0],b[3]);
311 display_polynomial(a); printf(" * "); display_polynomial(b);
312 printf(" = "); display_polynomial(c); printf("\n");