applied cryptography - protocols, algorithms, and source code in c

Instead of using the bits in the tap sequence to

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Unformatted text preview: bits together (see Figure 16.4), the resultant LFSR will be maximal length; it will cycle through 232 - 1 values before repeating. The C code for this LFSR looks like: int LFSR () { static unsigned long ShiftRegister = 1; /* Anything but 0. */ ShiftRegister = ((((ShiftRegister >> 31) ^ (ShiftRegister >> 6) ^ (ShiftRegister >> 4) ^ (ShiftRegister >> 2) ^ (ShiftRegister >> 1) ^ ShiftRegister)) & 0×00000001) << 31) | (ShiftRegister >> 1) ; return ShiftRegister & 0×00000001; } Figure 16.4 32-bit long maximal-length LFSR. Table 16.2 Some Primitive Plynomials Mod 2 (1, 0) (2, 1, 0) (3, 1, 0) (4, 1, 0) (5, 2, 0) (6, 1, 0) (7, 1, 0) (7, 3, 0) (8, 4, 3, 2, 0) (9, 4, 0) (10, 3, 0) (11, 2, 0) (12, 6, 4, 1, 0) (13, 4, 3, 1, 0) (14, 5, 3, 1, 0) (15, 1, 0) (16, 5, 3, 2, 0) (17, 3, 0) (17, 5, 0) (17, 6, 0) (18, 7, 0) (36, 11, 0) (68, 9, 0) (97, 6, 0) (36, 6, 5, 4, 2, 1, 0) (68, 7, 5, 1, 0) (98, 11, 0) (37, 6, 4, 1, 0) (69, 6, 5, 2, 0) (98, 7, 4, 3, 1, 0) (37, 5, 4, 3, 2, 1, 0) (70, 5, 3, 1, 0) (99, 7, 5, 4, 0) (38, 6, 5, 1, 0) (71, 6, 0) (100, 37, 0) (39, 4, 0) (71, 5, 3, 1, 0) (100, 8, 7, 2, 0) (40, 5, 4, 3, 0) (72, 10, 9, 3, 0) (101, 7, 6, 1, 0) (41, 3, 0) (72, 6, 4, 3, 2, 1, 0) (102, 6 5 3 0) (42, 7, 4, 3, 0) (73, 25, 0) (103, 9, 9) (42, 5, 4, 3, 2, 1, 0) (73, 4, 3, 2, 0) (104, 11, 10, 1, 0) (43, 6, 4, 3, 0) (74, 7, 4, 3, 0) (105, 16, 0) (44, 6, 5, 2, 0) (75, 6, 3, 1, 0) (106, 15, 0) (45, 4, 3, 1, 0) (76, 5, 4, 2, 0) (107, 9, 7, 4, 0) (46, 8, 7, 6, 0) (77, 6, 5, 2, 0) (108, 31, 0) (46, 8, 5, 3, 2, 1, 0) (78, 7, 2, 1, 0) (109, 5, 4, 2, 0) (47, 5, 0) (79, 9, 0) (110, 6, 4, 1, 0) (48, 9, 7, 4, 0) (79, 4, 3, 2, 0) (111, 10, 0) (48, 7, 5, 4, 2, 1, 0) (80, 9, 4, 2, 0) (111, 49, 0) (49, 9, 0) (80, 7, 5, 3, 2, 1, 0) (113, 9, 0) (49, 6, 5, 4, 0) (81, 4, 0) (113, 15, 0) (50, 4, 3, 2, 0) (82, 9, 6, 4, 0) (113, 30, 0) (18, 5, 2, 1, 0) (51, 6, 3, 1, 0) (82, 8, 7, 6, 1, 0) (114, 11, 2, 1, 0) (19, 5, 2, 1, 0) (52, 3, 0) (83, 7, 4, 2, 0) (115, 8, 7, 5, 0) (20, 3, 0) (53, 6, 2, 1...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.

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