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

Additional theory on clock controlled shift registers

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Unformatted text preview: computer’s word size) in parallel. This scheme uses an array of words that is the length of the LFSR, with each bit position in the words representing a different LFSR. Assuming all the feedback polynomials are the same, this can run pretty quickly. In general, the best way to update shift registers is to multiply the current state by suitable binary matrices [901]. It is also possible to modify the LFSR’s feedback scheme. The resultant generator is no better cryptographically, but it still has a maximal period and is easy to implement in software [1272]. Instead of using the bits in the tap sequence to generate the new left-most bit, each bit in the tap sequence is XORed with the output of the generator and replaced; then the output of the generator becomes the new left-most bit (see Figure 16.5). This is sometimes called a Galois configuration. In C, this looks like: #define mask 0×80000057 static unsigned long ShiftRegister=1; void seed_LFSR (unsigned long seed) { if (seed == 0) /* avoid calamity */ seed = 1; ShiftRegister = seed; } int modified_LFSR (void) { if (ShiftRegister & 0×00000001) { ShiftRegister = ((ShiftRegister ^ mask >> 1) | 0×8000000; return 1; } else { ShiftRegister >>= 1; return 0; } } Figure 16.5 Galois LFSR. The savings here is that all the XORs can be done as a single operation. This can also be parallelized, and the different feedback polynomials can be different. The Galois configuration can also be faster in hardware, especially in custom VLSI implementations. In general, if you are using hardware that is good at shifts, use a Fibonacci configuration; if you can exploit parallelism, use a Galois configuration. 16.3 Design and Analysis of Stream Ciphers Most practical stream-cipher designs center around LFSRs. In the early days of electronics, they were very easy to build. A shift register is nothing more than an array of bit memories and the feedback sequence is just a series of XOR gates. Even in VLSI circuitry, a LFSR-based stream cipher can give you a lot of security with only a few logic gates. The problem with LFSRs is that they...
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