Unformatted text preview: operation is XOR. — FCSR/LFSR Stop-and-Go Generator. Register-1 is a FCSR, and Registers-2 and -3 are LFSRs. The combining operation is addition with carry. Figure 17.6 Concoction Generator. — LFSR/FCSR Stop-and-Go Generator. Register-1 is a LFSR, and Registers-2 and -3 are FCSRs. The combining operation is XOR. Shrinking Generators
There are four basic generator types using FCSRs: — FCSR Shrinking Generator. A shrinking generator with FCSRs instead of LFSRs. — FCSR/LFSR Shrinking Generator. A shrinking generator with a LFSR shrinking a FCSR. — LFSR/FCSR Shrinking Generator: A shrinking generator with a FCSR shrinking a LFSR. Figure 17.7 Alternating stop-and-go generators. — FCSR Self-Shrinking Generator. A self-shrinking generator with a FCSR instead of a LFSR. 17.6 Nonlinear-Feedback Shift Registers
It is easy to imagine a more complicated feedback sequence than the ones used in LFSRs or FCSRs. The problem is that there isn’t any mathematical theory that can analyze them. You’ll get something, but who knows what it is? In particular, here are some problems with nonlinear-feedback shift register sequences. — There may be biases, such as more ones than zeros or fewer runs than expected, in the output sequence. — The maximum period of the sequence may be much lower than expected. — The period of the sequence might be different for different starting values. — The sequence may appear random for a while, but then “dead end” into a single value. (This can easily be solved by XORing the nonlinear function with the rightmost bit.) On the plus side, if there is no theory to analyze nonlinear-feedback shift registers for security, there are few tools to cryptanalyze stream ciphers based on them. We can use nonlinear-feedback shift registers in stream-cipher design, but we have to be careful. In a nonlinear-feedback shift register, the feedback function can be anything you want (see Figure 17.8). Figure 17.8 A nonlinear-feedback shift register (probably insecure). Figure 17.9 3-bit nonlinear feedback shift register. F...
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- Fall '10
- Cryptography, Bruce Schneier, Applied Cryptography, EarthWeb, Search Search Tips