In this problem we will gain a little experience with more advanced stream ciphers that are...

   

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In this problem we will gain a little experience with more advanced stream ciphers that are built from individual LFSRs. Such ciphers can be secure. We consider the alternating stop- and-go generator introduced in the lecture. The three LFSRS are specified by the following polynomials and initial vectors: LFSR-1 x² + x + 1; (zo = 1; 0) LFSR-2 x³ + x + 1; (zo = 1; 0;0) LFSR-3 x5 + x² + 1; (zo = 1; 0; 0; 0; 0) (a) Draw the circuit diagram of the stream cipher. (b) Compute the first eight output bits. (c) It generally holds for stream ciphers build from LFSRS that the sequence length is the product of the sequence lengths of the individual LFSRs if the individual lengths are all relative prime. Is this condition fulfilled for the generator above? What is the length of the sequence generated? In this problem we will gain a little experience with more advanced stream ciphers that are built from individual LFSRs. Such ciphers can be secure. We consider the alternating stop- and-go generator introduced in the lecture. The three LFSRS are specified by the following polynomials and initial vectors: LFSR-1 x² + x + 1; (zo = 1; 0) LFSR-2 x³ + x + 1; (zo = 1; 0;0) LFSR-3 x5 + x² + 1; (zo = 1; 0; 0; 0; 0) (a) Draw the circuit diagram of the stream cipher. (b) Compute the first eight output bits. (c) It generally holds for stream ciphers build from LFSRS that the sequence length is the product of the sequence lengths of the individual LFSRs if the individual lengths are all relative prime. Is this condition fulfilled for the generator above? What is the length of the sequence generated?

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