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Algorithms for the generation of full-length shift- register sequences

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2 Author(s)

Two algorithms are presented for the generation of full-length shift-register cycles, also referred to as de Bruijn sequences. The first algorithm generates2^{k cdot g(n,k)full cycles of length2^{n}, using3n + k cdot g(n, k)bits of storage, wherekis a free parameter in the range1 leq k leq 2^{((n-4)/2)}, andg(n, k)is of the order ofn - 2 log k. The second algorithm generates about2^{n^{2}/4}full cycles of length2^{n}, using aboutn^{2}/2bits of storage. In both algorithms, the time required to produce the next bit from the lastnbits is close ton. A possible application to the construction of stream ciphers is indicated.

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Information Theory, IEEE Transactions on  (Volume:30 ,  Issue: 3 )