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

Two algorithms are presented for the generation of full-length shift-register cycles, also referred to as de Bruijn sequences. The first algorithm generates 2 k’g(n,k) full cycles of length 2”, using 3n + k . g( n, k) bits of storage, where k is a free parameter in the range 1 2 k I 2((n-4)/2), and g(n, k) is of the ‘order of n 210g k. The second algorithm generates about 2 n2/4 full cycles of length 2’J, using about n2/2 bits of storage. In both algorithms, the time required to produce the next bit from the last n bits is close to n. A possible application to the construction of stream ciphers is indicated.