Efficient Composited de Bruijn Sequence Generators
Bo Yang, Kalikinkar Mandal, Mark D. Aagaard, Guang Gong · IEEE Transactions on Computers · 2017
A binary de Bruijn sequence with period 2nis a sequence in which every tuple of n bits occurs exactly once. De Bruijn sequence generators have randomness properties that make them attractive for pseudorandom number generators and as building blocks for stream ciphers. Unfortunately, it is very difficult to find de Bruijn sequence generators with long periods (e.g., 2128) and most known de Bruijn sequence generators are computationally quite expensive. In this article, we present “OcDeb-k-n” and the first hardware implementation of de Bruijn sequence generators. OcDeb-k-n efficiently computes a composited de Bruijn sequence where k levels of composition are added to a de Bruijn sequence of period 2n. Numerically, OcDeb reduces the bit operations used for computing the feedback function significantly from Θ(k2+ nk) to Θ(k log k + logn). Furthermore, it enables efficient parallelization and hardware retiming. Comprehensive result analysis is conducted for 65 nm ASIC technology. For example, OcDeb-32-32 has an area of 643 GE with 1.45 Gbps performance, and with parallelization it generates up to 25.4 Gbps at the cost of 4,787 GE. The area of OcDeb-512-32 generating a de Bruijn sequence of period 2544is 7,304 GE and the performance is 1.25 Gbps.